Officers and Committees of the IGES/PDES Organization September 17, 1991 Officers Chair William Conroy IGES Project Manager J. C. Kelly PDES Project Manager Anthony Day Testing Project Manager Constance Bracken Associated Staff IPO Editor Joan Wellington Executive Assistant Melissa Andrews Clerk Typist Mona Randall Administrative Coordinator, NCGA Nancy Flower IGES Editor Kent Reed IGES Change Control Secretary Jim Johnson IGES Ballot Coordinator Melissa Andrews Configuration Control Admin. Gaylen Rinaudot iii Technical Committee Chairs Application Validation Methodology Mark Palmer Joel Petersen, deputy Architecture, Engineering, & Construction Joseph Halford Burt Gischner, IGES Coordinator PDES Composites Glen Ziolko Dictionary/Methodology Peter Eirich Drafting Robert Parks Greg Morea, deputy (IGES) Electrical Applications Larry O'Connell Bob Owens, deputy (IGES) Rob Fletcher, deputy (PDES) Finite Element Analysis Keith Hunten Form Features Mark Dunn Tom Kramer, deputy Geometry Tracy Whelan Noel Christensen, deputy Implementation Specifications Jim Fowler Implementors Bill Turcotte George Baker, co-chair Interoperability Testing Methodology Nellie Morack Gary Conkol, deputy Manufacturing Technology Greg Paul Dan Small, deputy Materials John Rumble Mechanical Product Definition Bill Cain PDES Development Methods Bill Danner PDES Presentation Neal Appel Product Life Cycle Support Rick Bsharah Shirley Goodman, deputy Product Structure Buzz Bloom (a) Qualification & Integration Yuhwei Yang David Sanford, deputy Recommended Practices George Baker Software Products Tom Baker George Coletta, deputy Standard Parts Bob Meagher co-chair (a) Ron Bale co-chair Technical Publications Camillo Marziani, deputy Test Case Design Jim Felt Ken Erman, deputy Testing Methodologies Alan Peltzman Tolerances William Burkett Martin Holland, deputy iv Steering Committee Officers Chair Jim Snyder Credentials Mike Nolan Liason Jim Nell Special Interest Groups CALS/IGES Lisa Deeds Ben Kassel, deputy CALS/PDES Shirley Goodman, co-chair Tamera Terrell, co-chair Related Organizations ISO/SC4 Brad Smith ISO/PMAG Jerry Weiss National PDES Testbed Chuck McLean PDES, Inc. Bob Kiggans U.S. TAG to ISO/SC4 Kal Brauner v Members of the IGES/PDES Organization The following individuals participated in the balloting process to develop this Specification. Altemueller, Jeff McDonnell Douglas Corporation Anderson, Bill D. Battelle Anderson, Robert E. Naval Aviation Depot Assiff, Thomas C. Electronic Data Systems Baker, George W. International TechneGroup Inc. Bares, Peter Intentia AB Barker, Raymond E. Caterpillar, Inc. Bartlett, Sue Mentor Graphics Corporation Beazley, William CALS Report Berenyi, Tibor A. Deere and Company Bernstein, Joe Boeing Computer Services Billingsley, Dan Naval Sea Systems Command Blaney, David H. United Technologies Bloom, Buzz Prime Computer Bracken, Constance L. Electronic Data Systems Bradford, James E. Allied Signal Brainin, Jack David Taylor Research Center Brauner, Kalman Boeing Co. Briggs, David D. Boeing Co. Bronder, Clare M. Adra Systems, Inc. Brooks, Richard J. McDonnell Douglas Corporation Burkett, William C. Lockheed Aeronautical Systems, Co. Burns, Bernard J. Naval Surface Warfare Cain, William D. Martin Marietta Energy Systems Calkins, Bruce SEACOSD Carpenter, Vickie Electronic Data Systems Casey, Eva W. Schlumberger Technologies CAD/CAM Chamberlain, Mark T. Hughes Aircraft Cheever, Richard W. Martin Marietta Chi, Kelly McDonnell Douglas Corporation Christensen, Noel C. Allied Signal, Inc. Clapp, Edward Autodesk, Inc. Cochran, Richard McDonnell Douglas Corporation Colsher, Robert IGES Data Analysis Conroy, William NIST/EDS Corn, Earleen Newport News Shipbuilding vi MEMBERS OF THE IGES/PDES ORGANIZATION Costello, Helen D. Lockheed Aeronautical Systems Co. Cox, Margery J. Newport News Shipbuilding Crusey, Jesse L. NIST Dai, Losheng Sikorsky Aircraft Danielson, Pamela R. General Dynamics Dawson, Laurel C. IBM Deeds, Lisa V. David Taylor Research Center Dellinger, David L. Boeing Commercial Airplanes DePauw, Spencer Caterpillar Inc. Downer, Ron CAD/CAE Consulting Services Dragoo, Alan E. IGES Data Analysis Corporation Dvorak, Andrew Bath Iron Works Easley, Preston Northrop Corporation Erman, Ken CADKEY, Inc. Fallon, Kristine K. Computer Technology Management, Inc. Farrell, Jill M. Lawrence Livermore National Laboratory Faulkner, John C. SDRC Fleming, Jim Cummins Engine Co., Inc. Fong, Henry H. MARC Analysis Research Corporation Fox, Mike A. O. GRN Technology Ltd. Francis, Ray M. Naval Weapons Center Freund, Kevin D. Appleton Co. Inc. Frimer, Morris Boeing Electronics Company Gauntlett,Clifford J. Autodesk, Inc. Genseal, Steve Caterpillar, Inc. Giguere, Marshall E. Data Exchange Associates Gilbert, Mitchell Grumman Aircraft Systems Gilbert, Chip Martin Marietta Corporation Gischner, Burton General Dynamics - Electric Boat Golish, Mike US Army CECERL - FS Goodman, Shirley A. NAVORDSTA Goosen, Ted General Dynamics Goult, Ray J. Cranfield Institute of Technology Gray, W. Harvey Martin Marietta Corporation Green, Ronald D. Boeing Grout, Steven J. Martin Marietta Gurga, Eugene F. J I Case Gygi, Michael McDonnell Douglas Corporation Haines, Mark International TechneGroup, Inc. Halford, Joseph D. EI Du Pont de Nemours Co. Hamilton, C.H. PDA Engineering Hanson, Eric International TechneGroup, Inc. Harrison, Randy J. Sandia National Laboratories Harrod, Jr., Dennette A. Computervision Harrow, Pat Harrow Associates Ltd. Hart, John R. Boeing Advanced Systems Company Harvie, Andrew Nova Scotia CAD/CAM Centre Hebert, Charles T. Boeing Hemmelgarn, Don International TechneGroup Inc. Hooper, Richard Eastman Kodak vii MEMBERS OF THE IGES/PDES ORGANIZATION Humphrey, Darrell Martin Marietta Data Systems Hunten, Keith General Dynamics Hussong, William A. Honeywell, Inc. Ippolito, Greg General Dynamics Isenberg, Madeleine R. Northrop Corporation Ivey, Robert L. Westinghouse Electric Corporation Jaeger, Dwight L. Los Alamos National Laboratory Jensen, David EDS - BOC Headquarters Johnson, Jim General Dynamics Jones, Alan K. Boeing Computer Services Jones, Douglas Accugraph Corporation Judd, Jon L. General Dynamics Jurrens, Kevin NIST Kamvar, Estandiar AT & T Bell Laboratories Kassel, Ben David Taylor Research Center Kato, Toru Toyota Motor Corporation Keith, Greg Automation Technology Products Kelly, J. C. Sandia National Laboratories Kemmerer, Sharon NIST Kennedy, Philip J. Electronic Data Systems Kenngott, Debbie AutoTrol Technology Corporation Kennicott, Philip Sandia National Laboratories Ker, Kenneth R. McDonnell Douglas Kohler, Rick XL Engineering Kontry, Karen L. Electronic Data Systems Krishnaswami, Ravi Electronic Data Systems Kromarek, Darrel V. Boeing Aerospace & Electronics Kshirsagar, Sudhir Proctor & Gamble Kuan, L. P. NET Inc. Ladd, Harry E. Du Pont Engineering Development Laboratory Larsen, Larry J. Boeing Commercial Airplanes Lazo, Pete L. Newport News Shipbuilding Lee, Kaiman NAVFAC DSO-1A Leung, Richard AT & T Lichten, Olga IBM Linsner, James D. Boeing Computer Services Little, Maureen Naval Civil Engineering Laboratory Lodewijks, Bart Philips Losinski, Mark Control Data Corporation Lovdahl, Richard H. Lovdahl & Associates Loye, William CADnetix Lucke, Virgil General Electric Company MacLatchie, Robert PlanPrint Company Magoon, Gary CADKEY, Inc. Makoski, Thomas International TechneGroup Inc. Martino, Linda IBM Marz, Steven D. Integraph Corporation Marziani, Camillo Boeing Helicopters Mathew, Abraham Integraph Corporation Mays, James L. Naval Supply Systems Command viii MEMBERS OF THE IGES/PDES ORGANIZATION Messcher, Walter US Dept. of Transportation Miller, Rex D. Xerox Corporation Miller, Darin General Dynamics Mindel, Carolyn F. SDRC Montano, Allan M. Electronic Data Systems Morack, Nellie CDI Transportation Group Morea, Gregory General Dynamics - Electric Boat Morgan, Donald E. General Electric Aircraft Engines Morrill, Charles B. IBM Motz, Philip Cincinnati Milacron Murphy, James NAVSEA/NIDDESC Mylavarapu, Rao S. Electronic Data Systems Nairn, Bill CAD-CAM Data Exchange Technical Centre/UK Nelson, Paul A. Hughes Aircraft Company Nguyen, Hakim CADKEY, Inc. Nolan, Michael F. Rosetta Technology, Inc. O'Connell, Larry Sandia National Laboratories Oakes, Jr., William R. Los Alamos National Laboratories Overbeek, Michael D. International TechneGroup Inc. Owens, Bob Martin Marietta Paine, Louis C. Electronic Data Systems Palmer, Mark NIST Panzica, Connie General Motors Parker, Lawrence O. GM/Hughes Electronics Parks, Curtis H. NIST Parks, Robert E. Sandia National Laboratories Paschelke, Robert Point Control Company Paul, Greg A. General Dynamics Pearson, Mark CAD-CAM Data Exchange Technical Centre/UK Peltzman, Alan Peltzman Associates Petersen, Joel S. IBM Corporation Phelps, Freda Sun Microsystems Pilkenton, Stephen General Dynamics Prince, Anthony Integraph Corporation Purdon, James C. Schlumberger Technologies CAD/CAM Ranke, Guus Nederlandse Philips Bedryven BV Rau, Timothy R. NASA Space Station Freedom Program Reed, Kent NIST Rehg, Ed Texas Instruments Reid, E. A. Caterpillar, Inc. Remington, David O. NOVA University Rinaudot, Gaylen R. NIST Robinson, Gloria R. Electronic Data Systems Rodenberger, C. Mark General Dynamics Roth, Gloria R. Electronic Data Systems Sabine, Anne Newport News Shipbuilding Sadler, David Randolph NAVSEACOMBATSYSTENGSTA Sasser, Vickie Electronic Data Systems Schachtner, Steven R. Martin Marietta Scheets, William R. Caterpillar, Inc. ix MEMBERS OF THE IGES/PDES ORGANIZATION Schilli, Bruno University of Karlsruhe RPK Schmid, Randy CADAM Inc. Schroeter, Dirk J. Martin Marietta Schwander, Chris M. EI Du Pont de Nemours Co. Scott, Gladys E. Newport News Shipbuilding Scott, Ronald McDonnell Douglas Corporation Sherwood, Kenneth CADAM Inc. Siemon, Mark US Navy Skidmore, Lindsay Naval Weapons Support Center Slack, Francine Electronic Data Systems Small, Daniel H. Boeing Computer Systems Smith, Bradford M. NIST Smith, Robert E. Boeing Defense & Space Group Stark, Chuck South Carolina Research Authority/NIST Stoddard, Charles L. Pratt and Whitney Stone, Donald D. Hughes Aircraft Company Szmrecsanyi, Emery Chrysler Motor Corporation Taylor, Herb AutoTrol Technology Corporation Thompson, Jr., C. B. Southern Company Services, Inc. Tittle, Fremont Control Data Corporation Tompkins, Edwin B. Johns Hopkins University Torossian, Julie A. Electronic Data Systems Turcotte, William IGES Data Analysis Corporation Turner, James A. University of Michigan APRL Weideman, Christian IVF Wellington, Joan NIST Wells, Michael Rosetta Technologies, Inc. Wester, Ronald O. General Electric Company Whelan, Tracy M. CAMAX Systems, Inc. Williams, Anne McDonnell Douglas Corporation Wilson, Peter R. Rensselaer Polytechnic Institute Winfrey, R. C. Digital Equipment Company Wooley, Daniel Newport News Shipbuilding Wright, Debora J. Sikorsky Aircraft Yang, Sheree Ford Aerospace Corporation x Foreword This version of the Specification differs from its predecessors more in form than in content. A complete reorganization of the sections, to place the entity type definitions in an ascending numerical order, has been a long-standing goal of the IGES/PDES Organization (IPO). The major changes are the result of approximately 75 Request For Change submissions, developed by the various technical committees and approved as technical Edit Change Orders (ECOs) through mail ballots by the General Assembly, and approximately 20 editorial Edit Change Orders issued by the IGES Project Committee. The majority of the new entity types and form numbers introduced in this version of the Specification were created to improve the quality and robustness of data exchange in the application disciplines of Drafting, Electrical, and AEC. Numerous technical clarifications and technical additions have been made to geometry entities. The single most significant change is the addition of unambiguous requirements on the Directory Entry (DE) fields as applied to each of the individual entity types and form numbers. Most of the changes have been highlighted by the placement of the relevant ECO numbers in the margins. Some ECOs were so all-encompassing (e.g., providing consistent nomenclature in Parame- ter Data descriptions) that it was impractical to indicate each occurrence. Some ECOs superseded others and some removed sections in their entirety, so it was simply not possible to include highlights for all of the ECOs. When comparing this version with the previous one, sections highlighted by an ECO number should be examined very carefully because the change may consist of the addition or deletion of a single word (e.g., "not"), but this change could radically alter the technical content of the data representation. This version also marks a milestone in demonstrating the utility of the Specification. All of the technical illustrations were generated from data files that conform to the Specification. That is to say, the text and graphics in this document exist entirely in electronic form, and the pages were produced on a laser-imaging printer using device driver software that combines the output of a LaTEX document preparation system and the raster image output of an IGES postprocessing system. Use of this technology has resulted in a harmonization of the illustrations (consistent text and line font appearance) and the highest possible resolution, which in this case is 300 dots per inch. Several entities have been moved from the Untested Entities Appendix into the body of the Speci- fication, and most new entities and forms appear in that appendix. The MACRO Entity has been moved from the body of the Specification to the Untested Entities Appendix. The Binary Form has been deprecated and moved to a new appendix. This Specification is being published as a NIST report to provide the baseline technical document for standardization by the American National Standards Institute and to provide the document with greater exposure to the user community. The format differs from that of a normal NIST report to facilitate the standardization process. xi This page intentionally left blank. xii Contents Officers and Staff of the IGES/PDES Organization iii Members of the IGES/PDES Organization vi Foreword xi 1 General 1 1.1 Purpose : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Field of Application : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.3 Conformance to the Specification : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.3.1 Conformance rules for data files. : : : : : : : : : : : : : : : : : : : : : : : : 2 1.3.2 Conformance rules for preprocessors. : : : : : : : : : : : : : : : : : : : : : 2 1.3.3 Conformance rules for postprocessors. : : : : : : : : : : : : : : : : : : : : : 2 1.4 Untested Entities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.5 Concepts of Product Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.6 Concepts of the File Structure : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.7 Concepts of Information Structures for Geometric Models : : : : : : : : : : : : : : 4 1.7.1 Property Entity. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.7.2 Associativity Entities. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.7.3 View Entity. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.7.4 Drawing Entity. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.7.5 Transformation Matrix Entity. : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.7.6 Implementor-Defined Entities. : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.8 Appendices : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2 Data Form 7 2.1 General : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.1.1 Defaults. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 xiii CONTENTS 2.2 ASCII Form : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.2.1 Sequence Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.2.2 Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.2.2.1 Integer Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.2.2.2 Real Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.2.2.3 String Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.2.2.4 Pointer Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.2.2.5 Language Statement Constants. : : : : : : : : : : : : : : : : : : : 10 2.2.2.6 Logical Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.2.3 Rules for Forming and Interpreting Free Formatted Data. : : : : : : : : : : 10 2.2.3.1 Parameter and Record Delimiter Combinations. : : : : : : : : : : 11 2.2.4 File Structure. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.2.4.1 Start Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.2.4.2 Global Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.2.4.3 Directory Entry Section. : : : : : : : : : : : : : : : : : : : : : : : 17 2.2.4.4 Parameter Data Section. : : : : : : : : : : : : : : : : : : : : : : : 25 2.2.4.5 Terminate Section. : : : : : : : : : : : : : : : : : : : : : : : : : : 28 2.3 Compressed ASCII Format : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 29 2.3.1 File Structure. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 29 3 Classes of Entities 31 3.1 General : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 31 3.2 Curve and Surface Geometry Entities : : : : : : : : : : : : : : : : : : : : : : : : : 31 3.2.1 Entity Type/Type Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : 31 3.2.2 Coordinate Systems. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 32 3.2.3 Multiple Transformation Entities. : : : : : : : : : : : : : : : : : : : : : : : 33 3.2.4 Directionality. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 33 3.3 Constructive Solid Geometry Entities : : : : : : : : : : : : : : : : : : : : : : : : : 36 3.3.1 Entity Type/Type Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : 36 3.3.2 Constructive Solid Geometry Models. : : : : : : : : : : : : : : : : : : : : : 36 3.4 B-Rep Solid Entities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 38 3.4.1 Entity Type/Type Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : 38 3.4.2 Topology for B-Rep Solid Models. : : : : : : : : : : : : : : : : : : : : : : : 38 3.4.3 Analytical Surfaces for B-Rep Solid Models. : : : : : : : : : : : : : : : : : 39 3.4.3.1 Entity Type/Type Numbers. : : : : : : : : : : : : : : : : : : : : : 40 xiv CONTENTS 3.4.3.2 Parameterization of Analytical Surfaces. : : : : : : : : : : : : : : 40 3.5 Annotation Entities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 41 3.5.1 Entity Type/Type Number. : : : : : : : : : : : : : : : : : : : : : : : : : : 41 3.5.2 Construction. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 41 3.5.3 Definition Space. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 41 3.5.4 Dimension Attributes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 3.5.4.1 General. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 3.5.4.2 Usage Rules. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 3.6 Structure Entities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 46 3.6.1 Entity Type/Type Number. : : : : : : : : : : : : : : : : : : : : : : : : : : 46 3.6.2 Subfigures. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 46 3.6.3 Connectivity. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 47 3.6.3.1 Connectivity Entities. : : : : : : : : : : : : : : : : : : : : : : : : : 47 3.6.3.2 Entity Relationships. : : : : : : : : : : : : : : : : : : : : : : : : : 47 3.6.3.3 Information Display. : : : : : : : : : : : : : : : : : : : : : : : : : 49 3.6.3.4 Additional Considerations. : : : : : : : : : : : : : : : : : : : : : : 49 3.6.4 External Reference Linkage. : : : : : : : : : : : : : : : : : : : : : : : : : : 49 3.6.5 Drawings and Views. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 52 3.6.6 Finite Element Modeling. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 53 3.6.7 Attribute Tables. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 53 4 Entity Types 57 4.1 General : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 57 4.2 Null Entity (Type 0) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 58 4.3 Circular Arc Entity (Type 100) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 59 4.4 Composite Curve Entity (Type 102) : : : : : : : : : : : : : : : : : : : : : : : : : : 62 4.5 Conic Arc Entity (Type 104) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 67 4.6 Copious Data Entity (Type 106) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 73 4.7 Centerline Entity (Type 106, Form 20-21) : : : : : : : : : : : : : : : : : : : : : : : 77 4.8 Section Entity (Type 106, Forms 31-38) : : : : : : : : : : : : : : : : : : : : : : : : 79 4.9 Witness Line Entity (Type 106, Form 40) : : : : : : : : : : : : : : : : : : : : : : : 82 4.10 Plane Entity (Type 108) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 84 4.11 Line Entity (Type 110) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 88 4.12 Parametric Spline Curve Entity (Type 112) : : : : : : : : : : : : : : : : : : : : : : 90 4.13 Parametric Spline Surface Entity (Type 114) : : : : : : : : : : : : : : : : : : : : : 94 xv CONTENTS 4.14 Point Entity (Type 116) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 98 4.15 Ruled Surface Entity (Type 118) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 100 4.16 Surface of Revolution Entity (Type 120) : : : : : : : : : : : : : : : : : : : : : : : : 104 4.17 Tabulated Cylinder Entity (Type 122) : : : : : : : : : : : : : : : : : : : : : : : : : 107 4.18 Direction Entity (Type 123) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 110 4.19 Transformation Matrix Entity (Type 124) : : : : : : : : : : : : : : : : : : : : : : : 111 4.20 Flash Entity (Type 125) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 119 4.21 Rational B-Spline Curve Entity (Type 126) : : : : : : : : : : : : : : : : : : : : : : 122 4.22 Rational B-Spline Surface Entity (Type 128) : : : : : : : : : : : : : : : : : : : : : 124 4.23 Offset Curve Entity (Type 130) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 127 4.24 Connect Point Entity (Type 132) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 129 4.25 Node Entity (Type 134) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 132 4.26 Finite Element Entity (Type 136) : : : : : : : : : : : : : : : : : : : : : : : : : : : 135 4.27 Nodal Displacement and Rotation Entity (Type 138) : : : : : : : : : : : : : : : : 149 4.28 Offset Surface Entity (Type 140) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 152 4.29 Boundary Entity (Type 141) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 155 4.30 Curve on a Parametric Surface Entity (Type 142) : : : : : : : : : : : : : : : : : : 156 4.31 Bounded Surface Entity (Type 143) : : : : : : : : : : : : : : : : : : : : : : : : : : 158 4.32 Trimmed (Parametric) Surface Entity (Type 144) : : : : : : : : : : : : : : : : : : 159 4.33 Nodal Results Entity (Type 146) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 161 4.34 Element Results Entity (Type 148) : : : : : : : : : : : : : : : : : : : : : : : : : : : 162 4.35 Block Entity (Type 150) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 163 4.36 Right Angular Wedge Entity (Type 152) : : : : : : : : : : : : : : : : : : : : : : : 165 4.37 Right Circular Cylinder Entity (Type 154) : : : : : : : : : : : : : : : : : : : : : : 167 4.38 Right Circular Cone Frustum Entity (Type 156) : : : : : : : : : : : : : : : : : : : 169 4.39 Sphere Entity (Type 158) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 171 4.40 Torus Entity (Type 160) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 173 4.41 Solid of Revolution Entity (Type 162) : : : : : : : : : : : : : : : : : : : : : : : : : 175 4.42 Solid of Linear Extrusion Entity (Type 164) : : : : : : : : : : : : : : : : : : : : : 178 4.43 Ellipsoid Entity (Type 168) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 180 4.44 Boolean Tree Entity (Type 180) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 182 4.45 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Entity (Type 514) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 423 A Part File Examples 425 B Spline Curves and Surfaces 447 B.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 447 B.2 Spline Functions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 447 B.3 Spline Curves : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 448 B.4 Rational B-spline Curves : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 449 B.5 Spline Surfaces : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 450 B.6 Rational B-spline Surfaces : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 451 C Conic Arcs 453 D Color-Space Mappings 455 E ASCII Form Conversion Utility 457 F Obsolete Entities 471 F.1 General : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 471 F.2 Obsolete Associativity Instance Entities (Type 402) : 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(Type 123) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 487 G.3 Finite Element Entity (Type 136) : : : : : : : : : : : : : : : : : : : : : : : : : : : 488 G.4 Boundary Entity (Type 141) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 491 xx CONTENTS G.5 Bounded Surface Entity (Type 143) : : : : : : : : : : : : : : : : : : : : : : : : : : 495 G.6 Nodal Results Entity (Type 146) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 498 G.7 Element Results Entity (Type 148) : : : : : : : : : : : : : : : : : : : : : : : : : : : 501 G.8 Selected Component Entity (Type 182) : : : : : : : : : : : : : : : : : : : : : : : : 504 G.9 Manifold Solid B-Rep Object Entity (Type 186) : : : : : : : : : : : : : : : : : : : 505 G.10 Plane Surface Entity (Type 190) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 511 G.11 Right Circular Cylindrical Surface Entity (Type 192) : : : : : : : : : : : : : : : : 514 G.12 Right Circular Conical Surface Entity (Type 194) : : : : 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: : : : : : : : : : : : : : : : : : 575 G.25 Units Data Entity (Type 316) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 584 G.26 Segmented Views Visible Associativity : : : : : : : : : : : : : : : : : : : : : : : : : 587 G.27 Piping Flow Associativity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 589 G.28 Dimensioned Geometry Associativity : : : : : : : : : : : : : : : : : : : : : : : : : 593 xxi CONTENTS G.29 Drawing Entity (Type 404, Form 1) : : : : : : : : : : : : : : : : : : : : : : : : : : 599 G.30 Intercharacter Spacing Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : 601 G.31 Line Font Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 602 G.32 Highlight Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 607 G.33 Pick Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 608 G.34 Uniform Rectangular Grid Property : : : : : : : : : : : : : : : : : : : : : : : : : : 609 G.35 Associativity Group Type Property : : : : : : : : : : : : : : : : : : : : : : : : : : 610 G.36 Level to PWB Layer Map Property : : : : : : : : : : : : : : : : : : : : : : : : : : 612 G.37 PWB Artwork Stackup Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : 615 G.38 PWB Drilled Hole Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 616 G.39 Generic Data Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 618 G.40 Dimension Units Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 620 G.41 Dimension Tolerance Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 622 G.42 Dimension Display Data Property : : : : : : : : : : : : : : : : : : : : : : : : : : : 625 G.43 Basic Dimension Property : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 629 G.44 Perspective View Entity (Type 410, Form 1) : : : : : : : : : : : : : : : : : : : : : 630 G.45 External Reference Entity (Type 416, Form 3) : : : : : : : : : : : : : : : : : : : : 633 G.46 External Reference Entity (Type 416, Form 4) : : : : : : : : : : : : : : : : : : : : 634 G.47 Vertex Entity (Type 502) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 635 G.47.1 Vertex List Entity (Type 502, Form 1) : : : : : : : : : : : : : : : : : : : : 635 G.48 Edge Entity (Type 504) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 637 G.48.1 Edge List Entity (Type 504, Form 1) : : : : : : : : : : : : : : : : : : : : : 637 G.49 Loop Entity (Type 508) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 639 G.50 Face Entity (Type 510) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 641 G.51 Shell Entity (Type 514) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 643 H Parallel Projections from Perspective Views 645 I Deprecated Binary Form 647 I.1 Constants : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 647 I.1.1 Integer Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 647 I.1.2 Real Numbers. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 649 I.1.3 String Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 649 I.1.4 Pointers. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 649 I.1.5 Language Constants. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 649 xxii CONTENTS I.2 File Structure : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 652 I.2.1 Binary Flag Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 652 I.2.2 Start Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 654 I.2.3 Global Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 655 I.2.4 Directory Entry Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 656 I.2.5 Parameter Data Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : 656 I.2.6 Terminate Section. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 658 J List of References 660 K Glossary 663 L Index of Entities 677 xxiii List of Figures 1 Categories of Product Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 Format of the Start section in the ASCII Form : : : : : : : : : : : : : : : : : : : : 12 3 Format of the Directory Entry (DE) Section in the ASCII Form : : : : : : : : : : 18 4 Format of the Parameter Data (PD) section in the ASCII Form : : : : : : : : : : 27 5 Format of the Terminate section in the ASCII Form : : : : : : : : : : : : : : : : : 28 6 General file structure in the Compressed ASCII Format : : : : : : : : : : : : : : : 30 7 Multiple Transformation Cases : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 34 8 Interpretation of ZT Displacement (Depth) for Annotation Entities : : : : : : : : 42 9 Entity Usage According to System Category. : : : : : : : : : : : : : : : : : : : : : 45 10 Subfigure Structures : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 48 11 General Connectivity Pointer Diagram : : : : : : : : : : : : : : : : : : : : : : : : : 50 12 External Linkages : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 51 13 Finite Element Modeling File Structure : : : : : : : : : : : : : : : : : : : : : : : : 54 14 Finite Element Modeling Logical Structure : : : : : : : : : : : : : : : : : : : : : : 55 15 Examples Defined Using the Circular Arc Entity : : : : : : : : : : : : : : : : : : : 61 16 Parameterization of the Composite Curve : : : : : : : : : : : : : : : : : : : : : : : 64 17 Example Defined Using the Composite Curve Entity : : : : : : : : : : : : : : : : : 66 18 Examples Defined Using the Conic Arc Entity : : : : : : : : : : : : : : : : : : : : 69 19 Examples Defined Using the Centerline Entity : : : : : : : : : : : : : : : : : : : : 78 20 Definition of Patterns for the Section Entity : : : : : : : : : : : : : : : : : : : : : 81 21 Examples Defined Using the Witness Line Entity : : : : : : : : : : : : : : : : : : : 83 22 Examples Defined Using the Plane Entity : : : : : : : : : : : : : : : : : : : : : : : 85 23 Examples Defined Using the Line Entity : : : : : : : : : : : : : : : : : : : : : : : : 89 24 Parameters of the Parametric Spline Curve Entity : : : : : : : : : : : : : : : : : : 91 25 Examples Defined Using the Parametric Spline Curve Entity : : : : : : : : : : : : 91 26 Parameters of the Parametric Spline Surface Entity : : : : : : : : : : : : : : : : : 95 xxiv LIST OF FIGURES 27 Examples Defined Using the Point Entity : : : : : : : : : : : : : : : : : : : : : : : 99 28 Examples Defined Using the Ruled Surface Entity : : : : : : : : : : : : : : : : : : 101 29 Parameters of the Ruled Surface Entity : : : : : : : : : : : : : : : : : : : : : : : : 102 30 Examples Defined Using the Surface of Revolution Entity : : : : : : : : : : : : : : 105 31 Parameters of the Surface of Revolution Entity : : : : : : : : : : : : : : : : : : : : 105 32 Parameters of the Tabulated Cylinder Entity : : : : : : : : : : : : : : : : : : : : : 108 33 Example of the Transformation Matrix Coordinate Systems : : : : : : : : : : : : : 112 34 Notation for FEM-specific Forms of the Transformation Matrix Entity : : : : : : : 117 35 Definition of Shapes for the Flash Entity : : : : : : : : : : : : : : : : : : : : : : : 120 36 Nodal Displacement Coordinate Systems : : : : : : : : : : : : : : : : : : : : : : : 133 37 Finite Element Topology Set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 137 38 Offset Surface in 3-D Euclidean Space : : : : : : : : : : : : : : : : : : : : : : : : : 153 39 Parameters of the CSG Block Entity : : : : : : : : : : : : : : : : : : : : : : : : : : 164 40 Parameters of the CSG Right Angular Wedge Entity : : : : : : : : : : : : : : : : : 166 41 Parameters of the CSG Right Circular Cylinder Entity : : : : : : : : : : : : : : : 168 42 Parameters of the CSG Right Circular Cone Frustum Entity : : : : : : : : : : : : 170 43 Parameters of the CSG Sphere Entity : : : : : : : : : : : : : : : : : : : : : : : : : 172 44 Parameters of the CSG Torus Entity : : : : : : : : : : : : : : : : : : : : : : : : : : 174 45 Parameters of the CSG Solid of Revolution Entity : : : : : : : : : : : : : : : : : : 177 46 Parameters of the CSG Solid of Linear Extrusion Entity : : : : : : : : : : : : : : : 179 47 Parameters of the CSG Ellipsoid Entity : : : : : : : : : : : : : : : : : : : : : : : : 181 48 Construction of Leaders for the Angular Dimension Entity : : : : : : : : : : : : : 194 49 Examples Defined Using the Angular Dimension Entity : : : : : : : : : : : : : : : 195 50 Examples Defined Using the Diameter Dimension Entity : : : : : : : : : : : : : : 198 51 Parameters of the Flag Note Entity : : : : : : : : : : : : : : : : : : : : : : : : : : 201 52 Examples Defined Using the Flag Note Entity : : : : : : : : : : : : : : : : : : : : 202 53 Examples Defined Using the General Label Entity : : : : : : : : : : : : : : : : : : 204 54 General Note Font Specified by FC 19 : : : : : : : : : : : : : : : : : : : : : : : : : 207 55 General Note Font Specified by FC 1001 : : : : : : : : : : : : : : : : : : : : : : : : 208 56 General Note Font Specified by FC 1002 : : : : : : : : : : : : : : : : : : : : : : : : 209 57 General Note Font Specified by FC 1003 : : : : : : : : : : : : : : : : : : : : : : : : 210 58 Examples Defined Using the General Note Entity : : : : : : : : : : : : : : : : : : 215 59 General Note Text Construction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 216 60 General Note Example of Text Operations : : : : : : : : : : : : : : : : : : : : : : 217 xxv LIST OF FIGURES 61 Examples of Drafting Symbols That Exceed Text Box Height : : : : : : : : : : : : 218 62 Examples Defined Using the Leader Entity : : : : : : : : : : : : : : : : : : : : : : 226 63 Structure of Leaders Internal to a Dimension : : : : : : : : : : : : : : : : : : : : : 227 64 Definition of Arrowhead Types for the Leader (Arrow) Entity : : : : : : : : : : : : 228 65 Examples Defined Using Form 0 of the Linear Dimension Entity : : : : : : : : : : 230 66 Examples Defined Using the Ordinate Dimension Entity : : : : : : : : : : : : : : : 232 67 Examples Defined Using the Point Dimension Entity : : : : : : : : : : : : : : : : : 234 68 Examples Defined Using the Radius Dimension Entity : : : : : : : : : : : : : : : : 236 69 Examples Defined Using the General Symbol Entity : : : : : : : : : : : : : : : : : 238 70 Predefined Fill Patterns for the Sectioned Area Entity : : : : : : : : : : : : : : : : 242 71 Examples of Nested Definition Curves : : : : : : : : : : : : : : : : : : : : : : : : : 243 72 Examples of Illegal Definition Curves : : : : : : : : : : : : : : : : : : : : : : : : : 243 73 Example of Illegal Relationship for Definition Curves : : : : : : : : : : : : : : : : 244 74 Example of Two Ways to Define an Area : : : : : : : : : : : : : : : : : : : : : : : 244 75 Relationships Between Entities in an Associativity : : : : : : : : : : : : : : : : : : 247 76 Line Font Definition Using Form Number 1 (Template Subfigure) : : : : : : : : : 252 77 Line Font Definition Using Form Number 2 (Visible-Blank Pattern) : : : : : : : : 253 78 Example of a Character Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : 258 79 Example of a Character Definition : : : : : : : : : : : : : : : : : : : : : : : : : : : 259 80 Dimensioned Geometry Associativity : : : : : : : : : : : : : : : : : : : : : : : : : 319 81 Using Clipping Planes with a View in a Drawing : : : : : : : : : : : : : : : : : : : 333 82 Parameters of the Drawing Entity : : : : : : : : : : : : : : : : : : : : : : : : : : : 334 83 Measurement of the Line Widening Property Values : : : : : : : : : : : : : : : : : 342 84 Relationship Between Properties Used to Represent a Composite Material : : : : : 357 ___ 85 Use of the Vector D to Define the Element Material Coordinate System : : : : : : 362 86 Internal Load and Strain Sign Convention : : : : : : : : : : : : : : : : : : : : : : : 364 87 Relationship Between Subfigure Definition and Subfigure Instance : : : : : : : : : 398 88 Orthographic Parallel Projection of AB on a View Plane : : : : : : : : : : : : : : 403 89 View Coordinate System : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 403 90 Planes Defining the View Volume : : : : : : : : : : : : : : : : : : : : : : : : : : : 404 91 Relationship Between the Nodal Load/Constraint Entity and Tabular Data Properties413 A1 Electrical Part Example : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 426 A2 Mechanical Part Example : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 429 A3 Drawing and View Example : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 437 xxvi LIST OF FIGURES F1 Obsolete General Note Font specified by FC 0 : : : : : : : : : : : : : : : : : : : : 482 G1 Finite Element Topology Set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 489 G2 Hierarchical nature of the MSBO : : : : : : : : : : : : : : : : : : : : : : : : : : : : 509 G3 Construction of the MSBO : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 510 G4 Defining data for unparameterized plane surface (Form Number = 0). : : : : : : : 513 G5 Defining data for parameterized plane surface (Form Number = 1). : : : : : : : : 513 G6 Defining data for unparameterized right circular cylindrical surface (Form Number = 0). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 516 G7 Defining data for parameterized right circular cylindrical surface (Form Number = 1). : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 517 G8 Defining data for unparameterized right circular conical surface (Form Number = 0).520 G9 Defining data for parameterized right circular conical surface (Form Number = 1). 520 G10 Defining data for unparameterized spherical surface (Form Number = 0). : : : : : 523 G11 Defining data for parameterized spherical surface (Form Number = 1). : : : : : : 523 G12 Defining data for unparameterized toroidal surface (Form Number = 0). : : : : : : 526 G13 Defining data for parameterized toroidal surface (Form Number = 1). : : : : : : : 526 G14 Examples Defined Using the Curve Dimension Entity : : : : : : : : : : : : : : : : 528 G15 General Note Font (OCR-B) Specified by FC 19 : : : : : : : : : : : : : : : : : : : 530 G16 Text Containment Area : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 537 G17 Character Height, Inter-line Spacing : : : : : : : : : : : : : : : : : : : : : : : : : : 537 G18 Character Width, Interspace, Box Width : : : : : : : : : : : : : : : : : : : : : : : 538 G19 Examples of Fixed Width Character Interspace : : : : : : : : : : : : : : : : : : : : 538 G20 Rotation, Slant and Character Angle : : : : : : : : : : : : : : : : : : : : : : : : : : 539 G21 Text Containment Area : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 539 G22 Character Height, Width, Interspace, Box Width : : : : : : : : : : : : : : : : : : : 540 G23 Character Height, Width, Interspace, Box Width : : : : : : : : : : : : : : : : : : : 541 G24 Example Defined Using the Ordinate Dimension Entity : : : : : : : : : : : : : : : 544 G25 Example Defined Using the Radius Dimension Entity : : : : : : : : : : : : : : : : 546 G26 Examples of Symbols Defined Using New Form Numbers of the General Symbol Entity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 549 G27 Predefined Fill Patterns for the Sectioned Area Entity : : : : : : : : : : : : : : : : 551 G28 Examples of Standard and Inverted Crosshatching. : : : : : : : : : : : : : : : : : : 558 G29 Parameters of the Isoceles Triangle Macro in Example 1 in Text : : : : : : : : : : 576 G30 Repeated Parallelograms Created by Macro Example 2 in Text : : : : : : : : : : : 578 G31 Concentric Circles Created by Macro Example 3 in Text : : : : : : : : : : : : : : : 580 xxvii LIST OF FIGURES G32 Ground Symbol Created by Macro Example 4 in Text : : : : : : : : : : : : : : : : 582 G33 Use of DOF with Angular Dimensions. : : : : : : : : : : : : : : : : : : : : : : : : 597 G34 Use of DOF with Linear and Ordinate Dimensions. : : : : : : : : : : : : : : : : : 597 G35 Use of DLF. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 598 G36 Illustrations of Line Font Patterns for Different Values of LFPC : : : : : : : : : : 604 G37 Examples of tolerance formats (UTOL = 0.01, LTOL = -0.02) : : : : : : : : : : : 624 G38 Placement of Text Using TP and TL. : : : : : : : : : : : : : : : : : : : : : : : : : 628 G39 Definition of a Perspective View : : : : : : : : : : : : : : : : : : : : : : : : : : : : 632 I40 Format of the Control Byte Used in the Binary Form : : : : : : : : : : : : : : : : 648 I41 Format of an Integer Number in the Binary Form : : : : : : : : : : : : : : : : : : 648 I42 Format of a Real Number in the Binary Form : : : : : : : : : : : : : : : : : : : : 650 I43 Structure of a String Constant in the Binary Form : : : : : : : : : : : : : : : : : : 651 I44 General File Structure in the Binary Form : : : : : : : : : : : : : : : : : : : : : : 651 I45 Format of the Binary Flag Section in the Binary Form : : : : : : : : : : : : : : : : 653 I46 Format of the Start Section in the Binary Form : : : : : : : : : : : : : : : : : : : 655 I47 Format of the Global Section in the Binary Form : : : : : : : : : : : : : : : : : : : 655 I48 Format of the Directory Entry (DE) Section in the Binary Form : : : : : : : : : : 657 I49 Format of the Parameter Data (PD) Section in the Binary Form : : : : : : : : : : 658 I50 Format of the Terminate Section in the Binary Form : : : : : : : : : : : : : : : : : 659 xxviii List of Tables 1 Parameters in the Global Section : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 2 Directory Entry (DE) Section : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 19 3 Examples of Physical Parent-Child Relationships : : : : : : : : : : : : : : : : : : : 35 4 Finite Element Topology Set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 136 5 Character Names for the Symbol and Drafting Fonts : : : : : : : : : : : : : : : : : 211 6 Electrical Attribute List (ALT=2) : : : : : : : : : : : : : : : : : : : : : : : : : : : 271 7 AEC Attribute List (ALT=3) : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 285 8 Process Plant Attribute list (ALT=4) : : : : : : : : : : : : : : : : : : : : : : : : : 287 9 Electrical and PWA Manufacturing Attribute List (ALT=5) : : : : : : : : : : : : 291 G1 Finite Element Topology Set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 488 G2 Description of TYPE Numbers for the Nodal and Element Results Entities : : : : 500 xxix 1. General 1.1 Purpose This Specification establishes information structures to be used for the digital representation and communication of product definition data. Use of this Specification permits the compatible ex- change of product definition data used by various Computer-Aided Design and Computer-Aided Manufacturing (CAD/CAM) systems. 1.2 Field of Application This Specification defines a file structure format, a language format, and the representation of geo- metric, topological, and nongeometric product definition data in these formats. Product definition data represented in these formats will be exchanged through a variety of physical media. The specific features and protocols for the communications media are the subject of other standards. The methodology for representing product definition data in this Specification is extensible and independent of the modeling methods used. Chapter 1 is general in nature and defines the overall purpose and objectives of this Specification. Chapter 2 defines the communications file structure and format. It explains the function of each of the sections of a file. Chapter 3 introduces the four classes of entities: curve and surface geometry, constructive solid geometry, annotation, and structure. Chapter 4 describes the details of each individual entity. In Chapter 4, the product is described in terms of geometric and nongeometric information, with nongeometric information being divided into annotation, definition, and organization. The geometry category consists of elements such as points, curves, surfaces, and solids that model the product. The annotation category consists of those elements which are used to clarify or enhance the geometry, including dimensions, drafting notation, and text. The definition category provides the ability to define specific properties or characteristics of individual entities or collections of data entities. The organization category identifies groupings of elements from geometric, annotation, or property data which are to be evaluated and manipulated as single items. 1.3 Conformance to the Specification ECO588 The conformance rules given here are based on three principles. First, conformance is defined in terms of a conforming data file. Second, conformance is defined for a single processor in isolation (i.e., not in terms of interoperability). Third, conformance is defined separately for preprocessor and postprocessor. This section details the minimum conformance criteria for processors. All processors claiming con- formance to this version of the Specification must adhere to the general rules below. In addition, 1 1. GENERAL conforming processors must adhere to the rules appropriate to specific features such as entities. 1.3.1 Conformance rules for data files. A conforming data file shall be syntactically and structurally correct as defined by this (or a previous) version of the Specification. This applies to all sections of the data file. 1.3.2 Conformance rules for preprocessors. A preprocessor which claims conformance to this specification must satisfy the following rule: o A conforming preprocessor shall create conforming data files. 1.3.3 Conformance rules for postprocessors. A postprocessor which claims conformance to this specification must satisfy the following rules: o A conforming postprocessor shall be capable of reading (though not necessarily translating) any conforming data file. o A conforming postprocessor shall not halt or abort because it encounters a conforming data file containing some feature or entity which it was not designed to translate. 1.4 Untested Entities It is the policy of the organization to ensure that entities are tested before being introduced into the Specification. In cases where this testing is not yet complete, the entity is included in Appendix G. A prospective implementor is warned that, despite the fact that Appendix G entities represent the best judgment of the organization, there is a chance that changes will be required before these entities are introduced into the body of the Specification. If these entities are judged useful and implementation is attempted, the results of the attempt will be useful to the IGES/PDES Organization. Contact the IGES/PDES Administration Office at the National Institute of Standards and Technology to report problems and successes. 1.5 Concepts of Product Definition This Specification is concerned with the data required to describe and communicate the essential engineering characteristics of physical objects such as manufactured products. Such products are described in terms of their physical shape, dimensions, and information which further describes or explains the product. The processes which generate or utilize the product definition data typically include design, engineering analysis, production planning, fabrication, material handling, assembly, inspection, marketing, and field service. The requirements for a common data communication format for product definition can be understood in terms of today's CAD/CAM environment. Traditionally, engineering drawings and associated documentation are used to communicate product definition data. Commercial interactive graph- ics systems, originally developed as aids to producing these two-dimensional drawings, are rapidly developing sophisticated three-dimensional solid modeling. In parallel, extensive research work is being conducted in advanced geometric modeling techniques (e.g., parametric representations and solid primitives) and in CAM applications utilizing product definition data in manufacturing (e.g., NC machining and computer-controlled coordinate measurement). The result is rapid growth of 2 1.6 CONCEPTS OF THE FILE STRUCTURE o ADMINISTRATIVE Product Identification Product Structure o DESIGN/ANALYSIS Idealized Models o BASIC SHAPE Geometric Topological o AUGMENTING PHYSICAL CHARACTERISTICS Dimensions and Tolerances Intrinsic Properties o PROCESSING INFORMATION o PRESENTATIONAL INFORMATION Figure 1. Categories of Product Definition CAD/CAM applications, allowing exchange of product definition data, which usually employ in- compatible data representations and formats. In addressing this compatibility problem, this Spec- ification is concerned with needs and capabilities of current and advanced methods of CAD/CAM product definition development. Product definition data may be categorized by their principal roles in defining a product. An example of such a categorization is presented in Figure 1. This Specification specifies communication formats (information structures) for subsets of the product definition. 1.6 Concepts of the File Structure A format to allow the exchange of a product definition between CAD/CAM systems must, as a minimum, support the communication of geometric data, annotation, and organization of the data. The file format defined by this Specification treats the product definition as a file of entities. Each entity is represented in an application-independent format, to and from which the native represen- tation of a specific CAD/CAM system can be mapped. The entity representations provided in this Specification include forms common to the CAD/CAM systems currently available and forms which support the system technologies currently emerging. The fundamental unit of data in the file is the entity. Entities are categorized as geometry and nongeometry. Geometry entities represent the definition of the physical shape and include points, curves, surfaces, solids, and relations which are collections of similarly structured entities. Nonge- ometry entities typically serve to enrich the model by providing a viewing perspective in which a 3 1. GENERAL planar drawing may be composed and by providing annotation and dimensioning appropriate to the drawing. Nongeometry entities further serve to provide specific attributes or characteristics for individual entities or groups of entities and to provide definitions and instances for groupings of entities. The definitions of these groupings may reside in another file. Typical nongeometry entities for drawing definition, annotation, and dimensioning are the view, drawing, general note, witness line, and leader. Typical nongeometry entities for attributes and groupings are the property and the associativity entities. A file consists of five or six sections: Flag (in the case of the binary or compressed ASCII form), Start, Global, Directory Entry, Parameter Data, and Terminate. A file may include any number of entities of any type as required to represent the product definition. Each entity occurrence consists of a directory entry and a parameter data entry. The directory entry provides an index and includes descriptive attributes about the data. The parameter data provides the specific entity definition. The directory data are organized in fixed fields and are consistent for all entities to provide simple access to frequently used descriptive data. The parameter data are entity-specific and are variable in length and format. The directory data and parameter data for all entities in the file are organized into separate sections, with pointers providing bidirectional links between the directory entry and parameter data for each entity. The Specification provides for groupings whose definitions will be found in a file other than the one in which they are used (see Section 3.6.4). Each entity defined by the file structure in Chapter 2 has a specific assigned entity type number. While not all are assigned at this time, entity type numbers 0000 through 0599 and 0700 through 5000 are allocated for specific assignment. Entity type numbers 0600 through 0699 and 10000 ECO532 through 99999 are for implementor-defined (i.e., macro) entities. For implementor-defined entities, see Section 1.7.6. Some entity types include a form number as an attribute. The form number serves to further define or classify an entity within its specific type. The entity set includes a provision for associativities and properties. The Associativity Entity provides a mechanism to establish relationships among entities and to define the meaning of the relationship. The Property Entity allows specific characteristics, such as line widening, to be as- signed to an entity or collection of entities. Each entity format includes a structure for an arbitrary number of pointers to associativities and properties. The file structure provides for both predefined associativities and properties to be included in the Specification and unique definitions which will ECO532 be defined by the implementor. 1.7 Concepts of Information Structures for Geometric Models The geometric model refers to the entity set defined in Chapter 4, and comprises an entity-based product definition file. The entity types, as described above, are categorized as geometry and nongeometry. In general, the geometry entities are defined independently of one another (surfaces are an exception). Features have been provided to define and compose relationships among entities to enhance the model. The nongeometry entities include structures in which an entity may be defined by a collection of other entities and structures which are independent. Several entity types which are used to provide relations or definitions are essential to the file structure methodology of this Specification and are described below. 1.7.1 Property Entity. The Property Entity (Type 406) allows nongeometric numeric or tex- tual information to be related to any entity. Any entity occurrence may reference one or more property entity occurrences as required. In addition, a value which is contained in a property may 4 1.7 CONCEPTS OF INFORMATION STRUCTURES FOR GEOMETRIC MODELS be displayed as text when an additional pointer (See Section 2.2.4.4.2) of the property points to a Text Display Template Entity (Type 312). Property Entities may exist independently of other entities. In this case, the property is defined to be a property of the level indicated in the Level Field of the Directory Entry (DE) of the property. This allows a property to apply to all entities of a given level or for the assignment of an application's function to a level. Because the Level Field in a DE is also allowed to point to a Definition Levels Property Entity (Type 406, Form 1), properties may be applied to multiple levels. 1.7.2 Associativity Entities. The Associativity Entities are designed for use when several en- tities must be logically related to one another. In the case of implementor-defined associativities, two types of entities are involved: Associativity Definition and Associativity Instance. The Asso- ciativity Definition Entity (Type 302) is used to specify the structure of the logical relationship, and the Associativity Instance Entity (Type 402) is used to specify the information involved in a particular occurrence of the relationship. Some associativities are specifically defined as part of this Specification in Section 4.76.1. 1.7.3 View Entity. A drawing or equivalent human-readable representation of the geometric model of a product is a two-dimensional projection of a selected subset of the model, together with nongeometric information such as text. The View Entity (Type 410) and Views Visible Associativity Entities (Type 402, Forms 3 and 4) control such representations. These provide information for orientation, clipping, line removal, and other characteristics associated with individual views rather than with the model itself. 1.7.4 Drawing Entity. The Drawing Entity (Type 404) allows a set of views to be identified and arranged for human presentation. Note that the View and Drawing Entities contain only the rules and parameters for extracting drawings from the geometric model. The actual product definition is not duplicated in various views, eliminating risk of conflicting or ambiguous information. 1.7.5 Transformation Matrix Entity. The Transformation Matrix Entity (Type 124) allows translation and rotation to be applied as needed to any entity in the construction of the model and to the development of views and drawings of the model. 1.7.6 Implementor-Defined Entities. This Specification allows implementors to include enti- ties in their files that are not defined in this document but which have specific implementor meanings. ECO532 This feature supports the objective of the Specification to act as an archiving format where the re- ceiving system is the same as the sending system. In this way, the implementor is able to archive those data forms which may be unique to a particular system. From time to time, files with such implementor-defined entities are used with applications which attempt to edit the file. In this situation, processing problems can arise because, without an entity definition, the editor cannot know which parameter values are pointers that have to be updated, and which are simply data values that should not be updated. This problem can be avoided by using macro definitions and instances of Macro Entities with entity type numbers in the range of 5001 to 9999 inclusively. (See Section G.24 for information on how to use the macro capabilities of the Specification.) This means that for each different implementor- defined entity type, there will be a Macro Definition Entity (Type 306). In order to accomplish the desired result, all that needs to be present in the parameter data for these macro definitions is the 5 1. GENERAL first MACRO statement which defines the parameter list, and an ENDM statement to terminate the definition. 1.8 Appendices As an aid to the implementor/user, a series of appendices is included with this Specification. Ap- pendix A gives three part file examples. Appendix B explains spline representation and approaches for conversion techniques. Appendix C discusses the numerical stability of conic arcs. Appendix D provides mappings between color spaces. Appendix E provides a set of FORTRAN utilities to con- vert physical file structures in the ASCII Form from the regular ASCII Format to the Compressed ASCII Format and back. Appendix F itemizes entities from previous versions which have been made obsolete by this version. Appendix G includes new entities which have not received sufficient implementation testing for inclusion in the main body of the Specification. Appendix H presents ancillary information about perspective views. For reference, Appendix I provides the deprecated binary representation of data. In addition, a List of References, a Glossary, and an Index of Entities are included. 6 2. Data Form 2.1 General An ASCII [ANSI68, ANSI77] form is defined in this Specification to represent data. (A now depre- ECO529 cated Binary Form is described in Appendix I.) ECO531 2.1.1 Defaults. A specific interpretation of an omitted item has been provided in some cases. ECO502 Such defaults tend to reduce the redundancy of the file, but may reduce legibility. Caution should be exercised in generalizing the interpretation of any default beyond that explicitly provided in the Specification. Furthermore, distinctions may be needed among empty fields, blank fields, and a zero field. The appearance of consecutive field delimiters or a field delimiter immediately followed by a record delimiter is an empty field. Notice that empty fields are possible only in free formatted data. The field containing only blanks will be referred to as a blank field. The numeric field with only one digit, where that digit is a zero will be said to have the value 0 and will be called a zero field. A pointer constant represented by any of the three following strings: an empty field; a blank field; or a zero field; requires an explicit interpretation for this single default condition. 2.2 ASCII Form The ASCII Form has two format types: a fixed (80 character) line length format and a compressed format. In the fixed line length ASCII format, the entire file is partitioned into 80 character units beginning with the first character in the file. These units are called lines. The term "column" refers to the character position in a line. The file is divided into sections. The section identification character shall occupy Column 73 of each line. Columns 74 through 80 are specified for the section sequence number of each line. Every line in the file must have a sequence number, i.e., completely blank ECO500 lines are not permitted. For the Compressed ASCII Format, the Directory Entry and Parameter Data Sections are excepted from the above three rules, and will be defined in a later section. The remaining columns are assigned to fields as defined in the file section description. The term "record" refers to the set of parameters for one entity within one file section. A record consists of one or more lines. 2.2.1 Sequence Numbers. A sequence number is a string of from one to seven digits and is the means of indexing lines within the various sections of the data file. The sequence numbers for each section begin with 1 (0000001) and continue sequentially without interruption to the value corresponding to the number of lines in the section. A sequence number may have either leading zeros or leading blanks and is right-justified in its field in the line (Columns 74-80). The sequence number is preceded in the line by a single letter code in Column 73 identifying the section in which the line resides: 7 2.2 ASCII FORM _______________________________________________ |___________Section___________|__Letter_Code__|_ | Flag (not always present) | B or C | | Start | S | | Global | G | | Directory Entry | D | | Parameter Data | P | |__Terminate__________________|_______T________| Letter codes "B" and "C" are used to signify binary (see Appendix I) and compressed ASCII (see Section 2.3.1) information, respectively. 2.2.2 Constants. This Specification defines six types of constants: integer (or fixed point), real (or floating point), string, pointer, language statement, and logical. Regardless of whether the constants appear in a fixed or free format, certain rules apply to their formation, interpretation, and display as text: o Blanks are only significant in string and language statement constants. A numeric field of all ECO502 blanks is considered to denote the default value for that field where a meaning for that default value has been defined in the Specification. No blanks are allowed between the beginning of a numeric constant (i.e., its sign, first numeric digit, or decimal point) and the end of that constant (i.e., the last character position allocated in fixed format or the delimiter character in free format). Leading blanks in the parameters containing numeric constants are ignored. Blanks between the end of any constant and the delimiter following the constant are not allowed. o Numeric constants shall not contain embedded commas. o The absolute magnitude of an integer constant may not exceed the value 2**(N-1)-1, where N is the number of bits used to represent the integer value (Global Parameter 7). Similarly, the absolute magnitude and precision of a real constant may not exceed that indi- cated by Global Parameters 8-9 (for single precision) and 10-11 (for double precision). o Only string and language statement constants may cross field/line boundaries. When such a constant does cross a boundary, it is considered to extend to the last usable column on the current line and then to continue with the first column on the succeeding line. The last usable column on lines in the Parameter Data Section is Column 64; on lines in all other sections it is Column 72. A string constant may not be broken before the Hollerith delimiter (H). o A numeric constant may be either signed or unsigned. If signed, the leading plus or minus determines the sense of the constant. If unsigned, the sense is assumed to be non-negative. 2.2.2.1 Integer Constants. An integer constant (sometimes called a fixed point constant) is always an exact representation of an integer value. It may assume a positive, negative, or zero value. It may assume only an integral value. The form of an integer constant is an optional sign followed by a non-empty string of digits. The digit string is interpreted as a decimal number. The following are examples of valid integer constants (assuming the value of Global Parameter 7 is 32): 8 2.2 ASCII FORM 1 150 2147483647 +3451 0 -10 -2147483647 2.2.2.2 Real Constants. A real constant (sometimes called a floating point constant) is a pro- cessor approximation of the value of a real number. It may assume a positive, negative, or zero value. The following rules and examples apply to real constants as parameter data or as processed for text display. o A real constant may be a basic real constant, a basic real constant followed by an exponent, or an integer constant followed by an exponent. o A real constant may be of either single or double precision. The distinction is in the precision of the processor's representation of the real number which is specified in Global Parameters 8 through 11. A double precision constant may be either a basic real constant followed by a double precision exponent or an integer constant followed by a double precision exponent. o The form of a basic real constant is, in order, an optional sign, an integer part, a decimal point, and a fractional part. Both the integer part and the fractional part are strings of digits; either of these parts may be omitted but not both. A basic real constant is interpreted as a decimal number. o The form of a real exponent is the letter E followed by an optionally signed integer constant. A real exponent denotes a decimal power of ten by which the preceding constant is multiplied. o The form of a double precision exponent is the letter D followed by an optionally signed integer constant. A double precision exponent denotes a decimal power of ten by which the preceding constant is multiplied. The following are examples of valid real constants: 256.091 0. -0.58 +4.21 1.36E1 -1.3E-02 0.1E-3 1.E+4 145.98763D4 -2145.980001D-5 0.123456789D+09 -.43E2 2.2.2.3 String Constants. String constants are represented in the Hollerith form as specified in Appendix C of the current FORTRAN Standard [ANSI78]. A string constant is an arbitrary sequence of ASCII characters. Blanks, parameter delimiters, and record delimiters are treated simply as characters within the string. There is no limit on the length of a string constant. The form of a string constant is a nonzero, unsigned integer constant (character count), followed by the letter H, followed by a string of characters consisting of the number of contiguous characters specified by the character count. No ASCII control characters, i.e., hexadecimal 00 through 1F and ECO531 hexadecimal 7F, may appear in the string of characters. The following are examples of valid string constants: 3H123 10HABC.,;ABCD 8H0.457E03 12H HELLO THERE 9 2.2 ASCII FORM 2.2.2.4 Pointer Constants. A pointer constant is represented by a string of zero to seven ECO502 characters. An empty field, a blank field, and a zero value are all equivalent. However, such null pointers are valid only where the meaning of the null value for that pointer has been specifically provided. Furthermore, a negative integer in the field is valid only where the interpretation of a negative field has been explained. Pointer constants are used to identify a line in either the same or a different section of the data file. The magnitude of the pointer constant corresponds to the sequence number of the referenced line, and the referenced file section is determined by the context of the reference. Pointer constants are unsigned except where they are alternative parameters in a field. Pointer constants whose magnitude requires fewer than seven digits may use leading zeros or leading blanks in fixed format fields. 2.2.2.5 Language Statement Constants. The language statement constant is an arbitrary character string made up of alphanumeric, punctuation, and blank characters from the ASCII char- acter set. The language statement constant is not preceded by the character count and the Hollerith delimiter, H, as is the string constant. Section G.24 defines the syntax of the language statement constant as used for the Macro Entity. The length of the language statement constant is determined by means of the Parameter Data line count in the Directory Entry record for the entity (see Directory Entry Parameter 14). 2.2.2.6 Logical Constants. A logical constant has only two values. These values are specified in the current FORTRAN standard [ANSI78]. In exchange files, where logical constants are expected, the unsigned integer 0 will denote the logical value .FALSE. and the unsigned integer 1 will denote the value .TRUE. . The form of a logical constant is an unsigned integer consisting of a single digit. The digits 2 through 9 may not be used as logical constants. The digit is interpreted as a logical value. 2.2.3 Rules for Forming and Interpreting Free Formatted Data. The data in several sections of a file may be entered in free format. The free format will apply to a range of columns of a line in the section and to the same range of columns of successive lines as needed. This free format feature allows the specification of parameters in the prescribed order without restricting the placement of the parameter to a particular location on a line. When free format is permitted, the following rules apply (in addition to those in Section 2.2.2): o The parameter delimiter (Global Parameter 1_defaulting to a comma) is used to separate parameters. o The record delimiter (Global Parameter 2_defaulting to a semicolon) is used to terminate the record (i.e., to terminate a list of parameters). o When two parameter delimiters, or a parameter and record delimiter, appear adjacent to each other, or are separated by only blanks, the delimited parameter is considered not to have been specified in the file and should be given its default value. Unless specifically noted, the default value for a numeric parameter is zero, and the default value for a string parameter is null ECO540 (see NULL STRING in Appendix K). Pointer constants can be defaulted only when a specific ECO502 definition of the meaning of the default field has been provided in this Specification. It is the responsibility of the preprocessor to ensure that these default values are reasonable for the particular parameter in question. o When a record delimiter appears before the list of parameters is complete, all remaining pa- rameters should be given their default values (see above for a discussion of assigning default 10 2.2 ASCII FORM values). In the case of early termination of a Parameter Data record, either or both groups ECO502 of the additional parameters of Section 2.2.4.4.2 need not be present. This is valid because the pointer count in the parameter preceding the unused pointers has been defaulted to zero. Thus, the unused pointers are not expected. o The end of the data portion of the physical line (i.e., Column 72 in the Global Section, and Column 64 in the Parameter Data Section) is not to be construed to act as either a parameter delimiter or a record delimiter. o The parameter delimiter and record delimiter characters do not maintain their special signifi- cance when included within a string constant. o A numeric constant, including its trailing delimiter, cannot extend across a line boundary. 2.2.3.1 Parameter and Record Delimiter Combinations. The following ASCII characters are prohibited from being used as either Global Parameter 1 (Parameter Delimiter) or Global Pa- rameter 2 (Record Delimiter) because they will cause parsing difficulties in the postprocessor. ______________________________________________ | || Hexadecimal | |__________Name__________|______Range______|__ | The Control Symbols | 0-1F, 7F | | The Space Character | 20 | | The Digits 0 through 9 | 30-39 | | The Characters + - . | 2B, 2D, 2E | |__The_Letters_D_E_H______|__44,_45,_48_______| Only four forms of legitimate syntax are allowed for the first characters of the Global Section defining the two delimiters. They are (where ff and fi represent ASCII characters): _________________________________________________________________ | Form | Interpretation | | |Parameter Delimiter Record Delimiter | |___________________|______Character_____________Character_____|_ | 1. ,, | , ; | | 2. 1Hffff1Hfiff | ff fi | | 3. 1Hffffff | ff ; | |__4._,1Hfi,________|___________,_____________________fi_________ | 2.2.4 File Structure. The file contains six subsections which must appear in order as follows: a. Flag Section (Not always present) b. Start Section c. Global Section d. Directory Entry Section e. Parameter Data Section f. Terminate Section 11 2.2 ASCII FORM These sections are contiguous with no intervening blank lines. The Flag Section of the file is used, ECO500 when present, to indicate that the file is in the Binary Form (see Appendix I) or in the Compressed ASCII Format (see Section 2.3.1). 2.2.4.1 Start Section. The Start Section of the file is designed to provide a human-readable prologue to the file. There must be at least one start record. All records in the section shall have the letter S in Column 73 and a sequence number in Column 74 through 80 (see Section 2.2.1). The information in Columns 1 through 72 need not be formatted in any special way except that the ASCII character set shall be used. An example of a Start Section is shown in Figure 2. 2.2.4.2 Global Section. The Global Section of the file contains the information describing the preprocessor and information needed by the postprocessor to handle the file. All records in the Global Section shall contain the letter G in Column 73 and a sequence number (see Section 2.2.1). The first two global parameters are used to define the parameter delimiter and record delimiter characters if necessary. The default characters are "comma" and "semicolon" respectively. The parameters for the Global Section are input in free format as described in Section 2.2.3. As implied in Section 2.2.3, the global parameters will end with the record delimiter. If the Global Section specifies new delimiter characters, they take over immediately and are used in the Global Section as well as the rest of the file. This is possible because the comma and semicolon delimiter specifications are the first two global parameters. The parameters in the Global Section are described in Table 1 and the paragraphs that follow. Unless explicitly stated, no defaults are provided. |1| 72 |73| 80|| ________________________________________________________________________________________________________ |This section is a human readable prologue to the file. | | | |S0000001 | |It can contain an arbitrary number of lines |S0000002 | | . |S0000003 | | .. | .. | | | . | |using ASCII characters in columns 1-72. |S000000N | | | | Figure 2. Format of the Start section in the ASCII Form 12 2.2 ASCII FORM Table 1. Parameters in the Global Section Index__ Type___ Description___ 1 String Parameter delimiter character (default is comma) 2 String Record delimiter character (default is semicolon) 3 String Product identification from sending system 4 String File name 5 String System ID 6 String Preprocessor version 7 Integer Number of binary bits for integer representation 8 Integer Maximum power of ten representable in a single precision floating point number on the sending system 9 Integer Number of significant digits in a single precision floating point number on the sending system 10 Integer Maximum power of ten representable in a double precision floating point number on the sending system 11 Integer Number of significant digits in a double precision floating point number on the sending system 12 String Product identification for the receiving system 13 Real Model space scale (example: .125 indicates a ratio of 1 unit model space to 8 units real world) 14 Integer Unit flag 15 String Units. 16 Integer Maximum number of line weight gradations (1-32768). Refer to the Directory Entry Parameter 12 (see Section 2.2.4.3.12) for use of this parameter. (Default = 1) ECO544 17 Real Width of maximum line weight in units. Refer to the Directory Entry Parame- ECO545 ter 12 (see Section 2.2.4.3.12) for use of this parameter. 18 String Date & time of exchange file generation 13HYYMMDD.HHNNSS where: ECO565 YY is last 2 digits of year HH is hour (00-23) MM is month (01-12) NN is minute (00-59) DD is day (01-31) SS is second (00-59) 19 Real Minimum user-intended resolution or granularity of the model expressed in units defined by Parameter 15 (example .0001) 20 Real Approximate maximum coordinate value occurring in the model expressed in units defined by Parameter 15. (Example: 1000.0 means for all coordinates |X|; |Y |; |Z| 1000:) 21 String Name of author 22 String Author's organization 23 Integer Integer value corresponding to the version of the Specification used to create this file. 24 Integer Drafting standard in compliance to which the data encoded in this file was generated. 25 String Date and time the model was created or last modified, whichever occurred last, ECO565 13HYYMMDD.HHNNSS (see index 18) 13 2.2 ASCII FORM 2.2.4.2.1 Parameter Delimiter Character. This parameter indicates which character is used to separate parameter values in the Global and Parameter Data sections. Each occurrence of this character denotes the end of the current parameter and the start of the next parameter. Two exceptions exist: (1) string constants in which the delimiter character may be part of the string; (2) language statements in which the delimiter character may be a part of the language syntax. The default value is a comma. See Section 2.2.3. 2.2.4.2.2 Record Delimiter. This parameter indicates which character is used to denote the end of a list of parameters in the Global Section and each Parameter Data Section Entry. Each occurrence of this character denotes the end of the current parameter and of the current parameter list. Two exceptions exist: (1) string constants in which the delimiter character may be part of the string; (2) language statements in which the delimiter character may be a part of the language syntax. The default value is a semicolon. See Section 2.2.3. 2.2.4.2.3 Product Identification From Sender. This is the name or identifier which is used by the sender to reference this product. 2.2.4.2.4 File Name. This is the name of the exchange file. 2.2.4.2.5 System ID. This parameter is an identification code which should uniquely identify the system software which generated this file. It includes the complete vendor's name, the name by which the system is marketed, and the product ID/version number and/or release date of software. 2.2.4.2.6 Preprocessor Version. This parameter identifies the version and/or release date of the preprocessor which created this file. 2.2.4.2.7 Number of Binary Bits for Integer Representation. This parameter indicates how many bits are present in the integer representation of the sending system. This parameter sets limits on the range of values for integer parameters in the file. 2.2.4.2.8 Single Precision Magnitude. This parameter indicates the maximum power of ten which may be represented as a single precision floating point number on the sending system. 2.2.4.2.9 Single Precision Significance. This parameter indicates the number of decimal dig- its of significance which can be accurately represented in the single precision floating point repre- sentation on the sending system. 2.2.4.2.10 Double Precision Magnitude. This parameter indicates the maximum power of ten which may be represented as a double precision floating point number on the sending system. 2.2.4.2.11 Double Precision Significance. This parameter indicates the number of decimal digits of significance which can be accurately represented in the double precision floating point repre- sentation on the sending system. Example: For an IEEE floating point representation (see [IEEE85]) with 32 bits, the magnitude and significance parameters have the values 38 and 6, respectively; for a representation with 64 bits, the values are 308 and 15, respectively. 14 2.2 ASCII FORM 2.2.4.2.12 Product Identification for the Receiver. This is the name or identifier which is intended to be used by the receiver to reference this product. 2.2.4.2.13 Model Space Scale. The ratio of model space to real world space. 2.2.4.2.14 Unit Flag. An integer value denoting the measuring system used in the file. The values in the file are assumed to be: ____________________________________________________ |__Value__|_________Measuring_System__________|_____ | 1 |Inches | | 2 |Millimeters | | 3 |(See Parameter 15 for name of units) | | 4 |Feet | | 5 |Miles | | 6 |Meters | | 7 |Kilometers | | 8 |Mils (i.e., 0.001 inch) | | 9 |Microns | | 10 |Centimeters | |____11____|Microinches____________________________|_ This is the controlling definition of units. A value of 3 should only be used when it is intended to transfer data to a system using the same units, in which case Parameter 15 must be used to provide additional information as to those units. 2.2.4.2.15 Units. A string constant naming the model units in the system: ______________________________________ |_____Constant_____|__Model_Units__|__ | 2HIN or 4HINCH | Inches | | 2HMM | Millimeters | | 2HFT | Feet | | 2HMI | Miles | | 1HM | Meters | | 2HKM | Kilometers | | 3HMIL | Mils | | 2HUM | Microns | | 2HCM | Centimeters | |_______3HUIN_______|__Microinches___|_ When the unit flag is given a value of 3, the string constant naming the desired unit should conform to [MIL12] or [IEEE260]. 2.2.4.2.16 Maximum Number of Line Weight Gradations. This is the number of equal subdivisions of line thickness. The default value is 1. ECO544 2.2.4.2.17 Width of Maximum Line Weight in Units. This is the actual width of the ECO545 thickest line possible in the (scaled) file. 15 2.2 ASCII FORM ECO565 2.2.4.2.18 Date and Time of Exchange File Generation. This is a time stamp indicating when the exchange file was generated. 2.2.4.2.19 Minimum User-Intended Resolution. This parameter indicates the smallest dis- tance in model space units that the system should consider as discernable. Coordinate locations in the file which are less than this distance apart should be considered to be coincident. 2.2.4.2.20 Approximate Maximum Coordinate Value. This is the upper bound on the values of all coordinate data actually occurring in this model. The absolute magnitude of each of the coordinates in this model is less than or equal to this value. 2.2.4.2.21 Name of Author. The name of the person responsible for the creation of the data contained in this file. 2.2.4.2.22 Author's Organization. The organization or group with whom the author is asso- ciated. ECO609 2.2.4.2.23 Version Number. Each version of this Specification is assigned a unique integer value corresponding to that version. This field contains the integer value corresponding to the version of the Specification used to create this file. The values in the table below are valid for this Specification version, and will be added to for each successive version or ANSI Specification. If no valid integer number is entered in this field, the default value of 3 (corresponding to Version 2.0 [NBS83]) should be assumed. See the List of References for a full citation for each version. _______________________________________________________________ |__Value__|___________Version_____________|____Reference____|__ | 1 | 1.0 | [NBS80] | | 2 | ANSI Y14.26M - 1981 | [ANSI81] | | 3 | 2.0 | [NBS83] | | 4 | 3.0 | [NBS86] | | 5 |ASME/ANSI Y14.26M - 1987 | [ASME87] | | 6 | 4.0 | [NBS88] | | 7 | ASME Y14.26M - 1989 | [ASME89] | | 8 | 5.0 | [NIST90] | |____9____|______________5.1________________|This_document__|__ 2.2.4.2.24 Drafting Standard Code. The drafting standard according to which the data in this file was generated. _________________________________________________________________________ |__Code__|____________________Drafting_Standard_____________________|____ | 0 |None No standard specified | | 1 |ISO International Organization for Standardization | | 2 |AFNOR French Association for Standardization | | 3 |ANSI American National Standards Institute | | 4 |BSI British Standards Institute | | 5 |CSA Canadian Standards Association | | 6 |DIN German Institute for Standardization | |____7____|JIS________Japanese_Institute_for_Standardization__________|__ 16 2.2 ASCII FORM 2.2.4.2.25 Date and Time Model was Created/Modified. This is a time stamp indicating ECO565 when the model was created or last modified, whichever occurred last. If this information is not available, then this field should be defaulted by preprocessors. If no valid string is entered, then this field should be ignored by postprocessors. 2.2.4.3 Directory Entry Section. The Directory Entry Section has one directory entry for each entity in the file. The directory entry for each entity is fixed in size and contains twenty fields of eight characters each, spread across two consecutive eighty character lines. Data are right justified in each field. With the exception of the fields numbered 10, 16, 17, 18, and 20, entries in all fields in this section will be either integer constants or pointer constants. In this section, the word "number" is sometimes used in place of the phrase "integer constant." The purposes of the Directory Entry Section are to provide an index for the file and to contain attribute information for each entity. The order of the directory entries within the Directory Entry Section is arbitrary with the exception that a definition entity must precede all of its instances. Within the Directory Entry Section, a field consisting wholly of blanks is to be considered to have not been specified and should be given a default value where possible. Default values are not allowed in Fields 1, 2, 10, 11, 14, and 20. The actual values to be assigned as defaults will vary depending on the entity type. This rule does not apply to compressed ASCII. Some of the fields in the directory entry can contain either an attribute value or a pointer to an entity containing a set of such values. In these fields a positive value indicates an integer constant while for a negative value the absolute value should be taken and the result interpreted as a pointer constant. Since valid files have sequence numbers increasing from one, zero is a valid pointer value only when ECO502 a specific interpretation for a 0 value has been defined for that field in this Specification. In such cases, an empty field or a blank field is equivalent to the zero field. See Section 2.2.4.3.7 for one such instance involving the default instead of a pointer to a Transformation Matrix Entity. Figure 3 gives an abbreviated listing of the fields making up the directory entry for each entity. Table 2 and the following paragraphs describe each directory entry field. Note that Table 2 contains references to entities and form numbers defined in Appendix G. Elsewhere in this specification, figures similar to Figure 3 are used with individual entity definitions.ECO580 The same nomenclature is used, with the following additions and exceptions: o If the field is blank, it is defaulted, and the postprocessor will interpret it as a 0. (Exception: Fields 16, 17, which are undefined, and 18, which is treated as an empty text string.) o Explicit values in fields are the only allowed values, e.g., the Entity Type Number and the Form Number. o The symbol < n:a: > is used to indicated that the field has no meaning for this entity. A preprocessor must set the field to either 0 or blank. A postprocessor will ignore the value altogether. o In the Status Number Field, the following symbols are used: . The symbol (**) has the same meaning as < n:a: >; a preprocessor must set this field to 00. . The symbol (??) means that an appropriate value from the defined range for this field must be used for each instance of the entity. 17 2.2 ASCII FORM .An explicit numeric value (e.g., 00 or 02) is the only value that may be used in the field. The value 00 will often be used in place of ** for clarity, i.e., **??01** and 00??0100 are equivalent. o Footnotes are used to indicate that the values of some fields should be ignored under certain conditions. |1|| 8 9||| 16 17||| 24 |25|| 32|33|| 40 41||| 48 |49|| 56|57|| 64 65||| 72 |73|| 80||| |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | | Entity | Para- |Structure| Line | Level | View |Transfor-| Label | Status |Sequence | | Type | meter | | | | | | Display | | | | | | | Font | | | mation | |Number |Number | |Number | Data | |Pattern | | | Matrix | Assoc. | | | | # | ) | #; ) | #; ) | #; ) | 0; ) | 0; ) | 0; ) | # | D # | | | | | | | | | | | | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | | Entity | | | | | | | Entity | Entity |Sequence | | | Line | Color | Para- | Form |Reserved |Reserved | | | | | Type |Weight |Number | meter |Number | | | Label |Subscript|Number | |Number |Number | | Line | | | | |Number | | | | | | Count | | | | | | | | | | | | | | | | | | | # | # | #; ) | # | # | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Nomenclature: (n) - Field number n # - Integer ) - Pointer #; ) - Integer or pointer (pointer has negative sign) 0; ) - Zero or pointer Figure 3. Format of the Directory Entry (DE) Section in the ASCII Form 18 2.2 ASCII FORM Table 2. Directory Entry (DE) Section No.__ Field_Name____ Meaning_and_Notes_______ 1 Entity Type Number Identifies the entity type. 2 Parameter Data Pointer to the first line of the parameter data record for the entity. The letter P is not included. 3 Structure Negated pointer to the directory entry of the definition entity that specifies this entity's meaning. The letter D is not included. The integer values 0, 1, and 2 are permissible in this field but should be disregarded. 4 Line Font Pattern Line font pattern or negated pointer to the directory entry of a Line Font Definition Entity (Type 304). 5 Level Number of the level upon which the entity resides, or a negated pointer to the directory entry of a Definition Levels Property Entity (Type 406, Form 1) which contains a list of levels upon which the entity resides. 6 View Pointer to the directory entry of a View Entity (Type 410), or pointer to a Views Visible Associativity Instance (Type 402, Form 3 or 4), or integer zero (default). 7 Transformation Matrix Pointer to the directory entry of a Transformation Matrix Entity (Type 124) used in defining this entity; zero (de- fault) implies the identity transformation matrix and zero translation vector will be used. 8 Label Display Associativity Pointer to the directory entry of a label Display Associa- tivity (Type 402, Form 5). The value of zero indicates no label display associativity. 9 Status Number Provides four two-digit status values which are entered from left to right in the status number field in the order given below. 1-2 Blank Status 00 Visible 01 Blanked 3-4 Subordinate Entity Switch 00 Independent 01 Physically Dependent 02 Logically Dependent 03 Both (01) and (02) 5-6 Entity Use Flag 00 Geometry 01 Annotation 02 Definition 03 Other 04 Logical/Positional 05 2D Parametric 7-8 Hierarchy 00 Global top down 01 Global defer 02 Use hierarchy property 10 Section Code and Sequence Physical count of this line from the beginning of the Direc- Number tory Entry Section, preceded by the letter D (odd number). 11 Entity Type Number (Same as Field 1.) 19 2.2 ASCII FORM 12 Line Weight Number System display thickness; given as a gradation value in the range of 0 to the maximum (Parameter 16 of the Global Section). 13 Color Number Color number or negated pointer to the directory entry of a Color Definition Entity (Type 314). 14 Parameter Line Count Number of lines in the parameter data record for this en- Number tity. 15 Form Number Certain entities have different interpretations. These in- terpretations are uniquely identified by a form number. Possible form numbers are listed within each entity de- scription. 16 Reserved for future use 17 Reserved for future use 18 Entity Label Up to eight alphanumeric characters (right justified). 19 Entity Subscript Number 1 to 8 digit unsigned number associated with the label. 20 Section Code and Sequence Same meaning as Field 10 (even number). Number ECO580 2.2.4.3.1 Entity Type Number. The integer number indicating the type of entity. This num- ber must agree with the entity type number in the corresponding PD record. 2.2.4.3.2 Parameter Data. This is the sequence number of the first parameter data record for ECO580 this entity. The letter P is not included. This number must be in the range indicated by Field 4 on the Terminate Section (see Section 2.2.4.5). 2.2.4.3.3 Structure. Non-negative integer values are permitted in this field, but should be dis- regarded. (In versions prior to Version 3.0, non-negative integers were used in this field to designate version numbers.) For a negative value, the absolute value of this field is interpreted as a pointer to the structure definition entity which specifies the schema for this entity type number. ECO580 This field has meaning only for the Macro Instance Entity (see Appendix G), the Implementor- Defined Associativity Instance Entity (Type 402, Forms 5001-9999) and the Attribute Table Instance Entity (Type 422, Forms 0 and 1). 2.2.4.3.4 Line Font Pattern. This indicates a display pattern to be used to display a geometric entity. A positive value indicates that the receiving system's corresponding version of the solid, dashed, phantom, centerline, and dotted fonts should be used. A negative value indicates that the absolute value should be interpreted as a pointer to a Line Font Definition Entity (Type 304) which provides the information specifying the display pattern. __________________________________ |__Value__|______Pattern________|_ | 0 |No pattern specified | | 1 | Solid | | 2 | Dashed | | 3 | Phantom | | 4 | Centerline | |____5____|_______Dotted_________|_ 20 2.2 ASCII FORM Additional line font patterns may be assigned by using the Line Font Property Entity (Type 406, ECO530 Form 19) (see Section G.31). 2.2.4.3.5 Level. This value specifies a graphic display level or levels to be associated with this entity. A positive value indicates the graphic level on which this entity exists. A negative value indicates the absolute value is a pointer to a Definitions Level Property Entity (Type 406, Form 1) which contains a list of levels to be associated with the entity. This feature allows an entity to exist on multiple graphic levels. 2.2.4.3.6 View. Three options exist. This value is a pointer to the directory entry of a View Entity (Type 410), a pointer to an Associativity Instance (Type 402, Form 3 or 4, Views Visible), or the integer zero (default). The first option applies when the entity is visible in a single view. The second option applies when the entity is visible in more than one view. (Type 402, Form 4 applies when the display characteristics of the entity are view dependent.) The third option applies when the entity is displayed with the same characteristics in all views. 2.2.4.3.7 Transformation Matrix. This value is either a pointer to the directory entry of a Transformation Matrix Entity (Type 124) or the integer zero (default). Zero implies the identity rotation matrix and zero translation vector will be used. The Transformation Matrix Entity provides form numbers according to the form of the transformation matrix. See Section 4.19. 2.2.4.3.8 Label Display Associativity. This is a pointer to the directory entry of a Label Display Associativity (Type 402, Form 5) which defines how the entity's label and subscript are to be displayed in different views. A zero value indicates no Label Display Associativity is specified. 2.2.4.3.9 Status Number. This value contains four pieces of information which are concate- nated into a single integer number. The four two-digit values are concatenated from left to right in the order given below. 2.2.4.3.9.1 Blank Status. This value defines whether the entity is meant to be visible on the output device of the receiving system. A value of 00 implies the entity is to be displayed and a value of 01 implies the entity is not to be displayed. 2.2.4.3.9.2 Subordinate Entity Switch. This value indicates whether or not the entity is referenced by other entities in the file; and, if so, what type of relationship exists. An entity can be independent, physically dependent, logically dependent, or both physically and logically dependent. The values are defined as follows: 00: Independent. The entity is not referenced (i.e., pointed to) by any other entities in the file. It can exist alone in the native database. 01: Physically Dependent. This entity (the child) is referenced by another entity (the parent) in the file. The child cannot exist unless the parent exists. The matrix pointed to by the entity (as a child) must be applied to the entity's definition in order to determine its location in the parent's definition space (see Section 3.2.3). Entity A is subordinate to entity B if, and only if, the parameter data entry of entity B contains a pointer to entity A. The additional pointers as defined in Section 2.2.4.4.2 are ignored for 21 2.2 ASCII FORM the purposes of this definition. This implies that entities are NOT subordinate to the View (or Views Visible Associativity) Entity that defines the view within which the entity is displayed. The structure formed by a parent entity and its physically subordinate components is indivis- ible and may therefore be considered to form a single entity. The following are examples of physically subordinate entities: o A Leader Line Entity pointed to by a Linear Dimension Entity. o A Circular Arc Entity pointed to by a Plane Entity. o A Circular Arc Entity pointed to by a Composite Curve Entity. o A Composite Curve Entity pointed to by a Subfigure Definition Entity (note that the subfigure definition would NOT point to the constituent entities of the composite curve). Consider the following example: o Entity A is physically subordinate to entity B. o Entity A points to a Transformation Matrix M1. o Transformation Matrix M1 points to a Transformation Matrix M2. o Entity B is subordinate to a Subfigure Definition Entity C. o Entity B points to a Transformation Matrix M3. o Entity C is instanced in a Subfigure Instance D. o The parameter data of entity D specifies its scale factor as Sd and position as (Xd,Yd,Zd). o Entity D points to a Transformation Matrix M4. o Entity D points to a View Entity E. o The view scale factor defined in the parameter data of entity E is Se. o Entity E occurs within a drawing F at drawing coordinates (Fx,Fy). o Entity E points to a Transformation Matrix M5. In order to obtain the drawing space coordinates of entity A, the following operations are performed: 1. The coordinates of entity A are transformed by M1. 2. The coordinates resulting from the preceding step are transformed by M2. 3. The coordinates resulting from the preceding step are transformed by M3. 4. The coordinates resulting from the preceding step are scaled by Sd. 5. The coordinates resulting from the preceding step are transformed by M4. 6. The coordinates resulting from the preceding step are translated by the vector (Xd,Yd,Zd). The coordinates resulting from this step are the model space coordinates of entity A. 22 2.2 ASCII FORM 7. The coordinates resulting from the preceding step are transformed by M5. 8. The coordinates resulting from the preceding step are scaled by the scale factor Se. 9. The coordinates resulting from the preceding step are translated by the vector (Fx,Fy). 02: Logically Dependent. This entity (the child) can exist alone in the native database, but is referenced by some sort of logical grouping entity, or entities (the parents), such as Asso- ciativities. The matrix pointed to by the parent entity has no effect on the location of the child. An example of a logically subordinate entity is that of a Line Entity pointed to by a Group Associativity Entity. 03: Both Physically and Logically Dependent. This entity is physically dependent upon an- other entity in the file and is subject to the physical dependency rules described above. This entity is also referenced by one or more logical grouping entities, and is also subject to the logical dependency rules described above. Additionally, an entity cannot be physically and logically dependent upon the same parent entity. The case of an entity being both logically and physically subordinate refers to the fact that the Transformation Matrix pointed to by a parent entity is not applied to its logically subordinate children. An example of a logically and physically subordinate entity is that of a Line Entity occurring in a subfigure definition and pointed to by a Group Associativity Entity. 2.2.4.3.9.3 Entity Use Flag. This value indicates the intent of the entity. It classifies the entity as intending to serve in the following manners: 00: Geometry. This is the default value. The entity is used to define the geometry of the structure of the product. 01: Annotation. The entity is used to add annotation or description to the file. This includes geometric entities used to form annotation or description. 02: Definition. The entity is used in definition structures of the file. It is not intended to be valid outside of the other entities which reference the definition structure. An example is the entities in a Subfigure Definition which are intended to be valid in the Subfigure Instances that reference the Subfigure Definition. This class includes all entities in the 300 entity type number range. 03: Other. The entity is being used for other purposes such as defining structural features in the file. This category corresponds roughly to the 400 range, but there are exceptions. For example, a Subfigure Instance (Type 408) could define geometry, thus having an entity use flag = 00 or it could define a drawing format, thus having an entity use flag = 01. An Associativity Instance would ordinarily have the value 03. Exceptions include Associativities concerned with display where it would have the value 01. The View and Drawing Entities have value 01 (annotation). Transformation depends on its use: If used only for annotation (e.g., defining a view), the value is 01; if used for defining geometry or for defining geometry and annotation, value is 00. 04: Logical/Positional. The entity is used as a logical and/or positional reference by other enti- ties. This usage does not prevent the entity from referencing other entities or having its own attributes. Some entities which may be instanced in this way are Node, Connect Point, and Point when their primary use is as a reference. 23 2.2 ASCII FORM 05: 2-D Parametric. The entity takes its values in two-dimensional XY parameter space consid- ered as a subset of three dimensional XYZ space by ignoring the Z coordinate. The transfor- mation matrix from definition space to parameter space must be 2-dimensional (i.e., in Entity 124, Section 4.19, T3 = R13 = R31 = R32 = R23 = 0:0 and R33 = 1:0). In addition, the coordinates do not have units of length (i.e., the model space scale and units conversion do not apply). This is intended for use in defining curves on surfaces. 2.2.4.3.9.4 Hierarchy. This value indicates the relationship between entities in a hierarchical structure and is used to determine which entity's directory entry attributes should be applied. It applies to line font, view, entity level, blank status, line weight, and color number. Three values are provided: 00: All the above directory entry attributes will apply to entities physically subordinate to this entity. 01: None of the above directory entry attributes of this entity will apply to physically subordinate entities. The physically subordinate entities will use their own directory entry attributes. 02: Individual setting of each of above direct entry attributes are allowed. A Hierarchy Property Entity (Type 406, Form 10) (see Section 4.78.10) specifies whether 00 or 01 is applied for each directory entry attribute to physically subordinate entities. Example: If an entity A has 00 in its DE status digits 7 and 8, all entities subordinate to A will have the attributes assigned to A. Consequently, the attributes assigned to all entities subordinate to A are ignored. If an entity A has 01 in its DE status digits 7 and 8, the entities immediately subordinate to A will retain their own status. Consequently, the attributes assigned to A are ignored. 2.2.4.3.10 Sequence Number. A number which specifies the position of the DE line in the Directory Entry Section. The sequence number of the first DE line for any entity is always odd and the sequence number of the second line is always even. 2.2.4.3.11 Entity Type Number. This is the same as Field 1. 2.2.4.3.12 Line Weight Number. This value denotes the thickness (or width) with which an entity should be displayed. A specific series of possible thicknesses are specified by Global Parameters 16 and 17. The largest thickness possible is that specified in Global Parameter 17 and is denoted by setting the Line Weight Number equal to the value in Global Parameter 16. The smallest thickness possible is equal to the result of dividing Global Parameter 17 by Global Parameter 16 and is denoted by setting the Line Weight Number equal to 1. Thicknesses between the smallest and largest thickness are available in increments equal to the smallest possible thickness and are denoted by setting the Line Weight Number equal to the integer number of (adjacent) increments required. Thus, display thickness is: Line Weight Number * (Global Parameter 17/Global Parameter 16). A value of 0 indicates that the default line weight display of the receiving system is to be used. 24 2.2 ASCII FORM 2.2.4.3.13 Color Number. Field 13 either is a color number used for specifying color when the precise shade is unimportant or is a pointer to a more precise color definition. It is up to the receiving system to generate colors which approximately fit the following description. _______________________________________ |__Color_No.__|________Color_________|_||| | 0 |No color assigned | | 1 |Black | | 2 |Red | | 3 |Green | | 4 |Blue | || 5 |Yellow| || || 6 |Magenta| || | 7 |Cyan | |_______8_______|White________________|_ If the color number is negative, its absolute value is a pointer to the directory entry of a Color Definition Entity (Type 314). 2.2.4.3.14 Parameter Line Count Number. This is the number of lines in the Parameter Data Section which contain the parameter data record for this entity. This number must be greater ECO580 than zero, except for the Null Entity (Type 0). 2.2.4.3.15 Form Number. This value indicates an individual interpretation of the entity to be used when processing the parameter data for this entity. Some entity types allow multiple interpretations of their parameter data. This parameter along with the entity type number uniquely identify the interpretation of the parameter data. 2.2.4.3.16 Reserved Field. This field is reserved for future use and should be left blank. 2.2.4.3.17 Reserved Field. Same as Field 16. 2.2.4.3.18 Entity Label. This is the application-specified alphanumeric identifier or name for this entity. It is used in conjunction with the entity subscript number (Field 19) to provide the application-specified alphanumeric identifier for the entity. 2.2.4.3.19 Entity Subscript Number. This is a numeric qualifier for the entity label (Field 18). 2.2.4.3.20 Sequence Number. See Section 2.2.4.3.10. 2.2.4.4 Parameter Data Section. The Parameter Data Section of the file contains the param- eter data associated with each entity. The following information is true for all parameter data. 25 2.2 ASCII FORM 2.2.4.4.1 Parameter data are placed in free format (see Section 2.2.3) with the first field always containing the entity type number. Therefore, the entity type number and a parameter delimiter (default is comma) precede parameter one of each entity. The free format part of a parameter line ends in Column 64. Column 65 shall contain a blank. Columns 66 through 72 on all parameter lines contain the sequence number of the first line in the directory entry of the entity for which parameter data is being presented. Column 73 of all lines in the parameter section shall contain the letter P and Columns 74 through 80 shall contain the sequence number (see Section 2.2.1). 2.2.4.4.2 Two groups of parameters are defined at the end of the specified parameters for each entity. The first group of parameters may contain pointers to Associativity Instance, General Note, and/or Text Template Entities. The pointers to associativity instances are "back pointers" in that they point back from a member of an associativity instance to the associativity instance. These pointers may be required by the associativity definition. If the given entity references associated text, a pointer to the General Note (Type 212) may be included in the first group of pointers. If so, the indicated General Note specifies the string constant and the indicated display parameters. If instead, the given entity contains a string constant to be displayed, a pointer to a Text Template Entity (Type 312) may be included in the first group of pointers. The Text Template entities provide display parameters for text supplied by the entity which points to the template. The second group of parameters may contain pointers to one or more properties or attribute tables. Either group of parameters, or both, may be empty or may be defaulted to no pointers. When present, the pointers comprising these parameters are added after all the other specified (or defaulted) parameters, but ahead of the record delimiter as follows: Index__ Name____ Type___ Description___ .. . . . . .. .. .. Let NV = last parameter number NV+1 NA Integer Number of pointers to the DEs of Associativity Instances/Text Entities NV+2 DE1 Pointer Pointer to the DE of the first Associativity Instance/Text Entity .. . . . . .. .. .. NV+NA+1 DENA Pointer Pointer to the DE of the last Associativity Instance/Text Entity NV+NA+2 NP Integer Number of pointers to the DEs of Property or Attribute Table Entities NV+NA+3 DE Pointer Pointer to the DE of the the first Property or Attribute Table Entity .. . . . .. .. NV+NA+NP+2 DENP Pointer Pointer to the DE of the the last Property or Attribute Table Entity 2.2.4.4.3 Any desired comment may be added after the record delimiter. Note that additional lines may be used for this purpose by keeping the directory entry pointer in Columns 65-72 constant and including them in the count of parameter lines for the entity (DE Field 14). Figure 4 shows a Parameter Data Section. 26 2.2 ASCII FORM 1|| 64 ||66|| 72 73|| 80 || |_________________________________________________________________________________||_________|_________|_ |Entity type number followed by parameter delimiter followed by || DE | | |parameters separated by parameter delimiters ||Pointer |P0000001 | |_________________________________________________________________________________||_________|_________|_ |Parameters separated by parameter delimiters || DE | | |followed by record delimiter ||Pointer |P0000002 | |_________________________________________________________________________________||_________|_________|_ | || | | | .. || .. | .. | | . || . | . | | || | | Note: The DE pointer is the sequence number of the first directory entry line for this entity Figure 4. Format of the Parameter Data (PD) section in the ASCII Form 27 2.2 ASCII FORM ECO500 2.2.4.5 Terminate Section. There is only one line in the Terminate Section of the file. It is divided into ten fields of eight columns each. The Terminate Section must be the last line of the file. Note that there may be blank lines or other data after the file to "pad" a physical block or sector. This data is not part of the file. The Terminate Section has a "T" in Column 73 and Columns 74 through 80 contain the sequence number with a value of one (1). ECO518 Each field in the Terminate record contains a section identifier, left-justified in the field, and the last sequence number used in that section, right-justified in the field. The fields are defined in the table below and are shown in Figure 5. Note that leading zeroes are not required in sequence numbers. __________________________________________ |__Field__|Columns__|_______Section______|_ | 1 | 1-8 | Start | | 2 | 9-16 | Global | | 3 | 17-24 | Directory Entry | | 4 | 25-32 | Parameter Data | | 5-9 | 33-72 | (not used) | |___10___|___73-80____|_Terminate________|_ |1| 8 9|| 16 17|| 24 |25| 32|33| 40 41|| 48 |49| 56|57| 64 65|| 72 |73| 80|| ________________________________________________________________________________________________________ | | | | | | | |S0000020 |G0000003 |D0000500 |P0000261 | Not Used |T0000001 | | | | | | | | Figure 5. Format of the Terminate section in the ASCII Form 28 2.3 COMPRESSED ASCII FORMAT 2.3 Compressed ASCII Format The format described here is intended to serve as an alternative to the fixed line-length ASCII Format when the size of a file is a problem. The Compressed ASCII Format is intended to be simply converted to and from the fixed line length ASCII Format. An example of software to perform such conversions is presented in Appendix E. 2.3.1 File Structure. A single Flag Section record shall precede the Start Section and shall ECO517 contain the character "C" in character position 73 to identify the file as being in the Compressed ASCII Format. The Start, Global and Terminate Sections remain the same as those for the regular ASCII Format, while the Directory Entry Section and the Parameter Data Section are combined into a single Data Section. A record in the Data Section contains the data from the entity's Directory Entry record followed immediately by the data from its Parameter Data record. The first line of the Data record begins with the letter "D" followed without intervening blanks by an unsigned integer whose value is that of the sequence number of the corresponding Directory Entry record (see Figure 6). The "D" group of characters is followed by zero or more Directory Entry field specifiers. The field specifier consists of the symbol "@" (commercial at) followed by an unsigned inte- ger identifying the field being specified. The "@" group is followed by the character "_" (underscore) which is in turn followed by the value of the field ("@_"). No delimiter is used between the Directory Entry field specifiers, but the collection of field specifi- cations is terminated by a record delimiter character (default: ";"). The Directory Entry field numbers are the same as those used to identify the Directory Entry fields in the regular ASCII Format. Fields 2, 10, 11, and 20 are not specified because they are either redundant or meaningless in the Compressed ASCII Format. When several Directory Entry fields are being specified additional lines may be used. The sequence of field specifiers may be broken only between complete specifications, thus assuring that new lines will begin with the character "@". The Directory Entry field values need be specified only when they change. Thus a field retains its value from entity to entity unless a new value is explicitly stated. Only the first entity in a file is assured of containing a complete set of field specifications. The Directory Entry portion of the Data Section record is followed immediately by the Parameter Data portion. The data from the Parameter Data record begins on a new line and is the same in the Compressed ASCII Format as it is in the regular ASCII Format. Each line is of variable length, and terminates before character position 65, thus assuring that character position 65, if it existed (i.e., if the line were read into a fixed-length, 80-character buffer), would always contain a blank character. 29 2.3 COMPRESSED ASCII FORMAT |1|| 64 || 72 |73| 80|| |_______________________________________________________________________________________________________ | | |_____________________________________________________________________________________________C_________| | | |Start Section as it appears in the fixed line length ASCII Format S | |_______________________________________________________________________________________________________| |Global Section as it appears in the fixed line length ASCII Format G | |______________________________________________________________________________________________________|_ |D1@1_100 . .a.dditional field descriptions . . . | |__________________________________________________________________________________________| | |. .u.sing as many lines of up to 72 characters each . . . | |______________________________________________________________________________________| |. .a.s needed . . .; | |______________________________________|___________________________________________ |PD record belonging to DE #1 . . . | |__________________________________________________________________________________| | | |._.o.n_lines_of_up_to_64_characters_each_._._.;____|________________________________________ | |D3@ . . .; | |____________________________________________________________________________________________| |PD record belonging to DE #3 . . .; | |____________________________________________________________________|_ .. ._Remaining_Data_Section_entries_._._.___________________________________________________________________ |Terminate|Section_as_it_appears_in_the_fixed_line_length_ASCII_Format________________________T________||_ Note: Default record delimiter assumed Figure 6. General file structure in the Compressed ASCII Format 30 3. Classes of Entities 3.1 General This Chapter contains information pertaining generally to the classes of entities and their structures that occur in the product data exchange file. The four classes of entities defined in this Specification are curve and surface geometry entities, constructive solid geometry entities, annotation entities, and structure entities. Entity type numbers from 100 through 199 are generally reserved for geometry entities. 3.2 Curve and Surface Geometry Entities 3.2.1 Entity Type/Type Numbers. The following curve and surface geometry entities are defined in this Specification: ____________________________________________________________ | Entity | | |__Type_Number__|________________Entity_Type_____________|__ | 100 |Circular Arc | | 102 |Composite Curve | | 104 |Conic Arc | | 106 |Copious Data | | | Linear Path | | | Simple Closed Planar Curve | | 108 |Plane | | 110 |Line | | 112 |Parametric Spline Curve | | 114 |Parametric Spline Surface | | 116 |Point | | 118 |Ruled Surface | | 120 |Surface of Revolution | | 122 |Tabulated Cylinder | | 124 |Transformation Matrix | | 125 |Flash | | 126 |Rational B-Spline Curve | | 128 |Rational B-Spline Surface | | 130 |Offset Curve | | 140 |Offset Surface | | 141 |Boundary (see Appendix G) | | 142 |Curve on a Parametric Surface | | 143 |Bounded Surface (see Appendix G) | |________144________|Trimmed_Parametric_Surface________|____ 31 3.2 CURVE AND SURFACE GEOMETRY ENTITIES 3.2.2 Coordinate Systems. This section introduces a model space concept and a definition space concept. Model space is three-dimensional Euclidean space, the space in which the "model" (or product) being represented resides. The model space X, Y, Z coordinate system is a right-handed Cartesian coordinate system. It is fixed relative to the model. Definition space is also three-dimensional Euclidean space, but has its own right-handed Cartesian XT, YT, ZT coordinate system. In contrast to model space where a single fixed coordinate system exists, the definition space coordinate system may vary from entity to entity. The origin of a definition space coordinate system may be any point in model space, and the orientation may be arbitrary with respect to model space. It is assumed that the unit of length is always the same in both the model space and the definition space coordinate systems. The definition space concept allows the use of a temporary coordinate system in positioning certain geometric entities into model space. This concept plays a simplifying role that is most apparent in connection with those entities which can be contained within a single plane. Use of definition space entails initially describing an entity in definition space, and then converting this to a model space description. Thus, an orthogonal matrix and a translation vector are used to generate model space coordinates from definition space coordinates. The orthogonal matrix used for this purpose is called the defining matrix; both it and the translation vector are treated in the description of the Transformation Matrix Entity (see Section 4.19). The value of the determinant of an orthogonal matrix is always plus or minus one. In the case that the determinant is one, there are two equivalent points of view that can be taken concerning how the geometric entity is related to model space from its definition space description. In order to simplify the discussion that follows, the translation vector is assumed to be the zero vector. This implies that the origin of the definition space coordinate system coincides with the origin in the model space coordinate system. The first point of view imagines that the two coordinate systems are initially coincident (that is, X axis to XT axis, etc.), but that the XT, YT, ZT coordinate frame is free to rotate relative to the X, Y, Z frame. The geometry entity is then considered to be defined relative to the XT, YT, ZT frame, and the defining matrix then rotates this frame, geometry included, so that the geometry entity is positioned as desired relative to the X, Y, Z frame. The second point of view imagines that the XT, YT, ZT frame is initially situated so that the geometry entity within definition space is positioned in the desired manner relative to model space. The defining matrix then leaves the geometry entity fixed, but rotates the XT, YT, ZT frame. At the completion of the rotation, the XT, YT, ZT frame becomes the X, Y, Z frame. The result is that the geometry entity is then positioned as desired relative to the X, Y, Z frame. It is to be emphasized that the discussion here pertains to a single defining matrix whose action in transforming coordinates can be viewed intuitively in two ways. Each point of view stresses the temporary nature of the XT, YT, ZT system, insofar as what is ultimately of interest is the relationship of the geometry entity to the X, Y, Z frame. In a case when the geometry entity to be located within model space can be contained within a single plane, it can be seen that the definition space concept can be used in such a way that the geometry entity as initially described in definition space can be considered to lie in the XT, YT-plane (i.e., the plane ZT=0). From this, it is then convenient to also allow entities to be situated in definition space in any plane parallel to the XT, YT plane (i.e., ZT=arbitrary constant). Each entity is acted upon by a transformation matrix. This implies that each entity makes use of the definition space concept, i.e., is defined initially in definition space, and then transformed into model space. Thus the complete definition of a geometry entity, with respect to model space, involves the Transformation Matrix Entity. However, in some instances, it may very well be that the 32 3.2 CURVE AND SURFACE GEOMETRY ENTITIES transformation matrix will leave all coordinates unchanged. This will be the case exactly when the defining matrix is the identity rotation matrix and the translation vector is the zero vector. (In this situation, a convention is provided to prevent unnecessary processing. See the explanation given in Section 2.2.4.3.7 for Field 7 of the directory entry.) 3.2.3 Multiple Transformation Entities. There are only two cases in which entities can be operated on by multiple transformation entities. The first is the explicit case in which an entity points to a transformation entity through its Directory Entry Field 7, and that transformation entity, in turn, points to an additional transformation entity through its Directory Entry Field 7. This structure is illustrated in Figure 7(a). In the case illustrated by Figure 7(a), the points represented by entity XXX are first operated on ECO519 by matrix 1. The transformed points resulting from application of matrix 1 are then operated on by matrix 2. The other case is an implicit one in which two entities are in a parent/child relationship, and each points to a transformation entity through its respective Directory Entry Field 7. A parent/child relationship occurs when one entity (the parent) is pointing to another entity (the child). This structure is illustrated in Figure 7(b). In the case illustrated by Figure 7(b) the points represented by entity XXX are operated upon by matrix 2 and from that point on are transformed like the points in entity YYY, using matrix 1. A parent/child relationship between entities may also be created with a Single Parent Associativity Instance Entity (Type 402, Form 9). When the specific parent/child relationships shown in Table 3 occur, the implicit relation rule shall apply. Each of the relationships in Table 3 ordinarily results in the subordinate entity switch of the child entity being set to 01 (physically dependent). The exception is the case in which a preprocessor wishes to actually instance the child entity. In this case the child's subordinate entity switch is set to 02 (logically dependent), and the matrix pointed to by the parent has no effect on the location of the child (see Section 2.2.4.3.9.2). 3.2.4 Directionality. Within model space, all curves are directed. Such curves have associated end points; i.e., start point and terminate point. For each entity type, the manner of assigning direction is discussed within the description of each individual entity. Within the entity descriptions that follow, some refer to a "counterclockwise direction" with respect to a sense of rotation in the XT, YT plane. Since the XT, YT plane is located within three dimensional XT, YT, ZT space, this phrase is ambiguous unless a viewing direction is specified from which to view the rotation within the plane. The viewing direction is taken to be from the positive ZT axis looking "down" upon the XT, YT plane. Then, if a clock were imagined to be lying "face up" in the XT, YT plane, i.e., so as to be readable from the chosen viewing direction along the ZT axis - the phrase "counterclockwise direction" refers to the sense of rotation which is opposite the sense of rotation of the hands of the clock. This same notion of the meaning of counterclockwise carries over to any plane that is parallel to the XT, YT plane. 33 3.2 CURVE AND SURFACE GEOMETRY ENTITIES Figure 7. Multiple Transformation Cases 34 3.2 CURVE AND SURFACE GEOMETRY ENTITIES Table 3. Examples of Physical Parent-Child Relationships ____________________________________________________________________________________ |_______________Parent_______________|___________________Child____________________|_||| || Composite Curve |all|constituents || || Plane |bounding|curve || | Point |display symbol | || Ruled Surface |rail|curves || || Flash |defining|entity || || Surface of Revolution |axis,|generatrix || | Tabulated Cylinder |directrix | | Offset Curve |base curve | | Offset Surface |surface | || Trimmed Surface |surface| || | Angular Dimension |all subordinate entities | || Diameter Dimension |all|subordinate entities || | Flag Note |all subordinate entities | | General Label |all subordinate entities | | Linear Dimension |all subordinate entities | | Ordinate Dimension |all subordinate entities | | Point Dimension |all subordinate entities | || Radius Dimension |all|subordinate entities || || General Symbol |all|subordinate entities || || Sectioned Area |all|boundary curves || || Entity Label Display |all|leaders || || Connect Point |display|symbol, Text Display Templates || || Drawing |all|annotation entities || | Subfigure Definition |all associated entities | | Network Subfigure Definition |all associated entities, Text Display Tem- | | |plates and Connect Points | || || || || Nodal Display and Rotation |all|General Notes and Nodes || || Any entity with Entity Use |all|General Notes in text pointer field || |__Flag_=_00_or_01____________________|____________________________________________|_ 35 3.3 CONSTRUCTIVE SOLID GEOMETRY ENTITIES 3.3 Constructive Solid Geometry Entities 3.3.1 Entity Type/Type Numbers. The CSG Primitive Entities are a defined set of solid modeling primitive constructs to be used in all solid modelers_either directly in CSG modelers or in other types of modelers after conversion. CSG primitive entities include the following: _____________________________________________________ | Entity | | |__Type_Number__|____________Entity_Type_________|___ || 150 |Block| || || 152 |Right|Angular Wedge || || 154 |Right|Circular Cylinder || || 156 |Right|Circular Cone Frustum || | 158 |Sphere | | 160 |Torus | | 162 |Solid of Revolution | || 164 |Solid|of Linear Extrusion || |________168________|Ellipsoid_______________________| These primitive entities can be combined into more complex CSG solids using the following entities: _____________________________________________________ | Entity | | |__Type_Number__|____________Entity_Type_________|___ | 180 |Boolean Tree | | 182 |Selected Component (see Ap- | | |pendix G) | || || || | 184 |Solid Assembly | |________430________|Solid_Instance__________________| 3.3.2 Constructive Solid Geometry Models. The Constructive Solid Geometry (CSG) enti- ties support a standard format for one of the two mostly widely used solid model representations_ ECO610 CSG. The CSG entities in this section can be thought of as being one of two types_geometric or struc- tural. The geometric entities are volumetric primitives. These primitives include a block, wedge, cylinder, cone, sphere, torus, ellipsoid, solid of revolution and solid of linear extrusion. The model information for a primitive contains dimensions that define the shape of the primitive, point and vector coordinates that define the local coordinate system of the primitive, and an optional Directory Entry pointer to a transformation matrix which may be used to further position the primitive. If the point and vector coordinates defining the local coordinate system are not given values, the local coordinate system defaults to the global coordinate system. For the Solid of Revolution and Solid of Linear Extrusion Entities, the shape is partly defined indirectly, via a pointer to a planar boundary curve. The structural entities are the Boolean Tree, Solid Instance, and Solid Assembly Entities. The Boolean Tree Entity contains pointers to the elements of the tree, and operations such as union, difference, and intersection to be performed on these elements. Elements may be primitives, other boolean trees or solid instances. There may also be a Directory Entry pointer to a transformation matrix to relocate the entire boolean resultant. 36 3.3 CONSTRUCTIVE SOLID GEOMETRY ENTITIES The Solid Instance Entity contains a pointer to an entity representing a solid and a Directory Entry pointer to a transformation matrix by which the entity is to be transformed. It is a copy of the solid entity relocated in global space. The solid entity may be a primitive, boolean tree, another solid instance, or an assembly. A solid assembly is a collection of items that share a fixed geometric relationship. The relationship is a logical one and is not to be confused with a boolean union. If the faces of different items in an assembly touch, they are not removed, as they would be in a boolean union. The items of an assembly may include primitives, boolean trees, other assemblies, and solid instances. Corresponding to each item pointed to by the assembly is an optional pointer to a transformation matrix to be applied to that item. Thus, each item of the assembly can be moved independently. There is also an optional directory entry pointer to a global transformation matrix to be applied to the entire assembly of items. This global transformation matrix is applied after each of the individual transformation matrices are applied. The description of a solid model is an acyclic directed graph. The nodes in the graph are the various geometric and structural entities. This type of graph is like a tree structure, except that the branches of this graph may reconvene as a move is made down the graph, where down is the general direction from root to terminal node. There may be any number of root nodes, which represent the actual solid models. A root may even be within the branches of another root's graph. The terminal nodes are the primitives_the geometric entities. All the other nodes are structural entities. The structural entities are all able to point to each of the other structural entities as well as to primitives, with one exception. The boolean tree cannot point to an assembly. A CSG solid model is thus represented by appropriately combining geometric entities with structural entities to create a graph structure. 37 3.4 B-REP SOLID ENTITIES 3.4 B-Rep Solid Entities ECO603 3.4.1 Entity Type/Type Numbers. The Boundary Representation (B-Rep) Solid Model En- tities consist of a set of topological entities, a set of surface entities, and a set of curve entities. The following topological entities for B-Rep Solid Models are defined in this Specification: _________________________________________________________________________ | Entity | | |__Type_Number__|______________________Entity_Type___________________|___ | 186 |Manifold Solid B-Rep Object (see Appendix G) | | 502 |Vertex (see Appendix G) | | 504 |Edge (see Appendix G) | | 508 |Loop (see Appendix G) | | 510 |Face (see Appendix G) | |________514________|Shell_(see_Appendix_G)___________________________|__ Only the following surface entities may be used in the construction of B-Rep Solid Models: ___________________________________________________________ | Entity | | |__Type_Number__|_______________Entity_Type____________|___ | 114 |Parametric Spline Surface | | 118/1 |Ruled Surface | | 120 |Surface of Revolution | | 122 |Tabulated Cylinder | | 128 |Rational B-Spline Surface | | 140 |Offset Surface | | 190 |Plane Surface | | 192 |Right Circular Cylindrical Surface | | 194 |Right Circular Conical Surface | | 196 |Spherical Surface | |________198________|Toroidal_Surface____________________|_ Only the following curve entities may be used in the construction of B-Rep Solid Models: _________________________________________________ | Entity | | |__Type_Number__|__________Entity_Type_______|___ | 100 |Circular Arc | | 102 |Composite Curve | | 104 |Conic Arc | | 106/11 |2D Path | | 106/12 |3D Path | | 106/63 |Closed Planar Curve | | 110 |Line | | 112 |Parametric Spline Curve | | 126 |Rational B-Spline Curve | |________130________|Offset_Curve______________|_ 3.4.2 Topology for B-Rep Solid Models. In mechanical CAD systems the role of topology has been traditionally limited to its use in defining Boundary Representation (B-Rep) Solid Models. 38 3.4 B-REP SOLID ENTITIES Constraints have been placed on each topological entity with the intention that they be used in the specific application domain of B-Rep Solid Models. Should another application domain (e.g., AEC or FEM) require different constraints, then new form numbers of these entities should be created which limit the context or the utility of the entities. Each entity has its own set of constraints. A higher level entity (e.g., a loop) may impose constraints on a lower level entity (e.g., an edge). At the higher level, the constraints on the lower level entity are the sum of the constraints imposed by each entity in the chain between the higher and lower level entities. Several topological entities use an Orientation Flag (OF) to indicate whether the direction of a referenced entity agrees with or is opposed to the direction of the referencing entity. If the OF is TRUE then the direction of the referenced entity is correct but if the OF is FALSE then the direction of the referenced entity should be (conceptually) reversed. It can happen that there are several Orientation Flags in the chain of entities from the high level referencing entity to the low level referenced entity. 3.4.3 Analytical Surfaces for B-Rep Solid Models. The entities defined in this set encom- pass those commonly used for describing the surface geometry of B-Rep Solid Models. The surfaces specified here are defined in terms of point, vector and scalar quantities. In general, a point is used to provide positional information and a vector to provide directional information. One or more scalars provide dimensional data. The symbol convention used in the definition of these entities is shown in the following table. ____________Symbols_used_for_analytical_surfaces_____________ |__Symbol__|__Definition____________________________________|_ | a |Scalar quantity | | A | Vector quantity | | <> |Vector normalization | | a |Normalized vector (e.g., a = = A=|A|) | | * |Vector (cross) product | | . |Scalar product | | S(x; y; z) A|nalytic surface | | oe(u; v) P|arametric surface | |_____Sx_____|Partial_derivative_of_S_with_respect_to_x_____|_ 39 3.4 B-REP SOLID ENTITIES 3.4.3.1 Entity Type/Type Numbers. The following analytical surface entities for B-Rep Solid Models are defined in this Specification: ______________________________________________________________________________ | Entity | | |__Type_Number__|_________________________Entity_Type______________________|__ | 123 |Direction (see Appendix G) | | 190 |Plane Surface (see Appendix G) | | 192 |Right Circular Cylindrical Surface (see Appendix G) | | 194 |Right Circular Conical Surface (see Appendix G) | | 196 |Spherical Surface (see Appendix G) | |________198________|Toroidal_Surface_(see_Appendix_G)____________________|___ Note that the Plane Surface Entity (Type 190) may not be used as a clipping plane for a view, and several of these surfaces (plane, cylinder, and cone) are unbounded, i.e., they are infinite surfaces. With the exception of the Plane Surface, these surfaces shall only be used in conjunction with B-Rep Solid Models. 3.4.3.2 Parameterization of Analytical Surfaces. For those systems that use parameterized surfaces, a parameterization is defined for each surface. All the surfaces defined here include a point which forms the origin of a Local Coordinate System (LCS). Two direction vectors are used to complete the definition of the LCS. One is the local Z axis direction and the other is an approximation to the local X axis direction. Let z be the local Z axis direction and a be the approximate local X axis direction. The method for calculating the local X and Y axis directions is the following: o The vector a is projected onto the plane defined by the origin point P and the vector z to give the local X axis direction as x = . The local Y axis direction is then given by y = . 40 3.5 ANNOTATION ENTITIES 3.5 Annotation Entities 3.5.1 Entity Type/Type Number. The following annotation entities are defined in this Spec- ification: ______________________________________________________________ | Entity | | |__Type_Number__|________________Entity_Type______________|___ | 106 |Copious Data | | | Centerline | | | Section | | | Witness Line | | 202 |Angular Dimension | | 204 |Curve Dimension (see Appendix G) | | 206 |Diameter Dimension | | 208 |Flag Note | | 210 |General Label | | 212 |General Note | | 213 |New General Note (see Appendix G) | | 214 |Leader (Arrow) | | 216 |Linear Dimension | | 218 |Ordinate Dimension | | 220 |Point Dimension | | 222 |Radius Dimension | | 228 |General Symbol | |________230________|Sectioned_Area________________________|__ 3.5.2 Construction. Many annotation entities are constructed by using other entities. For example, the dimension entities may have 0, 1, or 2 pointers to Witness Line Entities (a form of Copious Data), 0, 1, or 2 pointers to Leader (Arrow) Entities and a pointer to a General Note Entity. For some annotation entities, a witness line or leader, although allowed, may not exist. For these cases the Parameter Data field pointer value can be set zero. If any constructive entity exists, but its display is suppressed, it can be set to blank status or, if allowed, the pointer value can be set to zero. 3.5.3 Definition Space. An annotation entity may be defined in XT, YT, ZT definition space (see the discussion in Section 3.2.2) or in a two-dimensional space associated with a Drawing Entity (Type 404). In the case of XT, YT, ZT definition space, a transformation matrix is applied to locate the annotation entity within model space. Within the XT, YT, ZT definition space, subordinate entities to an annotation entity may have different ZT displacements. For example, within the Linear Dimension, a different ZT value may be found in each of: General Note, Leader, and Witness Lines (which are pointed to in the Linear Dimension Parameter Data). An example showing the use of ZT displacement (DEPTH) is shown in Figure 8. While the option of having dimensions occupy different planes exists, it is expected that only a single plane will be used. The reason for its existence is due to the structure of annotation entities. As each dimension may comprise several subordinate entities, each subordinate entity by its definition has the ability to stand alone and may require its own ZT displacement; it is likely, though not necessary, that each ZT displacement is identical. 41 3.5 ANNOTATION ENTITIES Figure 8. Interpretation of ZT Displacement (Depth) for Annotation Entities 42 3.5 ANNOTATION ENTITIES 3.5.4 Dimension Attributes 3.5.4.1 General. Most of the dimension entities defined by this specification provide only enough data for the receiving system to restore a visually equivalent representation of the original; additional information (e.g., the geometry being dimensioned) is lost. Dimension attributes enable exchanging this added data to maximize the potential of functionally equivalent entity transfer between systems which support them. Receiving systems lacking CAD entities to contain all attribute data may find some portions useful, or they may ignore the attributes without losing the visual data. CAD system dimensioning capabilities can be grouped into one of three categories: 1. MANUAL - dimensions are constructed using lines, arcs, and text. 2. GENERATIVE - dimensions are generated automatically from selected geometry, but the association with the geometry is not maintained after creation. 3. ASSOCIATIVE - dimensions are generated automatically from selected geometry,and the as- sociation is maintained so that subsequent geometric change will cause a corresponding change in the dimension value; some associative systems with parametric design capabilities also can alter geometry if the dimension value is changed. Usage of dimension attribute entities will directly correspond to the CAD system's category. Cat- egory 1 systems will be unable to send any attributes, and will probably ignore them in received files. Category 2 systems will be able to send and receive the dimension properties: Dimension Units (Type 406, Form 28), Dimension Tolerance (Type 406, Form 29), Dimension Display Data (Type 406, Form 30), and Basic Dimension (Type 406, Form 31). Category 3 systems will be able to send and receive the Dimensioned Geometry Associativity (Type 402, Form 21); this entity groups the dimensioned geometry with the necessary dimension properties. Figure 9 illustrates category usage for a diameter dimension. 3.5.4.2 Usage Rules. Dimension properties may not be independent; they must be logically subordinate to at least one dimension entity; in some cases (e.g., the Dimension Units Property), more than one dimension can reference one property instance. Properties may be used in any combination which is consistent with dimension entity data; thus, the same dimension will never point to both the Dimension Tolerance and Basic Dimension properties because basic dimensions aren't toleranced. Property data must correspond to the data stored in the dimension(s) which reference the property. If the Dimensioned Geometry Associativity is used, the dimension entity and geometry will be logically subordinate to it, and any dimension properties will have logically subordinate status. The Dimensioned Geometry Associativity will always have only physically subordinate status; it will always be referenced only by one dimension entity's backpointer. Refer to Figure 9, category 3. Some systems maintain additional information about dimensions that is of a global nature, and some that is specific to a particular instance of a dimension. Some systems are able to associate a dimension with geometry in such a way that if the geometry is changed, the dimension value is automatically updated to reflect the new values. To support the variety of functionality available for dimensions, several Form Numbers of the Property Entity (Type 406) and a Dimensioned Geometry Associativity (Type 402, Form 21) are provided. All of these properties are optional, but none may exist independently in a file; each instance must be referenced by at least one dimension entity as described in Section 2.2.4.4.2. For example, in the 43 3.5 ANNOTATION ENTITIES case of the Dimension Units Property (Type 406, Form 28), it is possible that one instance of the property is sufficient for all of the dimensions in the drawing, or all Angular Dimensions (Type 202) may reference one instance while all Linear Dimensions (Type 216) reference another instance. A similar situation exists for the Dimension Tolerance Property (Type 406, Form 29). Some of the properties are unique to a particular dimension. For example, the Basic Dimension Property (Type 406, Form 31) contains the coordinates of the corners of a box to be drawn around the dimension text, so an instance of this property may be referenced by only one dimension. The same restriction applies to the Dimension Display Data Property (Type 406, Form 30). There is no restriction on the order in which these properties are referenced; any or all of them may be present in any combination. If present, some contain numeric values that are intended to replace the text string(s) in the General Note Entity (Types 212 and 213) that is referenced by the dimension in its PD section, or they may provide information for the interpretation of the text string(s). Several Form Numbers of the General Note Entity (Type 212) have been provided to indicate dimension types. Specifically, Form Numbers 1, 2, 3, 4, and 5 communicate information about text placement for dual and tolerance dimensions. The dimension attribute properties and the Form Numbers of the General Note should be used in a logically consistent, non-conflicting manner. 44 3.5 ANNOTATION ENTITIES Figure 9. Entity Usage According to System Category. 45 3.6 STRUCTURE ENTITIES 3.6 Structure Entities 3.6.1 Entity Type/Type Number. The following structure entities are defined in this Speci- fication: _____________________________________________________________________________________ | Entity | | |__Type_Number__|____________________________Entity_Type_________________________|___ | 0 |Null | | 132 |Connect Point | | 134 |Node | | 136 |Finite Element | | 138 |Nodal Displacement and Rotation | | 146 |Nodal Results (see Appendix G) | | 148 |Element Results (see Appendix G) | | 302 |Associativity Definition | | 304 |Line Font Definition | | 306 |MACRO Definition (see Appendix G) | | 308 |Subfigure Definition | | 310 |Text Font Definition | | 312 |Text Display Template | | 314 |Color Definition | | 316 |Units Data (see Appendix G) | | 320 |Network Subfigure Definition | | 322 |Attribute Table Definition | | 402 |Associativity Instance | | 404 |Drawing | | 406 |Property | | 408 |Singular Subfigure Instance | | 410 |View | | 412 |Rectangular Array Subfigure Instance | | 414 |Circular Array Subfigure Instance | | 416 |External Reference | | 418 |Nodal Load/Constraint | | 420 |Network Subfigure Instance | | 422 |Attribute Table Instance | | 600-699 |Implementor specified MACRO Instance (see Appendix G) | |____10000-99999____|Implementor_specified_MACRO_Instance_(see_Appendix_G)__|________ The following sections describe some of the uses of the structure entities. 3.6.2 Subfigures. Subfigures have been provided to enable the use of a collection of entities many times within the model at various locations, orientations, and scales. In some cases, the collection itself is specified by a Subfigure Definition Entity (Type 308) and each placement of the collection is specified by a Singular Subfigure Instance Entity (Type 408). The Network Subfigure Definition (Type 320) and Instance (Type 420) Entity pair is similar in concept but has some special features to accommodate the notion of connect point in a network. (Section 3.6.3 provides additional information about network subfigures.) In other cases, a Rectangular Array (Type 412) or a Circular Array (Type 414) Subfigure Instance Entity specifies a base entity to be copied according to one of these two overall patterns. 46 3.6 STRUCTURE ENTITIES Subfigures may be nested. For example, a Subfigure Definition Entity may include a Singular Subfigure Instance Entity as one entity in its collection. The notion of Depth of the Subfigure Definition Entity is used to convey nesting information. Figure 10 illustrates two instances of a Subfigure Definition having a Depth value of N. That Subfigure Definition Entity consists of two geometry entities and one Subfigure Instance Entity. The Subfigure Definition Entity corresponding to this instance entity then has a Depth value of N-1. A similar interpretation of Depth applies also to the Network Subfigure Definition and Instance Entity pair. In these cases, the X,Y,Z location and the scale factor(s) in the Subfigure Instance Entity help locate the Subfigure Definition Entity into the definition space of the referring Subfigure Definition Entity instead of into model space. Thus, the processing sequence in these cases is as follows: Each entity in the Subfigure Definition is operated upon by its defining matrix and translation vector. Each entity is now located within the definition space of the Subfigure Definition Entity. Then, the defining matrix and translation vector of the Subfigure Definition Entity are applied. The entity collection of the Subfigure Definition Entity is now located in the definition space of the Subfigure Instance Entity. Next, the scale factor(s) located in the parameter data of the Subfigure Instance Entity is (are) applied. This results in a scaling about the origin of the definition space of the Subfigure Instance Entity. Next, the defining matrix and translation vector of the Subfigure Instance Entity are applied. This locates the scaled entities either in model space or in the definition space of another Subfigure Definition Entity. Finally, the X,Y,Z translation data located in the parameter data of the Subfigure Instance Entity is applied. Note that this translation data can be relative to either model space or to the definition space of a Subfigure Definition Entity. It will be relative to a definition space exactly when the Subfigure Instance Entity is pointed to by another entity to which it is physically subordinate. 3.6.3 Connectivity. The following file structure shall be used to define logical (and the location for physical) connections between objects. A formed connection between two or more objects requires the data to represent the following: 1. the exact location of each connection point 2. the flow path formed and its identification (if any) 3. the physical connection between the objects (if any). These objects may include electrical or mechanical components such as transistors, pipes and valves, and air conditioning ductwork. Each connection formed defines a flow path between the objects, allowing a fluid (electricity, water, or air) to flow from one object to another. The Network Subfigure (Definition and Instance) Entities are used to represent the objects to be connected. The Connect Point Entity (Type 132) is used to represent the exact location of connection. The term "link" will refer to the logical representation of the flow path (signal) formed, and "flow-name" will refer to the flow path identifier. The term "join" will refer to the file entity or entities which represent the physical connection (geometries between the items). 3.6.3.1 Connectivity Entities. The entities used to implement connectivity include the Net- work Subfigure Definition (Type 320) and Network Subfigure Instance (Type 420) Entities, the Flow Associativity (Type 402, Form 18), the Connect Point Entity (Type 132), and the Text Display Tem- plate (Type 312; absolute = Form 0, incremental = Form 1). 3.6.3.2 Entity Relationships. A flow path (signal) may be formed between items by a link which references the items' connect points (entities) to be related. This creates an associativity 47 3.6 STRUCTURE ENTITIES Figure 10. Subfigure Structures 48 3.6 STRUCTURE ENTITIES among the connect points and thus the entities connected. The flow-name may be used to uniquely identify the particular signal formed. The join may be used to provide a graphical representation of the flow path. In electrical applications the join will be represented by geometric entities such as line, arc, subfigure, copious data, etc. In a piping application, an example of a join represented might be the section of pipe between a valve and a tank. The logical constructs (link and flow-name) shall be implemented by the Flow Associativity Entity which in turn identifies (by pointer) the entities which form the join. In electrical applications, for example, the items to be connected are components (i.e., resistor, 16-pin dual in-line package, etc.), or integrated circuit cells, represented and instanced by Network Subfigures. Each pin (or signal port) is a potential connection point in a flow path, thus each Network Subfigure has a Connect Point for each pin (or port). When such a subfigure is instanced, its connect points must also be instanced. An instanced Connect Point, when added to a flow path, is different from its definition which shall not be a member of any flow path. See Figure 11 for the basic entity relationships. 3.6.3.3 Information Display. The Network Subfigures, representing electrical components for example, often contain text describing the component and its pins. The Text Display Template (Type 312) allows text embedded in another entity to be displayed without redundant specification of the text string. The Text Display Template may be used to display reference designators and pin numbers. The absolute form, within a network subfigure, is recommended for the reference designator text. Each instance of the subfigure need only supply the text string. The pin number can be represented in the incremental form. All the pin numbers on a given side of a package outline having the same X, Y, and Z offsets relative to the pin whose number is to be displayed may use the same Text Display Template definition. 3.6.3.4 Additional Considerations. The situation is exactly the same for both logical and physical product representations. The only differences arise in the subfigure and join entities used. One file may contain both schematic and physical representations of a product. The Flow Associa- tivity Entity (Type 402, Form 18) contains a type flag to indicate the connection type (logical or physical). In this case, one Flow Associativity would represent the logical connection and a second the physical connection. The two associativities would be related by the pointers provided in the Flow Associativity. 3.6.4 External Reference Linkage. Linkages between entities can occur not only within a file, but also between entities in different files. Two entities shall be used in a referencing file to establish this linkage: the External Reference Entity (Type 416) which provides the actual linkage to the referenced file, and the External Reference File List Property Entity (Type 406, Form 12) which provides a list of the names of all the files referenced. Further, only directly referenced files shall be in this property's parameter list. Each file name listed in the parameter data of this property must match the name in the fourth global parameter of a referenced file. An External Reference File Index Associativity (Type 402, Form 12) is required in the referenced file when the Type 416, Form 0 or 2 is used (i.e., more than one referenced entity in the referenced file). This associativity provides a directory to the referenced entities within its file, and both relate a symbolic name to the directory entry of an entity within the file (see Figure 12). All symbolic names used within a set of files linked by references must be unique. Definitions may be nested, and a symbolic name used need be unique only on the nesting level on which it is used. 49 3.6 STRUCTURE ENTITIES Figure 11. General Connectivity Pointer Diagram 50 3.6 STRUCTURE ENTITIES Figure 12. External Linkages 51 3.6 STRUCTURE ENTITIES Because of the intricacy of the linkages, an example follows (refer to Figure 12). Consider a file containing a Subfigure Instance Entity (Type 408). The first item in its parameter data record is a pointer to the subfigure definition entry in the DE Section of the file. In the case that the Subfigure Definition Entity (Type 308) is to be contained in a library file, this first parameter is a pointer to an External Reference Entity (Type 416). That External Reference Entity will have in its parameter data record the name of the file which is to contain the definition and the symbolic name of the definition itself. The file name is the fourth global parameter in the referenced file. The symbolic name is a string which identifies the appropriate referenced definition. In the case of a library file which contains several definitions, each of which are expected to be referenced by other files, the External Reference Associativity (Type 402, Form 12) provides a "table of contents" of the available definitions in the file. The parameter data record of this associativity contains pairs of data: the symbolic name associated with the definition (the same one used in the Type 416 entity's parameter data record), and a pointer to the directory entry record which contains the desired definition. In the case that the entire external file is to be included (i.e., a super-subfigure), Form 1 of the Type 416 entity is used which does not contain a symbolic name in the parameter data record. In a similar manner, the referenced file does not contain an associativity Type 402, Form 12 entity; it is unneeded since the entire file is to be used. In either case, the External Reference File List Property (Type 406, Form 12) will be found in the referencing file. The parameter data record contains a simple list of the file names of the various external files referenced by this file. Once again, the file name used is that in the fourth global parameter of the referenced file. Note that this list contains only those file names that are directly referenced; it gives no information about files which may be referenced in turn by those files used by this file. A limitation of external referencing is that the backpointers (in the "backpointers to associativities" addition to an entity's parameters) cannot be used. If a pointer is required in each direction, separate external reference mechanisms must exist in each file (e.g., the double linkage between files A and B in Figure 12). A preprocessor implementor should use the external reference mechanism with care because of the burden placed on the postprocessor. 3.6.5 Drawings and Views. This Specification provides a mechanism for associating models and drawings so that there is consistency between them. The mechanism is based on the existing practices of some CAD/CAM graphic systems to define the views of a part on a drawing in terms of a single 3-dimensional (3-D) model. The Drawing Entity (Type 404) specifies a drawing of a given size within a special drawing space coordinate system. This entity can refer to one or more View Entities (Type 410) which will specify the projection from 3-D model space to the two-dimensional drawing space. Annotation Entities such as dimensioning can be defined directly in the drawing coordinate system, or can be defined in the 3-D model space and then be included in individual views. More than one drawing entity may be included in a file. In addition to being used in conjunction with the Drawing Entity, the view-specific display of parts of the model can be used to communicate hidden lines, phantom lines, etc. Graphic systems which do not have the ability to define drawing and views of models in this manner are not required to preprocess this construct into a file, but all systems with postprocessors must be able to process the drawing and View Entities in received files. 52 3.6 STRUCTURE ENTITIES 3.6.6 Finite Element Modeling. This section defines the entities and their relationships (point- ers) required to support the Finite Element Modeling (FEM) application and to display results of analysis on those systems which support finite element analysis postprocessing. The entities available for exchanging FEM data are illustrated in Figures 13 and 14. The left side of Figure 13 illustrates the relationships between the entities that define the model's parametric attributes. The right side illustrates the addition of the analysis results. Figure 14 illustrates the FEM entities used to define an example beam structure with accompanying material properties, a load, and a constraint. The entities defined in support of such analysis are the Element Entity (Type 136), Node Entity (Type 134), Load/Constraint Entity (Type 418), Tabular Data Property Entity (Type 406, Form 11), Nodal Results Entity (Type 146) and Element Results Entity (Type 148). The Nodal Results Entity is intended to supercede the Nodal Displacement and Rotation Entity (Type 138). Element (Type 136) defines a finite element to be used in the finite element model. Several finite elements are defined in the specification. Examples of an element are: BEAM, CTRIA, and DAMP. Specifically, the element entity specifies the topology type, number of nodes, and the element type name. Pointers locate the defining nodes and the material properties of the element. The connec- tivity of the nodes is implied in the order of the contained pointers and topology type. Node (Type 134) defines the grid points or nodes of the element. It contains the spatial values that define the node and a pointer to the coordinate system upon which it is defined. Load/Constraint (Type 418) is an entity that points to a node. It defines either a load or a constraint as applied to that node. It also contains a pointer to General Note Entities that define the load case. Property pointers point to the Tabular Data Entity that contains the values of the load or constraint vector. Tabular Data Property Entity (Type 406, Form 11) contains the material property data of the elements and the load/constraint data as required. The Nodal Results Entity is used to communicate nodal finite element analysis results data. It contains analysis results at FEM nodes that are independent of the FEM elements that are attached to them. (The Element Results Entity should be used if the analysis results data are dependent on FEM elements.) It is intended to supercede the old Nodal Displacement and Rotation Entity, as it permits far greater flexibility in the transfer of nodal results. The Element Results Entity is used to communicate FEM element results that vary within a FEM element. The data communicated may be results at various layers within the FEM element: at the FEM element/nodes, at the FEM centroid, at the FEM element gauss points, or any combination of these locations. For example, consider the extrapolated stress values at the nodes of several quadratic, plane-stress FEM elements. There is no guarantee that the nodal values of stress will be identical for adjacent FEM elements at common nodes. There are at least as many possible FEM element result values as there are finite elements that contain common nodes in their topologies. These data are different from the results data expressed at the same node in the Nodal Results Entity. 3.6.7 Attribute Tables. An attribute table (see Sections 4.75 and 4.86) is a collection of at- tribute definitions and values in the form of a single row or table. The structure consists of an Attribute Table Definition Entity (Type 322), where each attribute is defined by a name, a data- type, and a count. The attribute values are either supplied immediately after the attribute definition, or "instanced" via the Attribute Table Instance Entity (Type 422). One or more Attribute Table Instance Entities may point to the Attribute Table Definition Entity using the third field of their Directory Entry. 53 3.6 STRUCTURE ENTITIES Figure 13. Finite Element Modeling File Structure 54 3.6 STRUCTURE ENTITIES Figure 14. Finite Element Modeling Logical Structure 55 3.6 STRUCTURE ENTITIES Three types of Attribute Table Definition Entities and two types of Attribute Table Instance Entities are defined. The Attribute Table Definition Entity can have: (1) attribute definitions only, (2) attribute definitions followed immediately by the attribute values, or (3) attribute definitions followed by attribute values with each value followed by a Text Display Template. The Attribute Table Instance Entity can store: (1) a single row of attribute values, or (2) a table of rows of attribute values, stored in row-major order. 56 4. Entity Types 4.1 General This Chapter defines the entity types available to be used in the entity-based product definition file. Descriptions of the various Directory Entry fields were given in Section 2.2.4.3. The meanings of these fields remain the same across all entities. In this Chapter, those entities making extended use of Field 15 in the Directory Entry (Form Number) are indicated and the various options are listed. The Parameter Data record for each entity is also described in this Chapter. The fields for this record vary from entity to entity. Beginning with Version 4.0 of this Specification, those entities whose testing is not yet complete are included in the Appendix of Untested Entities (Appendix G in this document) rather than here in the body of the Specification (see Section 1.4). 57 4.2 NULL ENTITY (TYPE 0) 4.2 Null Entity (Type 0) ECO583 The Null Entity (Type 0) is intended to be ignored by a processor. It may contain an arbitrary amount of data in its PD data. When encountered by a processor, this entity should be skipped over and not processed. This entity is useful when editing a file. By changing the entity type number of an entity in a file to 0, one ensures that the entity will not be processed. Thus, the replacement of an entity in a file can easily be done by adding the replacement entity to the end of the DE and PD Sections and changing the replaced entity type number to 0. When editing a file to create a Null Entity, care should be taken to change both Entity Type Number Fields in the DE Section, as well as the first field of the first PD line. Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 0 | ) |< n:a: > |< n:a: > |< n:a: > |< n:a: > |< n:a: > |< n:a: > |******** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 0 |< n:a: > |< n:a: > |< n:a: > |< n:a: > | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ 58 4.3 CIRCULAR ARC ENTITY (TYPE 100) 4.3 Circular Arc Entity (Type 100) A circular arc is a connected portion of a parent circle which consists of more than one point. The definition space coordinate system is always chosen so that the circular arc lies in a plane either coincident with or parallel to the XT , Y T plane. A circular arc determines unique arc end points and an arc center point (the center of the parent circle). By considering the arc end points to be enumerated and listed in an ordered manner, start point first, followed by terminate point, a direction with respect to definition space can be associated with the arc. The ordering of the end points corresponds to the ordering necessary for the arc to be traced out in a counterclockwise manner. This convention serves to distinguish the desired circular arc from its complementary arc (complementary with respect to the parent circle). Refer to Section 3.2.4 for information relating to use of the term counterclockwise. The direction of the arc with respect to model space is determined by the original counterclockwise direction of the arc within definition space, in conjunction with the action of the transformation matrix on the arc. In the event that a parameterization is required but not given, the default parameterization is: C(t) = (X1 + R * cos t; Y1 + R * sin t; ZT ) for t2 t t3 where; for i = 2 and 3; q ____________________________ (i) R = (Xi - X1)2 + (Yi - Y1)2 (ii) ti is such that (R * cos ti; R * sin ti) = (Xi - X1; Yi - Y1) and 0 t2 < 2 * ss 0 t3 - t2 2 * ss Examples of the Circular Arc Entity are shown in Figure 15. In Example 2 of Figure 15, the solid arc is defined using point A as the start point and point B as the terminate point. If the complementary dashed arc were desired, the start point listed in the parameter data entry would be B, and the terminate point would be A. 59 4.3 CIRCULAR ARC ENTITY (TYPE 100) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 100 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 100 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 ZT Real Parallel ZT displacement of arc from XT, YT plane 2 X1 Real Arc center abscissa 3 Y1 Real Arc center ordinate 4 X2 Real Start point abscissa 5 Y2 Real Start point ordinate 6 X3 Real Terminate point abscissa 7 Y3 Real Terminate point ordinate Additional pointers as required (see Section 2.2.4.4.2). 60 4.3 CIRCULAR ARC ENTITY (TYPE 100) Figure 15. Examples Defined Using the Circular Arc Entity 61 4.4 COMPOSITE CURVE ENTITY (TYPE 102) 4.4 Composite Curve Entity (Type 102) A composite curve is a continuous curve that results from the grouping of certain individual con- stituent entities into a logical unit. ECO510 A composite curve is defined as an ordered list of entities consisting of point, connect point, and parameterized curve entities (excluding the Composite Curve Entity). The list of entities appears in the parameter data entry. There, each entity to appear in the defining list is indicated by means of a pointer to the directory entry of that entity. The order within the defining list is derived from the order of the listing of these pointers. Each constituent entity has its own transformation matrix and display attributes. Each constituent entity may have text or properties associated with it. Because the constituent entities are subordinate to the composite entity, the Subordinate Entity Switch (digits 3-4 in Directory Entry Field 9) of each constituent entity should indicate a physical dependency. A composite curve is a directed curve, having a start point and a terminate point. The direction of the composite curve is induced by the direction of the constituent curve entities (i.e., those constituent entities other than the point entity) in the following way: The start point for the composite curve is the start point of the first curve entity appearing in the defining list. The terminate point for the composite curve is the terminate point of the last curve entity appearing in the defining list. Within the defining list itself, the terminate point of each constituent curve entity has the same coordinates as the start point of the succeeding curve entity. The Point and Connect Point Entities are included as allowable entity types so that properties or general notes can be attached to either the start point or the terminate point of any constituent curve entities in the defining list. A logical connection relationship can be indicated by having two composite curves or a composite curve and a network subfigure reference the Connect Point Entity. For the special case of the logical connection of a connect point on one subfigure instance to a connect point on another subfigure instance, a composite curve is allowed whose list contains only two Connect Point Entities with no ECO524 intervening curve entity. In this case, the instance of the Composite Curve Entity is not a curve in the normal sense; it is not continuous and has no arc length. This usage is permitted in certain applications (i.e., FEM and AEC). There are certain restrictions regarding the use of the point entity in a composite entity. They are: 1. Two Point or Connect Point Entities cannot appear consecutively in the defining list unless they are the only entities in the composite curve. 2. If a Point or Connect Point Entity and a curve entity are adjacent in the defining list, then the coordinates of the Point or Connect Point Entity must agree with the coordinates of the terminate point of the curve entity whenever the curve entity precedes the Point or Connect Point Entity, and must agree with the coordinates of the start point of the curve entity whenever the curve entity follows the Point or Connect Point Entity. 3. A composite curve cannot consist of a Point Entity alone or a single Connect Point Entity. In the event that a parameterization is required but not given, the default parameterization of the composite curve is obtained from the parameterization of the constituent curves as defined below. As point and connect point entities do not contribute to the parameterization of a composite curve, they are not considered in this definition. 62 4.4 COMPOSITE CURVE ENTITY (TYPE 102) Let C be the composite curve; N be the number of constituent curves (N 1); CC(i) be the i-th constituent curve, for each i such that 1 i N ; P S(i) be the parametric value of the start of CC(i); P E(i) be the parametric value of the end of CC(i); T (0) be 0.0; P i T (i) be j=1(P E(j) - P S(j)), for each i such that 1 i N Then 1. The parametric values of C range from T (0) to T (N ) ; and 2. C(u) = CC(i)(u-T (i-1)+P S(i)) where u is a parametric value such that T (i-1) u T (i). A composite curve consisting solely of Point and/or Connect Point Entities will not be given a parameterization. As an example of a parameterization of a Composite Curve Entity, let N = 3, and for each i such that 1 i 3, let CC(i) be the i-th constituent curve of the composite curve C. Assume the parametric values of the start and end points of each CC(i) are given by the table: _______________________ |__i__|P_S(i)__|P_E(i)_ | | 1 |0.0 | 0.4 | | 2 |3.3 | 3.5 | |__3__|0.0___|__0.3___|_ Then T (0) = 0.0, T (1) = 0.4, T (2) = 0.6, T (3) = 0.9, and the composite curve C is defined from 0.0 to 0.9. This situation is illustrated in Figure 16. The curve combining CC(1), CC(2), and CC(3) represents the composite curve C. An example of a composite curve and its parameterization is shown in Figure 17. 63 4.4 COMPOSITE CURVE ENTITY (TYPE 102) Figure 16. Parameterization of the Composite Curve 64 4.4 COMPOSITE CURVE ENTITY (TYPE 102) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 102 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |???????? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 102 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: When the Hierarchy is set to Global Defer (01), all of the following are ignored and may be defaulted: Line Font Pattern, Line Weight, Color Number, Level, View, and Blank Status. Parameter Data Index__ Name____ Type___ Description___ 1 N Integer Number of entities 2 DE1 Pointer Pointer to the DE of the first constituent entity .. . . . .. .. 1+N DEN Pointer Pointer to the DE of the last constituent entity Additional pointers as required (see Section 2.2.4.4.2). 65 4.4 COMPOSITE CURVE ENTITY (TYPE 102) Figure 17. Example Defined Using the Composite Curve Entity 66 4.5 CONIC ARC ENTITY (TYPE 104) 4.5 Conic Arc Entity (Type 104) A conic arc is a bounded connected portion of a parent conic curve which consists of more than one point. The parent conic curve is either an ellipse, a parabola, or a hyperbola. The definition space coordinate system is always chosen so that the conic arc lies in a plane either coincident with or parallel to the XT , Y T plane. Within such a plane, a conic is defined by the six coefficients in the following equation. A * XT 2 + B * XT * Y T + C * Y T 2 + D * XT + E * Y T + F = 0 Each coefficient is a real number. The definitions of ellipse, parabola, and hyperbola in terms of these six coefficients are given below. A conic arc determines unique arc endpoints. A conic arc is defined within definition space by the six coefficients above and the two endpoints. By considering the conic arc endpoints to be enumerated and listed in an ordered manner, start point followed by terminate point, a direction with respect to definition space can be associated with the arc. In order for the desired elliptical arc to be distinguished from its complementary elliptical arc, the direction of the desired elliptical arc must be counterclockwise. In the case of a parabola or hyperbola, the parameters given in the parameter data section uniquely define a portion of the parabola or a portion of a branch of the hyperbola; therefore, the concept of a counterclockwise direction is not applied. (Refer to Section 3.2.4 for information concerning use of the term "counterclockwise.") The direction of the conic arc with respect to model space is determined by the original direction of the arc within definition space, in conjunction with the action of the transformation matrix on the arc. The definitions of the terms ellipse, parabola, and hyperbola are given in terms of the quantities Q1, Q2, and Q3. These quantities are: 2 3 A B=2 D=2 Q1 = determinant of 64 B=2 C E=2 75 D=2 E=2 F " # A B=2 Q2 = determinant of B=2 C Q3 = A + C A parent conic curve is: An ellipse if Q2 > 0 and Q1 * Q3 < 0. A hyperbola if Q2 < 0 and Q1 6= 0. A parabola if Q2 = 0 and Q1 6= 0. An example of each type of conic arc is shown in Figure 18. Those entities which can be represented as various degenerate forms of a conic equation (Point and Line) must not be put into the Entity Type 104, more appropriate entity types exist for these forms. 67 4.5 CONIC ARC ENTITY (TYPE 104) Because of the numerical sensitivity of the implicit form of the conic description, a receiving system not using that form as its internal representation for conics need not be expected to correctly process conics in this form unless they are put into a standard position in definition space. A Conic Arc Entity is said to be in a standard position in definition space provided each of its axes is parallel to either the XT axis or Y T axis and provided it is centered about the ZT axis. For a parabola, use the vertex as the origin. The conic is moved from this position in definition space to the desired position in space with a transformation matrix (Entity Type 124). The form number is regarded as purely informational by such a postprocessor. Further details may be found in Appendix C. 68 4.5 CONIC ARC ENTITY (TYPE 104) Figure 18. Examples Defined Using the Conic Arc Entity 69 4.5 CONIC ARC ENTITY (TYPE 104) In the event that a parameterization is required but not given, the default parameterization is: Parabola____ case A and E 6= 0:0 ifX1 < X2 C(t) = (t; -(A=E) * t2; ZT ) for t1 t t2 where; for i = 1 and 2; ti = Xi: ifX2 < X1 C(t) = (-t; -(A=E) * t2; ZT ) for t1 t t2 where; for i = 1 and 2; ti = -Xi: case C and D 6= 0:0 ifY1 < Y2 C(t) = (-(C=D) * t2; t; ZT ) for t1 t t2 where; for i = 1 and 2; ti = Yi: ifY2 < Y1 C(t) = (-(C=D) * t2; -t; ZT ) for t1 t t2 where; for i = 1 and 2; ti = -Yi: Ellipse__ C(t) = (a * cos t; b * sint; ZT ) for t1 t t2 where p ________ a = p -F=A____ b = -F=C and; for i = 1 and 2; ti is such that (i) (a * cos ti; b * sinti; ZT ) = (Xi; Yi; ZT ) (ii) 0 t1 2 * ss (iii) 0 t2 - t1 2 * ss 70 4.5 CONIC ARC ENTITY (TYPE 104) Hyperbola_____ case F * A < 0:0 and F * C > 0:0 let p ________ a = p -F=A__ b = F=C and, for i = 1; 2; ti is such that (i) (a * sec ti; b * tan ti; ZT ) = (Xi; Yi; ZT ) (ii) -ss=2 < t1; t2 < ss=2 if t1 < t2 C(t) = (a * sec t; b * tan t; ZT ) for t1 t t2 if t2 < t1 C(t) = (a * sec(-t); b * tan (-t); ZT ) for - t1 t -t2 case F * A > 0:0 and F * C < 0:0 let p ______ a = p F=A_____ b = -F=C and, for i = 1; 2 ti is such that (i) (a * tan ti; b * sec ti; ZT ) = (Xi; Yi; ZT ) (ii) -ss=2 < t1; t2 < ss=2 if t1 < t2 C(t) = (a * tan t; b * sec t; ZT ) for t1 t t2 if t2 < t1 C(t) = (a * tan (-t); b * sec(-t); ZT ) for - t1 t -t2 71 4.5 CONIC ARC ENTITY (TYPE 104) Field 15 of the directory entry accommodates a form number. For this entity, the options are as follows: __________________________________________________________________________________________ |__Form__|______________________________Meaning__________________________________________|_ | 0 |Form of parent conic curve must be determined from the general equation | | 1 |Parent conic curve is an ellipse (See Figure 18) | | 2 |Parent conic curve is a hyperbola (See Figure 18) | |____3____|Parent_conic_curve_is_a_parabola_(See_Figure_18)_____________________________|_ Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 104 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 104 | # | #; ) | # | # | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: Valid values of the Form Number are 0-3. Parameter Data Index__ Name____ Type___ Description___ 1 A Real Conic Coefficient 2 B Real Conic Coefficient 3 C Real Conic Coefficient 4 D Real Conic Coefficient 5 E Real Conic Coefficient 6 F Real Conic Coefficient 7 ZT Real ZT Coordinate of plane of definition 8 X1 Real Start Point Abscissa 9 Y1 Real Start Point Ordinate 10 X2 Real Terminate Point Abscissa 11 Y2 Real Terminate Point Ordinate Additional pointers as required (see Section 2.2.4.4.2). 72 4.6 COPIOUS DATA ENTITY (TYPE 106) 4.6 Copious Data Entity (Type 106) This entity stores data points in the form of pairs, triples, or sextuples. An interpretation flag value signifies which of these forms is being used. This value is one of the parameter data entries. The interpretation flag is abbreviated below by the letters IP. Data points within definition space which lie within a single plane are specified in the form of XT, YT coordinate pairs. In this case, the common ZT value is also needed. Data points arbitrarily located within definition space are specified in the form of XT, YT, ZT coordinate triples. Data points within definition space which have an associated vector are specified in the form of sextuples; the XT, YT, ZT coordinates are specified first, followed by the i, j, k coordinates of the vector associated with the point. (Note that, for an associated vector, no special meaning is implicit.) Field 15 of the Directory Entry accommodates a Form Number. For this entity, the options are as follows: ________________________________________________________________________________________________________ |__Form__||__________________________________________Meaning__________________________________________|_ | 1 |Data points in the form of coordinate pairs. All data points lie in a plane ZT= constant. | | |(IP=1) | | | | | 2 |Data points in the form of coordinate triples (IP=2) | | | | | 3 |Data points in the form of sextuples (IP=3) | | | | | 11 |Data points in the form of coordinate pairs which represent the vertices of a planar, | | | | | |piecewise linear curve (piecewise linear string is sometimes used). All data points lie in | | |a plane ZT=constant. (IP=1) | | | | | 12 |Data points in the form of coordinate triples which represent the vertices of a piecewise | | |linear curve (piecewise linear string is sometimes used) (IP=2) | | | | | 13 |Data points in the form of sextuples. The first triple of each sextuple represents the | | | | | |vertices of a piecewise linear curve (piecewise linear string is sometimes used). The | | |second triple is an associated vector. (IP=3) | | | | | 20 |Centerline Entity through points (IP=1) | | | | | 21 |Centerline Entity through circle centers (IP=1) | | | | | 31 |Section Entity Form 31 (IP=1) | | | | | 32 |Section Entity Form 32 (IP=1) | | | | | 33 |Section Entity Form 33 (IP=1) | | | | | 34 |Section Entity Form 34 (IP=1) | | | | | 35 |Section Entity Form 35 (IP=1) | | | | | 36 |Section Entity Form 36 (IP=1) | | | | | 37 |Section Entity Form 37 (IP=1) | | | | | 38 |Section Entity Form 38 (IP=1) | | | | | 40 |Witness Line Entity (IP=1) | | | | | 63 |Simple Closed Planar Curve Entity (IP=1) | |__________|___________________________________________________________________________________________|_ The linear path is an ordered set of points in either 2- or 3-dimensional space. These points define a series of linear segments along the consecutive points of the path. The segments may cross or be coincident with each other. Paths may close, i.e., the first path point may be identical to the last. 73 4.6 COPIOUS DATA ENTITY (TYPE 106) ECO526 The linear path is implemented as three forms of the Copious Data Entity (Type 106). Form 11 is for 2-dimensional paths, Form 12 is for 3-dimensional paths, and Form 63 is for 2-dimensional closed paths. This entity will be closely associated with properties indicating functionality and fabrication parameters, such as Line Widening. ECO501 In the event that a parameterization is required but not given for these linear path form numbers, the default parameterization is as defined below. It is consistent with the 0-1 parameterization of the Line Entity (Type 110) in that it results in local 0-1 parameterizations for each of the line segments of the path. Let C be the composite curve; P (i) be the i-th point in the definition of the path; N be the number of points in the definition of the path. Then 1. The parametric values, u, of C range from 0 to N - 1; and 2. C(u) = P (i + 1) + s * (P (i + 2) - P (i + 1)) where i u i + 1 0 i N - 1 s = u - i. Refer to the Centerline and Witness Line Entities for examples of Form Numbers 20, 21 and 40. Each of these annotation entities contains a description of how the associated copious data are to be interpreted. Forms 31-38 provide for the transfer of graphical information and are defined here for compatibility with previous versions of this Specification. The Sectioned Area Entity (Type 230) provides a more compact method for transferring this information. ECO526 A simple closed planar curve (Form 63) defines the boundary of a region in XY coordinate space. This entity must meet the constraints of a simple closed curve (see Appendix K) that lies in a plane ZT = constant. Parameterization for this entity may be provided; the default parameterization is the same as defined for the planar linear path (Form 11). The simple closed planar curve will be closely related to entities that require the functionality of a closed region. The simple closed planar curve is implemented as Form 63 of the Copious Data Entity (Type 106). 74 4.6 COPIOUS DATA ENTITY (TYPE 106) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 106 | ) |< n:a: > |< n:a: > | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 106 |< n:a: > | #; ) | # | 1-3 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 IP Integer Interpretation Flag 1 = x,y pairs, common z 2 = x,y,z coordinates 3 = x,y,z coordinates and i,j,k vectors 2 N Integer Number of n-tuples For IP=1 (x,y pairs, common z), i.e., for Form 1: 3 ZT Real Common z displacement 4 X1 Real First data point abscissa 5 Y1 Real First data point ordinate .. . . . .. .. 3+2*N YN Real Last data point ordinate For IP=2 (x,y,z triples), i.e., for Form 2: 3 X1 Real First data point x value 4 Y1 Real First data point y value 5 Z1 Real First data point z value .. . . . .. .. 2+3*N ZN Real Last data point z value For IP=3 (x,y,z,i,j,k sextuples), i.e., for Form 3: 3 X1 Real First data point x value 4 Y1 Real First data point y value 5 Z1 Real First data point z value 6 I1 Real First data point i value 7 J1 Real First data point j value 8 K1 Real First data point k value .. . . . .. .. 2+6*N KN Real Last data point k value Additional pointers as required (see Section 2.2.4.4.2). 75 4.6 COPIOUS DATA ENTITY (TYPE 106) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 106 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 106 | # | #; ) | # |11-13, 63 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 IP Integer Interpretation Flag 1 = x,y pairs, common z 2 = x,y,z coordinates 3 = x,y,z coordinates and i,j,k vectors 2 N Integer Number of n-tuples For IP=1 (x,y pairs, common z), i.e., for Forms 11, 63: 3 ZT Real Common z displacement 4 X1 Real First data point abscissa 5 Y1 Real First data point ordinate .. . . . .. .. 3+2*N YN Real Last data point ordinate For IP=2 (x,y,z triples), i.e., for Form 12: 3 X1 Real First data point x value 4 Y1 Real First data point y value 5 Z1 Real First data point z value .. . . . .. .. 2+3*N ZN Real Last data point z value For IP=3 (x,y,z,i,j,k sextuples), i.e., for Form 13: 3 X1 Real First data point x value 4 Y1 Real First data point y value 5 Z1 Real First data point z value 6 I1 Real First data point i value 7 J1 Real First data point j value 8 K1 Real First data point k value .. . . . .. .. 2+6*N KN Real Last data point k value Additional pointers as required (see Section 2.2.4.4.2). 76 4.7 CENTERLINE ENTITY (TYPE 106, FORM 20-21) 4.7 Centerline Entity (Type 106, Form 20-21) The Centerline Entity takes one of two forms. The first, as illustrated in Example 1 of Figure 19 appears as crosshairs and is normally used in conjunction with circles. The second type (Example 2) is a construction between 2 positions. The Centerline entities are defined as Form 20 or 21 of the Copious Data Entity. The associated matrix transforms the XT-YT plane of the centerline into model space. The coordinates of the centerline points describe the centerline display symbol. The display symbol is described by line segments where each line is from (Xn ; Yn ; Zn ) to (Xn+1 ; Yn+1 ; Zn+1 ) where n = 1; 3; 5; :::; N - 1: See Section 4.6 for more information about the Copious Data Entity (Type 106). Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 106 | ) |< n:a: > | 1 | #; ) | 0; ) | 0; ) | 0; ) |????01** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 106 | # | #; ) | # | 20-21 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 IP Integer Interpretation Flag: IP = 1 2 N Integer Number of data points: N is even ECO605 3 ZT Real Common z displacement 4 X1 Real First data point abscissa 5 Y1 Real First data point ordinate .. . . . .. .. 3+2*N YN Real Last data point ordinate Additional pointers as required (see Section 2.2.4.4.2). 77 4.7 CENTERLINE ENTITY (TYPE 106, FORM 20-21) Figure 19. Examples Defined Using the Centerline Entity 78 4.8 SECTION ENTITY (TYPE 106, FORMS 31-38) 4.8 Section Entity (Type 106, Forms 31-38) A Section Entity is defined as a Copious Data Entity (Type 106, Forms 31 to 38). The form number describes how the data are to be interpreted. These descriptions are included for compatibility with previous versions of the Specification. The Sectioned Area Entity (Type 230) provides a more compact method for transferring this information. The point data contains a list of points (Xn , Yn ), n=1, 2, . . ., N, (The Z value is constant and N is an even integer.) The display of the lines consists of solid line segments between the points (Xn ,Yn ,Z) and (Xn+1 ,Yn+1 ,Z) where n = 1,3,5, . . ., N-1. A portion of collinear line segments which appear to be a dashed line shall consist of point pairs for each dash. The defined line patterns are described below and illustrated in Figure 20. _______________________________________________________________________________________________________ |__Form__|______________________________Description_(see_[ANSI79])_______________________________|_____ | 31 |Parallel line segments from section edge to edge (Cast or malleable iron and general use | | |for all materials) | | | | | 32 |Parallel line segments in pairs with a gap between pairs (Steel) | | | | | 33 |Alternating pattern of a solid line and a set of collinear dash segments (Bronze, brass, | | |copper, and compositions) | | | | | 34 |Parallel lines in quadruples with a gap between groups (Rubber, plastic, and electrical | | |insulation) | | | | | 35 |Triples of parallel lines consisting of two solid lines and a set of collinear dash segments| | |between them with a gap between triples (Titanium and refractory material) | | | | | 36 |Parallel sets of collinear dash segments (Marble, slate, glass, porcelain) | | | | | 37 |Two perpendicular sets of parallel lines (White metal, zinc, lead, babbitt, and alloys) | | | | | 38 |Two perpendicular sets of lines with the principal set solid from edge to edge and the | | | | | |second set consisting of collinear dash segments alternating on the solid lines (Magne- | | |sium, aluminum, and aluminum alloys) | |__________|__________________________________________________________________________________________|_ See Section 4.6 for more information about the Copious Data Entity. 79 4.8 SECTION ENTITY (TYPE 106, FORMS 31-38) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 106 | ) |< n:a: > | 1 | #; ) | 0; ) | 0; ) | 0; ) |????01** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 106 | # | #; ) | # | 31-38 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 IP Integer Interpretation Flag: IP = 1 2 N Integer Number of data points: N is even 3 ZT Real Common z displacement 4 X1 Real First data point abscissa 5 Y1 Real First data point ordinate .. . . . .. .. 3+2*N YN Real Last data point ordinate Additional pointers as required (see Section 2.2.4.4.2). 80 4.8 SECTION ENTITY (TYPE 106, FORMS 31-38) Figure 20. Definition of Patterns for the Section Entity 81 4.9 WITNESS LINE ENTITY (TYPE 106, FORM 40) 4.9 Witness Line Entity (Type 106, Form 40) A Witness Line Entity is a Form Number 40 of a Copious Data Entity that contains one or more straight line segments associated with drafting entities of various types. Each line segment may be visible or invisible. Refer to Figure 21 for examples. Within the copious data, there will be the location from which the witness line gap must be main- tained. This point is indicated in the figure as P1. The location will be the first point in the copious data. P1 will be coincident with the geometry being dimensioned or equal to P2 when the location of the geometry is unknown. (Note: for those annotation methods that do not allow drafting entities to be displaced from the plane of annotation, "coincident with the geometry" indicates that a line normal to the plane of annotation connects P1 and the point on the geometry being dimensioned. Note that all points must be collinear, and that the number of points will be odd and at least 3 (i.e., 3, 5, 7, . .)., with alternating blank and displayed segments. The examples in Figure 21 show the blanking of segments and the order of points stored in the copious data.) See Section 4.6 for more information about the Copious Data Entity (Type 106). Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 106 | ) |< n:a: > | 1 | #; ) | 0; ) | 0; ) | 0; ) |????01** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 106 | # | #; ) | # | 40 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 IP Integer Interpretation Flag: IP = 1 ECO605 2 N Integer Number of data points: N 3 and odd 3 ZT Real Common z displacement 4 X1 Real First data point abscissa 5 Y1 Real First data point ordinate .. . . . .. .. 3+2*N YN Real Last data point ordinate Additional pointers as required (see Section 2.2.4.4.2). 82 4.9 WITNESS LINE ENTITY (TYPE 106, FORM 40) Figure 21. Examples Defined Using the Witness Line Entity 83 4.10 PLANE ENTITY (TYPE 108) 4.10 Plane Entity (Type 108) The plane entity can be used to represent an unbounded plane, as well as a bounded portion of a plane. In either of the above cases, the plane is defined within definition space by means of the coefficients A, B, C, D, where at least one of A, B, and C is nonzero and A * XT + B * Y T + C * ZT = D for each point lying in the plane, and having definition space coordinates (XT; Y T; ZT ). The definition space coordinates of a point, as well as a size parameter, can be specified in order to assist in defining a system-dependent display symbol. These values are parameter data entries six through nine, respectively. This information, together with the four coefficients defining the plane, provides sufficient information relative to definition space in order to be able to position the display symbol. (In the unbounded plane example of Figure 22, the curves and the crosshair together constitute the display symbol.) Setting the size parameter to zero indicates that a display symbol is not intended. ECO591 The case of a bounded portion of a fixed plane requires the existence of a pointer to a closed curve lying in the plane. This is parameter five. The only allowed coincident points for this curve are the start point and the terminate point. The case of an unbounded plane requires this pointer to be zero. ECO590 Use of the Single Parent Associativity has been deprecated (see Appendix F). This functionality should be implemented using the Trimmed (Parametric) Surface Entity (Type 144) or the Bounded Surface Entity (Type 143). Field 15 of the Directory Entry accommodates a form number. For this entity, the options are as follows: ____________________________________________________________________ |__Form__|_______________________Meaning____________________________| | +1 | Bounded planar portion is considered positive. | | |PTR must not be zero. | | | | | 0 |Plane is unbounded. PTR must be zero. | | | | | -1 |Bounded planar portion is considered negative (hole). | | |PTR must not be zero. | |_________|______________________________________________________|__ 84 4.10 PLANE ENTITY (TYPE 108) Figure 22. Examples Defined Using the Plane Entity 85 4.10 PLANE ENTITY (TYPE 108) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 108 | ) |< n:a: > |< n:a: > | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 108 |< n:a: > | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: When used as a view clipping plane, Entity Use Flag shall be Annotation (01), and Subor- dinate Entity Switch shall be Physically Dependent (01). Parameter Data Index__ Name____ Type___ Description___ 1 A Real Coefficients of Plane 2 B Real Coefficients of Plane 3 C Real Coefficients of Plane 4 D Real Coefficients of Plane 5 PTR Pointer Must be zero 6 X Real XT coordinate of location point for display symbol 7 Y Real YT coordinate of location point for display symbol 8 Z Real ZT coordinate of location point for display symbol 9 SIZE Real Size parameter for display symbol Additional pointers as required (see Section 2.2.4.4.2). 86 4.10 PLANE ENTITY (TYPE 108) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 108 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |???????? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 108 | # | #; ) | # |-1 or +1 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 A Real Coefficients of Plane 2 B Real Coefficients of Plane 3 C Real Coefficients of Plane 4 D Real Coefficients of Plane 5 PTR Pointer Pointer to the DE of the closed curve entity 6 X Real XT coordinate of location point for display symbol 7 Y Real YT coordinate of location point for display symbol 8 Z Real ZT coordinate of location point for display symbol 9 SIZE Real Size parameter for display symbol Additional pointers as required (see Section 2.2.4.4.2). 87 4.11 LINE ENTITY (TYPE 110) 4.11 Line Entity (Type 110) A line is a bounded, connected portion of a parent straight line which consists of more than one point. A line is defined by its end points. Each end point is specified relative to definition space by triple coordinates. With respect to definition space, a direction is associated with the line by considering the start point to be listed first and the terminate point second. The direction of the line with respect to model space is determined by the original direction of the line within definition space, in conjunction with the action of the transformation matrix on the line. Examples of the line entity are shown in Figure 23. In the event that a parameterization is required, the default parameterization is: C(t) = P1 + t * (P2 - P1) for 0 t 1 Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 110 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 110 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 X1 Real Start Point P 1 2 Y1 Real 3 Z1 Real 4 X2 Real Terminate Point P 2 5 Y2 Real 6 Z2 Real Additional pointers as required (see Section 2.2.4.4.2). 88 4.11 LINE ENTITY (TYPE 110) Figure 23. Examples Defined Using the Line Entity 89 4.12 PARAMETRIC SPLINE CURVE ENTITY (TYPE 112) 4.12 Parametric Spline Curve Entity (Type 112) The parametric spline curve is a sequence of parametric polynomial segments. The CTYPE value in Parameter 1 indicates the type of curve as it was represented in the sending (preprocessing) system before conversion to this entity. The N polynomial segments are delimited by the breakpoints T (1), T (2), ...,T (N + 1). The coor- dinates of the points in the i-th segment of the curve are given by the following cubic polynomials (the coefficients D, or C and D will be zero if the polynomials are of degrees 2 or 1, respectively): X(u) = AX(i) + BX(i) * s + CX(i) * s2 + DX(i) * s3 Y (u) = AY (i) + BY (i) * s + CY (i) * s2 + DY (i) * s3 Z(u) = AZ(i) + BZ(i) * s + CZ(i) * s2 + DZ(i) * s3 where T (i) u T (i + 1); i = 1; :::; N s = u - T (i) In order to avoid degeneracy, for each i at least one of the following nine real coefficients must be ECO557 nonzero: BX(i), CX(i), DX(i), BY (i), CY (i), DY (i), BZ(i), CZ(i), and DZ(i). If the spline is planar, it must be parameterized in terms of the X and Y polynomials only. The coefficient of the Z- polynomial will then be zero except, for each i , the AZ(i) term which indicates the Z-depth in definition space. The parameter H is used as an indicator of the smoothness of the curve. If H=0, the curve is continuous at all breakpoints. If H=1, the curve is continuous and has slope continuity (see Section 6.3 of [FAUX79]) at all breakpoints. If H=2, the curve is continuous and has both slope and curvature continuity at all breakpoints (see Section 6.3 of [FAUX79]). To enable determination of the terminate point and derivatives without computing the polynomials, the N -th polynomials and their derivatives are evaluated at u = T (N + 1). These data are divided by appropriate factorials and stored following the polynomial coefficients. For example, the name TPY3 will be used to designate 1/3! times the third derivative of the Y -polynomial for the N -th segment evaluated at u = T (N + 1) , the parameter value corresponding to the terminate point. Note that these data are redundant as they are derived from the data defining the N -th polynomial segment. Examples of a parametric spline are shown in Figure 24 and Figure 25; see Appendix B for additional mathematical details. 90 4.12 PARAMETRIC SPLINE CURVE ENTITY (TYPE 112) Figure 24. Parameters of the Parametric Spline Curve Entity Figure 25. Examples Defined Using the Parametric Spline Curve Entity 91 4.12 PARAMETRIC SPLINE CURVE ENTITY (TYPE 112) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 112 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 112 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 CTYPE Integer Spline Type: 1=Linear 2=Quadratic 3=Cubic 4=Wilson-Fowler 5=Modified Wilson-Fowler 6=B Spline 2 H Integer Degree of continuity with respect to arc length 3 NDIM Integer Number of dimensions: 2=planar 3=nonplanar 4 N Integer Number of segments 5 T(1) Real First break point of piecewise polynomial .. . . . .. .. 5+N T(N+1) Real Last break point of piecewise polynomial 6+N AX(1) Real X coordinate polynomial 7+N BX(1) Real 8+N CX(1) Real 9+N DX(1) Real 10+N AY(1) Real Y coordinate polynomial 11+N BY(1) Real 12+N CY(1) Real 13+N DY(1) Real 14+N AZ(1) Real Z coordinate polynomial 15+N BZ(1) Real 16+N CZ(1) Real 17+N DZ(1) Real .. . . . .. .. Subsequent X, Y, Z polynomials concluding with the twelve coefficients of the Nth polynomial segment. The parameters that follow comprise the evaluations of the polynomials of the N -th segment and their derivatives at the parameter value u = T (N + 1) corresponding to the terminate point. Sub- sequently, these evaluations are divided by appropriate factorials. 6+13*N TPX0 Real X value 7+13*N TPX1 Real X first derivative 92 4.12 PARAMETRIC SPLINE CURVE ENTITY (TYPE 112) 8+13*N TPX2 Real X second derivative/2! 9+13*N TPX3 Real X third derivative/3! 10+13*N TPY0 Real Y value 11+13*N TPY1 Real Y first derivative 12+13*N TPY2 Real Y second derivative/2! 13+13*N TPY3 Real Y third derivative/3! 14+13*N TPZ0 Real Z value 15+13*N TPZ1 Real Z first derivative 16+13*N TPZ2 Real Z second derivative/2! 17+13*N TPZ3 Real Z third derivative/3! ECO605 Additional pointers as required (see Section 2.2.4.4.2). 93 4.13 PARAMETRIC SPLINE SURFACE ENTITY (TYPE 114) 4.13 Parametric Spline Surface Entity (Type 114) The parametric spline surface is a grid of parametric polynomial patches. PTYPE in the Parameter Data Section indicates the type of patch under consideration. The M x N grid of patches is defined by the u breakpoints T U (1), . . ., T U (M + 1) and the v breakpoints T V (1), . .,.T V (N + 1). The coordinates of the points in each of the patches are given by the general bicubic polynomials (given here for the (i, j ) patch). X(u; v) = AX(i; j) + BX(i; j) * s + CX(i; j) * s2 + DX(i; j) * s3 + EX(i; j) * t + F X(i; j) * t * s + GX(i; j) * t * s2 + HX(i; j) * t * s3 + KX(i; j) * t2 + LX(i; j) * t2 * s + M X(i; j) * t2 * s2 + N X(i; j) * t2 * s3 + P X(i; j) * t3 + QX(i; j) * t3 * s + RX(i; j) * t3 * s2 + SX(i; j) * t3 * s3 Y (u; v) = ::: Z(u; v) = ::: where T U (i) u T U (i + 1); i = 1; :::; M s = u - T U (i) and T V (j) v T V (j + 1); j = 1; :::; N t = v - T V (j) Postprocessors shall ignore parameters with the indices 7+M+N+48*(k*N+(k-1)) through 6+M+N+48* (k*(N+1)), where k=1,2,3,...,M (i.e., the (N+1)-th row of patches) as well as 7+M+N+48*(M*(N+1)) through 6+M+N+48*(M+1)*(N+1) (i.e., the (M+1)-th column of patches). To maintain upward compatibility with previous versions of this Specification, the preprocessors must either enter a real number for each of these parameters or a series of parameter delimiters (see Section 2.2.3). These values act as placeholders in the parameter list. These parameters were intended to handle first, second, and third partial derivatives of the N -th row and M -th column of patches along the outer edge or boundary. However, these parameters can be computed by the receiving system, as needed, from the other parameter values contained in this entity, and therefore are not needed. An example of the bicubic surface is shown in Figure 26; consult Appendix B for additional details. 94 4.13 PARAMETRIC SPLINE SURFACE ENTITY (TYPE 114) Figure 26. Parameters of the Parametric Spline Surface Entity 95 4.13 PARAMETRIC SPLINE SURFACE ENTITY (TYPE 114) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 114 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 114 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 CTYPE Integer Spline Boundary Type: 1 = Linear 2 = Quadratic 3 = Cubic 4 = Wilson-Fowler 5 = Modified Wilson-Fowler 6 = B-spline 2 PTYPE Integer Patch Type: 1 = Cartesian Product 0 = Unspecified 3 M Integer Number of u segments 4 N Integer Number of v segments 5 TU(1) Real First breakpoint in u (u values of grid lines) .. . . . .. .. 5+M TU(M+1) Real Last breakpoint in u 6+M TV(1) Real First breakpoint in v (v values of grid lines) .. . . . .. .. 6+M+N TV(N+1) Real Last breakpoint in v 7+M+N AX(1,1) Real First X Coefficient of (1,1) Patch .. . . . .. .. 22+M+N SX(1,1) Real Last X Coefficient of (1,1) Patch 23+M+N AY(1,1) Real First Y Coefficient of (1,1) Patch .. . . . .. .. 38+M+N SY(1,1) Real Last Y Coefficient of (1,1) Patch 39+M+N AZ(1,1) Real First Z Coefficient of (1,1) Patch .. . . . .. .. 54+M+N SZ(1,1) Real Last Z Coefficient of (1,1) Patch 55+M+N AX(1,2) Real First X Coefficient of (1,2) Patch .. . . . .. .. 102+M+N SZ(1,2) Real Last Z Coefficient of (1,2) Patch .. . . . .. .. 7+M+N+48*(N-1) AX(1,N) Real First X Coefficient of (1,N) Patch 96 4.13 PARAMETRIC SPLINE SURFACE ENTITY (TYPE 114) .. . . . .. .. 6+M+N+48*N SZ(1,N) Real Last Z Coefficient of (1,N) Patch 7+M+N+48*N < n:a: > Real Beginning of Arbitrary Values .. . . . .. .. 6+M+N+48*(N+1) < n:a: > Real End of Arbitrary Values 7+M+N+48*(N+1) AX(2,1) Real First X Coefficient of (2,1) Patch .. . . . .. .. 6+M+N+48*(N+2) SZ(2,1) Real Last Z Coefficient of (2,1) Patch .. . . . .. .. 7+M+N+48*(2*N) AX(2,N) Real First X Coefficient of (2,N) Patch .. . . . .. .. 6+M+N+48*(2*N+1) SZ(2,N) Real Last Z Coefficient of (2,N) Patch 7+M+N+48*(2*N+1) < n:a: > Real Beginning of Arbitrary Values .. . . . .. .. 6+M+N+48*(2*N+2) < n:a: > Real Arbitrary Value .. . . . .. .. 7+M+N+48*[(J-1)*(N+1)+K-1] AX(J,K) Real First X Coefficient of (J,K) Patch .. . . . .. .. 6+M+N+48*[(J-1)*(N+1)+K] SZ(J,K) Real Last Z Coefficient of (J,K) Patch .. . . . .. .. 7+M+N+48*[(M-1)*(N+1)+N-1] AX(M,N) Real First X Coefficient of (M,N) Patch .. . . . .. .. 6+M+N+48*[(M-1)*(N+1)+N] SZ(M,N) Real Last Z Coefficient of (M,N) Patch 7+M+N+48*[(M-1)*(N+1)+N] < n:a: > Real Beginning of Arbitrary Values .. . . . .. .. 6+M+N+48*[(M-1)*(N+1)+(N+1)]< n:a: > Real Arbitrary Value 7+M+N+48*[M*(N+1)] < n:a: > Real Arbitrary Value .. . . . .. .. 6+M+N+48*[M*(N+1)+(N+1)] < n:a: > Real End of Arbitrary Values Additional pointers as required (see Section 2.2.4.4.2). 97 4.14 POINT ENTITY (TYPE 116) 4.14 Point Entity (Type 116) A point is defined by its coordinates in definition space. Examples of the Point Entity are shown in Figure 27. Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 116 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |???????? | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 116 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: If PD Index 4 (Pointer to Display Geometry) is 0 or defaulted, then Line Font Pattern, Line Weight, and Hierarchy are ignored. Parameter Data Index__ Name____ Type___ Description___ 1 X Real Coordinates of point 2 Y Real 3 Z Real ECO564 4 PTR Pointer Pointer to the DE of the Subfigure Definition Entity specifying the display symbol or zero. If zero, no display symbol specified. Additional pointers as required (see Section 2.2.4.4.2). 98 4.14 POINT ENTITY (TYPE 116) Figure 27. Examples Defined Using the Point Entity 99 4.15 RULED SURFACE ENTITY (TYPE 118) 4.15 Ruled Surface Entity (Type 118) A ruled surface is formed by moving a line connecting points of equal relative arc length (Form 0) or equal relative parametric value (Form 1) on two parametric curves from a start point to a terminate point on the curves. The parametric curves may be points, lines, circles, conics, parametric splines, rational B-splines, composite curves, or any parametric curves defined in this specification (both planar and nonplanar). Form 0: In this case, DE1 and DE2 specify the defining rail curves, but their given parameterizations are not the ones used to generate the ruled surface. In- stead, their arc length reparameterizations, C1 and C2 (respectively), are used. Form 1: In this case, DE1 and DE2 specify the defining rail curves, C1 and C2 (respectively). Moreover, their given parameterizations are the ones used to generate the ruled surface. Both Forms: In either case, if two curves are expressed parameterically by the functions (C1x(t); C1y(t); C1z(t)) and (C2x(s); C2y(s); C2z(s)), where a t b and c s d, then the coordinates of the points on the ruled surface can be written as: X(u; v) = (1 - v) * C1x(t) + v * C2x(s) Y (u; v) = (1 - v) * C1y(t) + v * C2y(s) Z(u; v) = (1 - v) * C1z(t) + v * C2z(s) where 0 u 1; 0 v 1; t = a + u * (b - a) s = c + u * (d - c); if DIRF LG = 0 s = d + u * (c - d); if DIRF LG = 1 C1(t) and C2(s) are said to be of equal relative parametric value if t and s are evaluated at the same u value. In case DIRFLG=0, then the first point of curve 1 is joined to the first point of curve 2 and the last point of curve 1 to last point of curve 2. If DIRFLG=1, then the first point of curve 1 is joined to the last point of curve 2, the last point of curve 1 to the first point of curve 2. If DEVFLG=1, then the surface is a developable surface (see [DOCA76]); if DEVFLG=0, the surface may or may not be a developable surface. Field 15 of the directory entry accommodates a form number. For this entity, the options are as follows: ______________________________________________ |__Form__|____________Meaning_____________|___ | 0 |Equal relative arc length | |____1____|Equal_relative_parametric_values__|_ The default is Form 0. Examples of the Ruled Surface Entity are shown in Figures 28 and 29. 100 4.15 RULED SURFACE ENTITY (TYPE 118) Figure 28. Examples Defined Using the Ruled Surface Entity 101 4.15 RULED SURFACE ENTITY (TYPE 118) Figure 29. Parameters of the Ruled Surface Entity 102 4.15 RULED SURFACE ENTITY (TYPE 118) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 118 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 118 | # | #; ) | # | # | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: Valid values of the Form Number are 0, 1. Parameter Data Index__ Name____ Type___ Description___ 1 DE1 Pointer Pointer to the DE of the first curve entity 2 DE2 Pointer Pointer to the DE of the second curve entity 3 DIRFLG Integer Direction flag: 0=Join first to first, last to last 1=Join first to last, last to first 4 DEVFLG Integer Developable surface flag: 1=Developable 0=Possibly not Additional pointers as required (see Section 2.2.4.4.2). 103 4.16 SURFACE OF REVOLUTION ENTITY (TYPE 120) 4.16 Surface of Revolution Entity (Type 120) A surface of revolution is defined by an axis of rotation (which must be a Line Entity), a generatrix, and start and terminate rotation angles. The surface is created by rotating the generatrix about the axis of rotation through the start and terminating angles. Since the axis of rotation is a Line Entity (Type 110), it contains in its parameter data section the coordinates of its start point first, followed by the coordinates of its terminate point. The angles of rotation are measured counterclockwise while looking in the direction of the start point of the Line Entity defining the axis of revolution from the terminate point of this line. The generatrix curve may be any curve entity to which a parameterization has been assigned. Examples of surfaces of revolution are given in Figure 30. The various parameters defining the Surface of Revolution Entity are illustrated in Figure 31. The Line Entity L defines a unique straight line. This straight line defines the axis of revolution. The axis is given the same direction as the direction assigned to the Line Entity L . Let R be the unique rigid motion leaving each point of the axis of revolution fixed and rotating each point in three dimensional Euclidean space, radians counterclockwise about the axis of revolution. R assigns to each element of three dimensional Euclidean space another element of three dimensional Euclidean space. The curve C is the generatrix of the surface of revolution. For each real number in the interval [a,b] that defines its domain, C assigns an element of three dimensional Euclidean space. SA and TA denote the start angle and terminate angle, measured in radians, of the surface of revolution to be defined. SA and TA are constrained so that 0 < T A - SA 2ss. The surface of revolution S defined by this entity is the surface that is swept by rotating the generatrix curve C from the angle SA to the angle TA, counterclockwise about the directed axis of revolution. The default parameterization for the surface of revolution S shall be given by S(x; ) = R (C(x)) for each pair of real numbers (x; ) such that a x b and SA T A. 104 4.16 SURFACE OF REVOLUTION ENTITY (TYPE 120) Figure 30. Examples Defined Using the Surface of Revolution Entity Figure 31. Parameters of the Surface of Revolution Entity 105 4.16 SURFACE OF REVOLUTION ENTITY (TYPE 120) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 120 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 120 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 L Pointer Pointer to the DE of the Line Entity (axis of revolution) 2 C Pointer Pointer to the DE of the generatrix entity 3 SA Real Start angle in radians 4 TA Real Terminate angle in radians Additional pointers as required (see Section 2.2.4.4.2). 106 4.17 TABULATED CYLINDER ENTITY (TYPE 122) 4.17 Tabulated Cylinder Entity (Type 122) A tabulated cylinder is a surface formed by moving a line segment called the generatrix parallel to itself along a curve called the directrix. This curve may be a line, circular arc, conic arc, parametric spline curve, rational B-spline curve, or composite curve. It must be pointed out that different parameterizations of the generating curves will produce differ- ent parameterized surfaces, but the underlying point set surface will still be the same. Assuming a parameterization u on the directrix and v on the generatrix, both of which run from 0 to 1, we can express the points on the surface by: X(u; v) = CX(u) + v * (LX - CX(0)) Y (u; v) = CY (u) + v * (LY - CY (0)) Z(u; v) = CZ(u) + v * (LZ - CZ(0)) where 0 u 1; 0 v 1 and CX; CY; CZ represent the X; Y; Z components, respectively, along the di- rectrix curve, while (CX(0); CY (0); CZ(0)) and (LX; LY; LZ) represent the coordinates of the start and terminate points, respectively, of the gen- eratrix. An example of the tabulated cylinder is shown in Figure 32. 107 4.17 TABULATED CYLINDER ENTITY (TYPE 122) Figure 32. Parameters of the Tabulated Cylinder Entity 108 4.17 TABULATED CYLINDER ENTITY (TYPE 122) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 122 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 122 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 DE Pointer Pointer to the DE of the directrix curve entity 2 LX Real Coordinates of the terminate point of the generatrix. The start point of the generatrix is identical with the start point of the directrix. 3 LY Real 4 LZ Real Additional pointers as required (see Section 2.2.4.4.2). 109 4.18 DIRECTION ENTITY (TYPE 123) 4.18 Direction Entity (Type 123) ECO603 The definition of this entity can be found in Appendix G (see Section G.2). 110 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) 4.19 Transformation Matrix Entity (Type 124) The Transformation Matrix Entity transforms three-row column vectors by means of a matrix mul- tiplication and then a vector addition. The notation for this transformation is: 2 3 2 3 2 3 2 3 R11 R12 R13 XIN P U T T1 XOU T P U T 4 R21 R22 R23 5 4 Y IN P U T 5 + 4 T2 5 = 4 Y OU T P U T 5 R31 R32 R33 ZIN P U T T3 ZOU T P U T Here, col [ XINPUT, YINPUT, ZINPUT ] (i.e., the column vector) is the vector being transformed, and col [ XOUTPUT, YOUTPUT, ZOUTPUT ] is the column vector resulting from this transfor- mation. R = [Rij] is a 3 row by 3 column matrix of real numbers, and T = col [ T1,T2,T3 ] is a three-row column vector of real numbers. Thus, 12 real numbers are required for a Transformation Matrix Entity. This entity can be considered to be an "operator" entity in that it starts with the input vector, operates on it as described above, and produces the output vector. Frequently, the input vector lists the coordinates of some point in one coordinate system, and the output vector lists the coordinates of that same point in a second coordinate system. The matrix R and the translation vector T then express a general relationship between the two coordinate systems. By considering special input vectors such as col [ 1,0,0 ], col [ 0,1,0 ], and col [ 0,0,1 ] and computing the corresponding output results, a geometric appreciation of the spatial relationship between the two coordinate systems can be gained. For example, for 2 3 2 3 0 0 1 0 R = 4 0 1 0 5 ; T = 4 0 5 -1 0 0 0 the spatial relationship of the input and output coordinate systems is given in Figure 33. All coordinate systems are assumed to be orthogonal, Cartesian, and right-handed unless specifically noted otherwise. Following are three specific areas where the Transformation Matrix Entity is used to transform coordinates between coordinate systems. Each example area illustrates a specific choice of input and output coordinate systems. Other choices of coordinate systems may be appropriate in other application areas. The usual situation for this type of use of the Transformation Matrix Entity is when the input vector refers to the definition space coordinate system for a certain entity, and the output vector refers to the model space coordinate system (See Section 3.2.2). In this case, the matrix R is referred to as the defining matrix, and the Transformation Matrix Entity defining R and T is pointed to in field seven (transformation matrix field) of the directory entry of the entity (See Section 2.2.4.3.7). In this use of the Transformation Matrix Entity, the matrix R is subject to the restrictions given in Form 0 and Form 1 below. A second situation is the case when the input vector refers to the model space coordinate system and the output vector refers to a viewing coordinate system. In this case, the matrix R is referred to as a view matrix, and is subject to the restrictions given in Form 0 below. Note that when a planar entity is viewed at true length (i.e., the viewing plane is parallel to the plane containing the entity) then the rotation matrix pointed to by DE Field 7 of the Planar Entity will be the inverse (=matrix transpose) of the matrix pointed to by DE Field 7 of the View Entity (See Section 4.80). 111 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) A third situation involves finite element modeling applications. Here, it may be the case that an input coordinate system is related to an output coordinate system by a particular R and T , and, in turn, the output coordinate system is then taken as an input coordinate system for a second R and T combination, and so on. These coordinate systems are frequently called local coordinate systems. Model space is frequently called the reference system. For example, the location of a finite element node may be given in one local coordinate system, which may serve as the input coordinate system for a second local coordinate system, which in turn serves as the input coordinate system for the model space coordinate system which is the reference system. Allowable forms of the matrix R for these applications are detailed in Forms 10, 11, and 12 below. Whenever coordinate systems are related successively to each other as described above, a basic result is that the combined effect of the individual coordinate system changes can be expressed in terms of a single matrix R and a single translation vector T . For example, if the coordinate system change involving the matrix R2 and the translation vector T 2 is to be applied following the coordinate system change involving the matrix R1 and the translation vector T 1, then the matrix R and the translation vector T expressing the combined changes are R=(R2) (R1) and T = (R2) (T 1) + T 2. Here, (R2) (R1) denotes matrix multiplication of 3x3 matrices, where multiplication order is impor- tant. The matrix R and the translation vector T are computed similarly whenever more than two coordinate system changes are to be applied successively. Successive coordinate system changes are specified by allowing a Transformation Matrix Entity to reference another Transformation Matrix Entity through Field 7 of the directory entry. In the ex- ample above, the Transformation Matrix Entity containing R1 and T 1 would contain in its directory entry field 7 a pointer to the Transformation Matrix Entity containing R2 and T 2. The general rule is that Transformation Matrix Entities applied earlier in a succession will reference Transformation Figure 33. Example of the Transformation Matrix Coordinate Systems 112 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) Matrix Entities applied later. Note that the matrix product (R2) (R1) in the example above does not appear explicitly in the data, but, if needed, must be computed according to the usual rules of matrix multiplication. A second example of coordinate systems being related successively (or "concatenated" or "stacked"), in addition to the finite element example mentioned above, involves one manner of locating into model space a conic arc that is in standard position in definition space. In this case, R1 and T 1 move the conic arc from its standard position to an arbitrary location in any plane in definition space satisfying ZT=constant. (Therefore, R133 = 1:0; R131 = R132 = R113 = R123 = 0:0. T 1 can be an arbitrary translation vector.) R2 and T 2 then position the relocated conic arc into model space. (R2 can be an arbitrary defining matrix and T 2 can be an arbitrary translation vector.) Note that for R1 and T 1, both the input vector and the output vector refer to the same coordinate system, namely, the definition space for the conic arc. A 3x3 matrix R is called orthogonal provided its transpose, Rt, yields a matrix inverse for R. The columns of an orthogonal matrix considered as vectors form an orthogonal collection of unit vectors. As (Rt)t = R, the transpose of an orthogonal matrix is again an orthogonal matrix. The determinant of an orthogonal matrix is equal to either plus one or minus one. In the event R is an orthogonal matrix with determinant equal to positive one, R can be expressed as a rotation about an axis passing through the origin. In this event, R is referred to as a rotation matrix. In the event R is an orthogonal matrix with determinant equal to negative one, R can be expressed as a rotation about an axis passing through the origin followed by a reflection about a plane passing through the origin perpendicular to the axis of rotation. Allowable Form Numbers The defining matrix of an entity must use either Form 0 or Form 1. A defining matrix associated with a View Entity (Type 410) must use Form 0. Special matrices representing Node Entity (Type 134) local coordinate systems must use Forms 10, 11, or 12. Form 0: (default) R is an orthogonal matrix with determinant equal to positive one. T is arbitrary. The columns of R taken in order form a right-handed triple in the output coordinate system. Form 1: R is an orthogonal matrix with determinant equal to negative one. T is arbitrary. The columns of R taken in order form a left-handed triple in the output coordinate system. Form 10: This form number conveys special information when used in conjunction with the Node Entity (Type 134) in Finite Element Applications. Refer to Figure 34(a) for notation. The matrix R and the vector T are used to transform coordinate data from the u1, u2, u3 coordinate system to the x,y,z local system. The u1,u2,u3 coordinate system has its origin at an arbitrary fixed point col [XOFF- SET, YOFFSET, ZOFFSET] in the x,y,z coordinate system and is assumed to be displaced parallel to that reference coordinate system. Thus, 2 3 2 3 1 0 0 XOF F SET R = 4 0 1 0 5 ; T = 4 Y OF F SET 5 0 0 1 ZOF F SET 113 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) so that 2 3 2 3 2 3 2 3 1 0 0 u1 XOF F SET XLOCAL 4 0 1 0 5 4 u2 5 + 4 Y OF F SET 5 = 4 Y LOCAL 5 0 0 1 u3 ZOF F SET ZLOCAL Note that the orientation of the two coordinate systems can be described by saying that the u1,u2,u3 coordinate system is the system obtained by imposing orthogo- nal curvilinear coordinates onto the x,y,z space and then constructing unit tangent vectors to the three curvilinear coordinate curves at the given fixed point to serve as basis vectors. In this special case of parallel displacement, the curvilinear coor- dinates imposed are identical to the existing x,y,z coordinates. Form 11: This form number conveys special information when used in conjunction with the Node Entity (Type 134) in Finite Element applications. Refer to Figure 34(b) for notation. The matrix R and the vector T are used to transform coordinate data from the u1, u2, u3 (node point) coordinate system to the x,y,z (local system) coordinate system. The u1, u2, u3 coordinate system has its origin at an arbitrary fixed point XOF F SET = r0 cos 0 r0 > 0 Y OF F SET = r0 sin 0 0 0 3600 ZOF F SET = z0 -1 < z0 < 1 for r0 = 0; take = 00 in the x,y,z coordinate system. The u1,u2,u3 system is the system obtained by im- posing orthogonal curvilinear coordinates onto the x,y,z space which are the cylin- drical coordinates (r,,z) with x = r cos y = r sin z = z; and then constructing unit tangent vectors to the three curvilinear coordinate curves at the given fixed point to serve as basis vectors. Thus, the relationship between the u1, u2, u3 and the x,y,z local coordinate system is given by: 114 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) 2 3 2 3 2 3 2 3 cos 0 - sin0 0 u1 XOF F SET XLOCAL 4 sin0 cos 0 0 5 4 u2 5 + 4 Y OF F SET 5 = 4 Y LOCAL 5 0 0 1 u3 ZOF F SET ZLOCAL Form 12: This form number conveys special information when used in conjunction with the Node Entity (Type 134) in Finite Element applications. Refer to Figure 34(c) for notation. The matrix R and the vector T are used to transform coordinate data from the u1, u2, u3 coordinate system to the x,y,z local system. The u1, u2, u3 coordinate system has its origin at an arbitrary fixed point XOF F SET = r0 sin0 sinOE0 r0 0 Y OF F SET = r0 sin0 cosOE0 0 0 1800 ZOF F SET = r0 cos0 0 OE0 < 3600 for r0 = 0; take 0 = OE0 = 00 for 0 = 00 or 1800; take OE0 = 00 in the x,y,z coordinate system. The u1, u2, u3 system is the system obtained by imposing orthogonal curvilinear coordinates onto the x,y,z space which are the spherical coordinates (r,,OE) with x = r sin cosOE y = r sin sinOE z = r cos and then constructing unit tangent vectors to the three curvilinear coordinate curves at the given fixed point to serve as basis vectors. Thus, the relationship between the u1, u2, u3 and the x,y,z local coordinate systems is given by: 2 3 2 3 2 3 2 3 sin 0 * cosOE0 cos0 * cosOE0 - sinOE0 u1 XOF F SET XLOCAL 4 sin 0 * sinOE0 cos0 * sinOE0 cos OE0 5 4 u2 5 + 4 Y OF F SET 5 = 4 Y LOCAL 5 cos 0 - sin0 0 u3 ZOF F SET ZLOCAL 115 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) See, Kaplan [KAPL52] or Hildebrand [HILD76] for a discussion of orthogonal curvilinear coordinate systems. 116 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) Figure 34. Notation for FEM-specific Forms of the Transformation Matrix Entity 117 4.19 TRANSFORMATION MATRIX ENTITY (TYPE 124) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 124 | ) |< n:a: > |< n:a: > |< n:a: > |< n:a: > | 0; ) |< n:a: > |******** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 124 |< n:a: > |< n:a: > | # | # | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: Valid values of the Form Number are 0, 1, 10, 11, 12. Parameter Data Index__ Name____ Type___ Description___ 1 R11 Real Top Row 2 R12 Real . 3 R13 Real . 4 T1 Real . 5 R21 Real Second Row 6 R22 Real . 7 R23 Real . 8 T2 Real . 9 R31 Real Third Row 10 R32 Real . 11 R33 Real . 12 T3 Real . Additional pointers as required (see Section 2.2.4.4.2). 118 4.20 FLASH ENTITY (TYPE 125) 4.20 Flash Entity (Type 125) A Flash Entity is a point in the ZT=0 plane that locates a specific instance of a particular closed area. That closed area can be defined in one of two ways. First, it can be an arbitrary closed area defined by any entity capable of defining a closed area. The points of this entity must all lie in the ZT=0 plane. Second, it can be a member of a predefined set of flash shapes. In the latter case, Parameters 3 through 5 of the Flash Entity control the final size of the flash. Figure 35 indicates the usage of those parameters for the specific flash forms. Parameters 3 through 5 are ignored for Form 0. Field 15 of the Directory Entry accomodates a form number. For this entity, the options are as follows: __________________________________________ |__Form__|__________Meaning___________|___ | 0 |Defined by referenced entity | | 1 |Circular | | 2 |Rectangle | | 3 |Donut | |____4____|Canoe________________________|_ Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 125 | ) |< n:a: > | 1 | #; ) | 0; ) | 0; ) | 0; ) |??????00 | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 125 | # | #; ) | # | # | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: Valid values of the Form Number are 0, 1, 2, 3, 4. Parameter Data Index__ Name____ Type___ Description___ 1 X Real X reference of flash 2 Y Real Y reference of flash 3 DIM1 Real First flash sizing parameter 4 DIM2 Real Second flash sizing parameter 5 ROT Real Rotation of flash about reference point in radians 6 DE Pointer Pointer to the DE of the referenced entity or zero Additional pointers as required (see Section 2.2.4.4.2). 119 4.20 FLASH ENTITY (TYPE 125) Figure 35. Definition of Shapes for the Flash Entity 120 4.20 FLASH ENTITY (TYPE 125) Figure 35. Definition Shapes for the Flash Entity (continued) 121 4.21 RATIONAL B-SPLINE CURVE ENTITY (TYPE 126) 4.21 Rational B-Spline Curve Entity (Type 126) The rational B-spline curve may represent analytic curves of general interest. This information is important to both the sending and receiving systems. The Directory Entry Form Number Pa- rameter is provided to communicate this information. It should be emphasized that use of this curve form should be restricted to communications between systems operating directly on rational ECO522 B-spline curves and not used as a replacement for the analytic forms for communication. For a brief description and a precise definition of rational B-spline curves, see Appendix B. If the rational B-spline curve represents a preferred curve type, the form number corresponds to the most preferred type. The preference order is from 1 through 5 followed by 0. For example, if the curve is a circle or circular arc, the form number is set to 2. If the curve is an ellipse with unequal major and minor axis lengths, the form number is set to 3. If the curve is not one of the preferred types, the form number is set to 0. If the curve lies entirely within a unique plane, the planar flag (PROP1) is set to 1, otherwise it is set to 0. If it is set to 1, the plane normal (Parameters 14+A+4*K through 16+A+4*K) contain a unit vector normal to the plane containing the curve. These fields exist but are ignored if the curve is nonplanar. ECO582 If the beginning and ending points on the curve, as defined by evaluating the curve at the starting and ending parameter values (i.e., V(0) and V(1)), are identical, then the curve is closed and PROP2 is set to 1. If they are not equal, PROP2 is set to 0. If the curve is rational (does not have all weights equal), PROP3 is set to 0. If all weights are equal to each other, the curve is polynomial and PROP3 is set to 1. The curve is polynomial since in this case all weights cancel and the denominator sums to 1 (see Appendix B). The weights must be positive real numbers. If the curve is periodic with respect to its parametric variable, set PROP4 to 1; otherwise set PROP4 to 0. The periodic flag is to be interpreted as purely informational. The curves which are flagged to be periodic are to be evaluated exactly the same as in the nonperiodic case. ECO522 Note that the control points are in the definition space of the curve. Field 15 of the Directory Entry accomodates a form number. For this entity, the options are as follows: ______________________________________________________ |__Form__|________________Meaning_________________|___ | 0 |Form of curve must be determined from | | |the rational B-spline parameters | | 1 |Line | | 2 |Circular arc | | 3 |Elliptical arc | | 4 |Parabolic arc | |____5____|Hyperbolic_arc____________________________|_ 122 4.21 RATIONAL B-SPLINE CURVE ENTITY (TYPE 126) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 126 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 126 | # | #; ) | # | # | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: Valid values of the Form Number are 0-5. Parameter Data Index__ Name____ Type___ Description___ 1 K Integer Upper index of sum. See Appendix B 2 M Integer Degree of basis functions 3 PROP1 Integer 0 = nonplanar, 1 = planar 4 PROP2 Integer 0 = open curve, 1 = closed curve 5 PROP3 Integer 0 = rational, 1 = polynomial 6 PROP4 Integer 0 = nonperiodic, 1 = periodic Let N = 1+K-M and A = N+2*M 7 T(-M) Real First value of knot sequence .. . . . .. .. 7+A T(N+M) Real Last value of knot sequence 8+A W(0) Real First weight .. . . . .. .. 8+A+K W(K) Real Last weight 9+A+K X0 Real First control point 10+A+K Y0 Real 11+A+K Z0 Real .. . . . .. .. 9+A+4*K XK Real Last control point 10+A+4*K YK Real 11+A+4*K ZK Real 12+A+4*K V(0) Real Starting parameter value 13+A+4*K V(1) Real Ending parameter value 14+A+4*K XNORM Real Unit normal (if curve is planar) 15+A+4*K YNORM Real 16+A+4*K ZNORM Real Additional pointers as required (see Section 2.2.4.4.2). 123 4.22 RATIONAL B-SPLINE SURFACE ENTITY (TYPE 128) 4.22 Rational B-Spline Surface Entity (Type 128) The rational B-spline surface represents various analytical surfaces of general interest. This in- formation is important to both the generating and receiving system. The Directory Entry Form ECO522 Number Parameter is provided to communicate such information. For a brief description and a precise definition of rational B-spline surfaces, see Appendix B. If the rational B-spline surface represents a preferred surface type, the form number corresponds to the most preferred type. The preference order is from 1 through 9 followed by 0. For example, if the surface is a right circular cylinder, the form number is set to 2. If the surface is a surface of revolution and also a torus, the form number is set to 5. If the surface is not one of the preferred types, the form number is set to 0. If, for each fixed value of the second parametric variable the resulting curves which are functions of the first parametric variable are closed, set PROP1 to 1; otherwise, set PROP1 to 0. Similarly, if for each fixed value of the first parametric variable the resulting curves which are functions of the ECO582 second parametric variable are closed, set PROP2 to 1; otherwise, set PROP2 to 0. Mathematically, this is described as follows: PROP1 shall be set to 1, if and only if, for each value of V (0) V V (1), the surface at (U (0); V ) evaluates to the same point as it does for (U (1); V ). Correspondingly, PROP2 shall be set to 1, if and only if, for each value of U (0) U U (1), the surface at (U; V (0)) evaluates to the same point as it does for (U; V (1)). If the surface is rational (does not have all weights equal), set PROP3 to 0. If all weights are equal to each other, the surface is polynomial and PROP3 is set to 1. The surface is polynomial since in this case all weights cancel and the denominator sums to one (see Appendix B). The weights must be positive real numbers. If the surface is periodic with respect to the first parametric variable, set PROP4 to 1; otherwise, set PROP4 to 0. If the surface is periodic with respect to the second parametric variable, set PROP5 to 1; otherwise, set PROP5 to 0. The periodic flags are to be interpreted as purely informational. The surfaces which are flagged to be periodic are to be evaluated exactly the same as in the nonperiodic case. ECO522 Note that the control points are in the definition space of the surface. Field 15 of the Directory Entry accomodates a form number. For this entity, the options are as follows: ______________________________________________________ |__Form__|_________________Meaning_________________|__ | 0 |Form of the surface must be determined | | |from the rational B-spline parameters | | 1 |Plane | | 2 |Right circular cylinder | | 3 |Cone | | 4 |Sphere | | 5 |Torus | | 6 |Surface of revolution | | 7 |Tabulated cylinder | | 8 |Ruled surface | |____9____|General_quadric_surface___________________|_ 124 4.22 RATIONAL B-SPLINE SURFACE ENTITY (TYPE 128) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 128 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 128 | # | #; ) | # | # | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: Valid values of the Form Number are 0-9. Parameter Data Index__ Name____ Type___ Description___ 1 K1 Integer Upper index of first sum. See Appendix B 2 K2 Integer Upper index of second sum. See Appendix B 3 M1 Integer Degree of first set of basis functions 4 M2 Integer Degree of second set of basis functions 5 PROP1 Integer 1 = Closed in first parametric variable direction 0 = Not closed 6 PROP2 Integer 1 = Closed in second parametric variable direction 0 = Not closed 7 PROP3 Integer 0 = Rational 1 = Polynomial 8 PROP4 Integer 0 = Nonperiodic in first parametric variable direction 1 = Periodic in first parametric variable direction 9 PROP5 Integer 0 = Nonperiodic in second parametric variable direction 1 = Periodic in second parametric variable direction Let N1 = 1+K1-M1, N2 = 1+K2-M2, A = N1+2*M1, B = N2+2*M2, C = (1+K1)*(1+K2) 10 S(-M1) Real First value of first knot sequence .. . . . .. .. 10+A S(N1+M1) Real Last value of first knot sequence 11+A T(-M2) Real First value of second knot sequence .. . . . .. .. 11+A+B T(N2+M2) Real Last value of second knot sequence 12+A+B W(0,0) Real First Weight 13+A+B W(1,0) Real .. . . . .. .. 11+A+B+C W(K1,K2) Real Last Weight 12+A+B+C X(0,0) Real First Control Point 13+A+B+C Y(0,0) Real 14+A+B+C Z(0,0) Real 125 4.22 RATIONAL B-SPLINE SURFACE ENTITY (TYPE 128) 15+A+B+C X(1,0) Real 16+A+B+C Y(1,0) Real 17+A+B+C Z(1,0) Real .. . . . .. .. 9+A+B+4*C X(K1,K2) Real Last Control Point 10+A+B+4*C Y(K1,K2) Real 11+A+B+4*C Z(K1,K2) Real 12+A+B+4*C U(0) Real Starting value for first parametric direction 13+A+B+4*C U(1) Real Ending value for first parametric direction 14+A+B+4*C V(0) Real Starting value for second parametric direction 15+A+B+4*C V(1) Real Ending value for second parametric direction Additional pointers as required (see Section 2.2.4.4.2). 126 4.23 OFFSET CURVE ENTITY (TYPE 130) 4.23 Offset Curve Entity (Type 130) The Offset Curve Entity contains the data necessary to determine the offset of a given curve C. This entity points to the base curve to be offset and contains the offset distance and additional pertinent information. No restriction is placed on the entity types of curves. Any parametric curve may be offset. It is the intent of this Specification to limit the applicability of offsets to curves which are planar and slope continuous. The offset curve lies in the plane which contains the base curve as follows: Let C denote a curve in definition space which is defined by r = r(t): Let T (t) denote the unit tangent at r(t) (See [FAUX79]). Let V be a unit vector normal to the plane which contains C. Then the offset curve is a curve defined as: O(t) = r(t) + f (s) * (V x T (t)); T T 1 t T T 2 a) if FLAG = 1, a uniform offset distance, f (s) = D1 b) if FLAG = 2, an offset distance varying linearly, f (s) = D1 + (D2 - D1) * (s - T D1)=(T D2 - T D1) with Case (i) PTYPE = 1 s = arc length along r from r(T T 1) to r(t), D1 = the offset at arc length value T D1, D2 = the offset at arc length value T D2 Case (ii) PTYPE = 2 s = t, D1 = the offset at parametric value T D1, D2 = the offset at parametric value T D2 c) if FLAG = 3, an offset distance defined by a function, f (s) is the NDIM-th coordinate function of the curve pointed to by DE2, with Case (i) PTYPE = 1 s = arc length along r from r(T T 1) to r(t), Case (ii) PTYPE = 2 s = t Note that T T 1 and T T 2 must be chosen to be in the domain of the base curve r(t). 127 4.23 OFFSET CURVE ENTITY (TYPE 130) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 130 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 130 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 DE1 Pointer Pointer to the DE of the curve entity to be offset. 2 FLAG Integer Offset distance flag: 1 = Single value offset, uniform distance 2 = Offset distance varying linearly 3 = Offset distance as a specified function. 3 DE2 Pointer Pointer to the DE of the curve entity, one coordinate of which describes the offset as a function of its parameter. or 0 (0 unless FLAG = 3) 4 NDIM Integer Pointer of particular coordinate of DE2 which describes offset as a function of its parameter. (only used if FLAG = 3) 5 PTYPE Integer Tapered offset type flag: 1 = Function of arc length 2 = Function of parameter (only used if FLAG=2 or 3) 6 D1 Real First offset distance. (only used if FLAG=1 or 2) 7 TD1 Real Arc length or parameter value, depending on PTYPE, of first offset distance. (only used if FLAG=2) 8 D2 Real Second offset distance. 9 TD2 Real Arc length or parameter value, depending on PTYPE, of second offset distance. (only used if FLAG=2) 10 VX Real X-component of unit vector normal to plane containing curve to be offset. 11 VY Real Y-component of unit vector normal to plane containing curve to be offset. 12 VZ Real Z-component of unit vector normal to plane containing curve to be offset. 13 TT1 Real Offset curve starting parameter value. 14 TT2 Real Offset curve ending parameter value. Additional Pointers as required (see Section 2.2.4.4.2). Parameter data not required for a particular case should be given zero values. For example, if the value of Parameter 2 is not 3, then Parameters 3 and 4 should be given zero values. 128 4.24 CONNECT POINT ENTITY (TYPE 132) 4.24 Connect Point Entity (Type 132) A Connect Point Entity describes a point of connection for zero, one or more entities. These entities include those required in piping diagrams, electrical and electronic schematics, and physical designs (e.g., printed wiring boards). The Connect Point Entity is referenced from either the Composite Curve (Type 102), Network Subfigure Definition (Type 320), Network Subfigure Instance (Type 420), or the Flow Associativity Instance (Type 402, Form 18); or it may stand alone in a file. The connect point may be displayed by the receiving system using default display parameters and/or symbols. Also see Section 3.6.3. TF. The Type Flag (TF) is an enumerated list that specifies a particular type of connection: ECO576 ___________________________________________________________ |__TF_Value__|_________________Meaning_________________|___ | 0 |Not Specified (default) | | 1 |Nonspecific logical point of connection | | 2 |Nonspecific physical point of connection | | 101 | Logical component pin | | 102 | Logical port connector | | 103 | Logical offpage connector | | 104 | Logical global signal connector | | 201 | Physical PWA surface mount pin | | 202 | Physical PWA blind pin | | 203 | Physical PWA thru-pin | |__5001-9999__|_Implementor_defined______________________|_ 129 4.24 CONNECT POINT ENTITY (TYPE 132) ECO576 FC. The Function Code (FC) is an enumerated list that specifies a particular function for the connection: ______________________________________________________________________________ |__FC_Value__|_______Meaning_______|_|___FC_Value__|_________Meaning_______|__ | 0 |Unspecified (default) | | 30 | Reset | | 1 |Input | | 31 | Blanking | | 2 |Output | | 32 | Test | | 3 |Input and Output | | 33 | Address | | 4 |Power (VCC) | | 34 | Control | | 5 |Ground | | 35 | Carry | | 6 |Anode | | 36 | Sum | | 7 |Cathode | | 37 | Write | | 8 |Emitter | | 38 | Sense | | 9 |Base | | 39 | V+ | | 10 |Collector | | 40 | Read | | 11 |Source | | 41 | Load | | 12 |Gate | | 42 | SYNC | | 13 |Drain | | 43 | Tri-State Output | | 14 |Case | | 44 | VDD | | 15 |Shield | | 45 | V- | | 16 |Inverting Input | | 46 | VEE | | 17 |Regulated Input | | 47 | Reference | | 18 |Booster Input | | 48 | Reference Bypass | | 19 |Unregulated Input | | 49 | Reference Supply | | 20 |Inverting Output | | 98 | Deferred | | 21 |Regulated Output | | 99 | No Connection | | 22 |Booster Output | | 5001-9999 | Implementor defined | | 23 |Unregulated Output | | | | | 24 |Sink | | | | | 25 |Strobe | | | | | 26 |Enable | | | | | 27 |Data | | | | | 28 |Clock | | | | |______29______|Set____________________|_|___________|________________________| 130 4.24 CONNECT POINT ENTITY (TYPE 132) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 132 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????04?? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 132 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: If PD Index 4 (Pointer to Display Geometry) is 0 or defaulted, then Line Font Pattern, Line Weight, and Hierarchy are ignored. Parameter Data ECO546 Index__ Name____ Type___ Description___ 1 X Real X coordinate of the connection point 2 Y Real Y coordinate of the connection point 3 Z Real Z coordinate of the connection point 4 PTR Pointer Pointer to the DE of the display symbol geometry entity, or null. If null, no display symbol specified. 5 TF Integer Type flag 6 FF Integer Function Flag: 0 = not specified 1 = electrical signal 2 = fluid flow path 7 CID String Connect Point Function Identifier (e.g., Pin Number or Nozzle Label) 8 PTTCID Pointer Pointer to the DE of the Text Display Template Entity for CID, or null. If null, no Text Display Template specified. 9 CFN String Connection Point Function Name 10 PTTCFN Pointer Pointer to the DE of the Text Display Template Entity for CFN, or null. If null, no Text Display Template specified. 11 CPID Integer Unique Connect Point Identifier 12 FC Integer Connect Point Function Code 13 SF Integer Swap Flag 0 = Connect point may be swapped (default) 1 = Connect point may not be swapped 14 PSFI Pointer Pointer to the DE of the "owner" Network Subfigure Instance Entity, or Network Subfigure Definition Entity, or zero. Additional pointers as required (see Section 2.2.4.4.2). 131 4.25 NODE ENTITY (TYPE 134) 4.25 Node Entity (Type 134) The Node Entity is a geometric point used in the definition of a finite element. Directory Entry field 7 points to a labeled definition coordinate system Transformation Matrix. The form number of the Transformation Matrix indicates the definition coordinate system type. Coordinate angles for the cylindrical and spherical coordinate systems are specified in degrees. Every node has a nodal displacement coordinate system associated with it. This is Form 10, 11, or 12 of the Transformation Matrix Entity which locates translational and rotational directions for load, restraint and displacement results. Again, the form number of the Transformation Matrix indicates the coordinate system type. The origin of the nodal displacement coordinate system is always the location of the node. However, the orientation of the nodal displacement axes depends on the location of the node and the type of displacement coordinate system being referenced. Cartesian (rectangular), cylindrical, and spherical are the three possible types. Figure 36 illustrates the definition of a node in the three coordinate systems. If the displacement coordinate system is Cartesian, then the nodal displacement axes are parallel to the respective referenced coordinate system. This is illustrated in Figure 36(a) Cartesian. For the cylindrical type displacement coordinate system, the orientation of the nodal displacement axes depends on the coordinate value of the node as defined in the referenced displacement coordinate system. The nodal displacement axes are respectively in the radial, tangential and axial directions as illustrated in Figure 36(b) Cylindrical. Finally, for spherical, the orientation of the nodal displacement axes depend on both the and OE coordinates of the node as defined in the referenced displacement coordinate system. The nodal displacement axes are respectively in the radial, meridional, and azimuthal directions as indicated in Figure 36(c) Spherical. If a node lies on the polar axis of either the cylindrical or spherical coordinate system, the nodal displacement axes are defined parallel to the referenced displacement coordinate system axes. For a cylindrical system the first axis is the = 0 axis and the third axis is the z axis. For a spherical system the first axis is the OE = 0 axis while the third axis is the = 0 axis. The remaining axis of both systems is defined by the appropriate cross product of the previously defined axes. 132 4.25 NODE ENTITY (TYPE 134) Figure 36. Nodal Displacement Coordinate Systems 133 4.25 NODE ENTITY (TYPE 134) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 134 | ) |< n:a: > |< n:a: > |< n:a: > |< n:a: > | ) |< n:a: > |????04** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 134 |< n:a: > | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: The Entity Subscript shall contain the Node Number. The Entity Label optionally may contain the Node Label. Parameter Data Index__ Name____ Type___ Description___ 1 X/R/R Real First nodal coordinate 2 Y// Real Second nodal coordinate 3 Z/Z/OE Real Third nodal coordinate 4 NDCSP Pointer Pointer to the DE of the Transformation Matrix Entity Form 10, 11 or 12 which defines the Nodal Displacement Coordinate System Entity. Default (zero) is Global Cartesian Coordinate System. Additional pointers as required (see Section 2.2.4.4.2). 134 4.26 FINITE ELEMENT ENTITY (TYPE 136) 4.26 Finite Element Entity (Type 136) A finite element is defined by an element topology (i.e., node connectivity) along with physical and material properties. Table 4 lists the data to define the element topology. Additional element topologies are defined in ECO515 Appendix G (see Section G.3). Figure 37 illustrates the node connectivity for each element topology. In Table 4 the element name is an English abbreviation or acronym describing the element. The element topology type is an integer number which will appear as the first parameter of the parameter data. The order is an integer identifying the order of an edge where: ______________________________ |__Value__|Order_of_Edge__|___ | 0 |Not applicable | | 1 |Linear | | 2 |Parabolic | |____3____|Cubic_____________|_ The number of nodes from Table 4 will appear as the second parameter of the finite element pa- rameter data. A missing node in the connectivity sequence will have its corresponding pointer value equal to zero. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 136 | ) |< n:a: > | #; ) |< n:a: > |< n:a: > |< n:a: > | 0; ) |******** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 136 |< n:a: > | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: The Entity Subscript shall contain the Element Number. The Entity Label optionally may contain the Element Label. Parameter Data Index__ Name____ Type___ Description___ 1 ITOP Integer Topology type 2 N Integer Number of nodes defining element (See Section 4.25). 3 DE1 Pointer Pointer to the DE of the first node defining element entity (See Section 4.25). .. . . . .. .. 2+N DEN Pointer Pointer to the DE of the last node defining element entity 3+N ETYP String Element type name Additional pointers as required (see Section 2.2.4.4.2). 135 4.26 FINITE ELEMENT ENTITY (TYPE 136) Table 4. Finite Element Topology Sety _____________________________________________________________________________ | Element | Element | Order | Number | Number | Number | | Name | Topology | | of Nodes | of Edges | of Faces | |______________|__Type____|__________|_____________|____________|____________| | BEAM | 1 | 1 | 2 | 1 | 0 | | LTRIA | 2 | 1 | 3 | 3 | 1 | | PTRIA | 3 | 2 | 6 | 3 | 1 | | CTRIA | 4 | 3 | 9 | 3 | 1 | | LQUAD | 5 | 1 | 4 | 4 | 1 | | PQUAD | 6 | 2 | 8 | 4 | 1 | | CQUAD | 7 | 3 | 12 | 4 | 1 | | PTSW | 8 | 2 | 12 | 9 | 5 | | CTSW | 9 | 3 | 18 | 9 | 5 | | PTS | 10 | 2 | 16 | 12 | 6 | | CTS | 11 | 3 | 24 | 12 | 6 | | LSOT | 12 | 1 | 4 | 6 | 4 | | PSOT | 13 | 2 | 10 | 6 | 4 | | LSOW | 14 | 1 | 6 | 9 | 5 | | PSOW | 15 | 2 | 15 | 9 | 5 | | CSOW | 16 | 3 | 24 | 9 | 5 | | LSO | 17 | 1 | 8 | 12 | 6 | | PSO | 18 | 2 | 20 | 12 | 6 | | CSO | 19 | 3 | 32 | 12 | 6 | | ALLIN | 20 | 1 | 2 | 1 | 0 | | APLIN | 21 | 2 | 3 | 1 | 0 | | ACLIN | 22 | 3 | 4 | 1 | 0 | | ALTRIA | 23 | 1 | 3 | 3 | 0 | | APTRIA | 24 | 2 | 6 | 3 | 0 | | ALQUAD | 25 | 1 | 4 | 4 | 0 | | APQUAD | 26 | 2 | 8 | 4 | 0 | | SPR | 27 | 0 | 2 | 0 | 0 | | GSPR | 28 | 0 | 1 | 0 | 0 | | DAMP | 29 | 0 | 2 | 0 | 0 | | GDAMP | 30 | 0 | 1 | 0 | 0 | | MASS | 31 | 0 | 1 | 0 | 0 | | RBDY | 32 | 0 | 2 | 0 | 0 | |__TBEAM___|_______33______|____1_____|_____3______|_____1______|_____0______| yAdditional element topologies are defined in Appendix G (see Section G.3). 136 4.26 FINITE ELEMENT ENTITY (TYPE 136) 1. BEAM E1=1,2 2. LTRIA - Linear Triangle E1=1,2 F1=1,2,3 E2=2,3 E3=3,1 3. PTRIA - Parabolic Triangle E1=1,2,3 F1=1,2,3,4,5,6 E2=3,4,5 E3=5,6,1 4. CTRIA - Cubic Triangle E1=1,2,3,4 F1=1,2,3,4,5,6,7,8,9 E2=4,5,6,7 E3=7,8,9,1 5. LQUAD - Linear Quadrilateral E1=1,2 F1=1,2,3,4 E2=2,3 E3=3,4 E4=4,1 6. PQUAD - Parabolic Quadrilateral E1=1,2,3 F1=1,2,3,4,5,6,7,8 E2=3,4,5 E3=5,6,7 E4=7,8,1 Figure 37. Finite Element Topology Set 137 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 138 4.26 FINITE ELEMENT ENTITY (TYPE 136) 7. CQUAD - Cubic Quadrilateral E1=1,2,3,4 F1=1,2,3,4,5,6,7,8,9,10,11,12 E2=4,5,6,7 E3=7,8,9,10 E4=10,11,12,1 8. PTSW - Parabolic Thick Shell Wedge E1=1,2,3 E4=7,8,9 E7=1,7 F1=1,2,3,4,5,6 E2=3,4,5 E5=9,10,11 E8=3,9 F2=7,8,9,10,11,12 E3=5,6,1 E6=11,12,7 E9=5,11 F3=1,2,3,9,8,7 F4=3,4,5,11,10,9 F5=5,6,1,7,12,11 9. CTSW - Cubic Thick Shell Wedge E1=1,2,3,4 E4=10,11,12,13 E7=1,10 E2=4,5,6,7 E5=13,14,15,16 E8=4,13 E3=7,8,9,1 E6=16,17,18,10 E9=7,16 F1=1,2,3,4,5,6,7,8,9 F2=10,11,12,13,14,15,16,17,18 F3=1,2,3,4,13,12,11,10 F4=4,5,6,7,16,15,14,13 F5=7,8,9,1,10,18,17,16 10. PTS - Parabolic Thick Shell E1=1,2,3 E5=9,10,11 E9=1,9 E2=3,4,5 E6=11,12,13 E10=3,11 E3=5,6,7 E7=13,14,15 E11=5,13 E4=7,8,1 E8=15,16,9 E12=7,15 F1=1,2,3,4,5,6,7,8 F4=3,4,5,13,12,11 F2=9,10,11,12,13,14,15,16 F5=5,6,7,15,14,13 F3=1,2,3,11,10,9 F6=7,8,1,9,16,15 11. CTS - Cubic Thick Shell E1=1,2,3,4 E5=13,14,15,16 E9=1,13 E2=4,5,6,7 E6=16,17,18,19 E10=4,16 E3=7,8,9,10 E7=19,20,21,22 E11=7,19 E4=10,11,12,1 E8=22,23,24,13 E12=10,22 F1=1,2,3,4,5,6,7,8,9,10,11,12 F2=13,14,15,16,17,18,19,20,21,22,23,24 F3=1,2,3,4,16,15,14,13 F4=4,5,6,7,19,18,17,16 F5=7,8,9,10,22,21,20,19 F6=10,11,12,1,13,24,23,22 Figure 37. Finite Element Topology Set (continued) 139 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 140 4.26 FINITE ELEMENT ENTITY (TYPE 136) 12. LSOT - Linear Solid Tetrahedron E1=1,2 E4=1,4 F1=1,2,3 E2=2,3 E5=2,4 F2=1,2,4 E3=3,1 E6=3,4 F3=2,3,4 F4=3,1,4 13. PSOT - Parabolic Solid Tetrahedron E1=1,2,3 E4=1,7,10 F1=1,2,3,4,5,6 E2=3,4,5 E5=3,8,10 F2=1,2,3,8,10,7 E3=5,6,1 E6=5,9,10 F3=3,4,5,9,10,8 F4=5,6,1,7,10,9 14. LSOW - Linear Solid Wedge E1=1,2 E4=4,5 E7=1,4 F1=1,2,3 E2=2,3 E5=5,6 E8=2,5 F2=4,5,6 E3=3,1 E6=6,4 E9=3,6 F3=1,2,5,4 F4=2,3,6,5 F5=3,1,4,6 15. PSOW - Parabolic Solid Wedge E1=1,2,3 E4=10,11,12 E7=1,7,10 E2=3,4,5 E5=12,13,14 E8=3,8,12 E3=5,6,1 E6=14,15,10 E9=5,9,14 F1=1,2,3,4,5,6 F2=10,11,12,13,14,15 F3=1,2,3,8,12,11,10,7 F4=3,4,5,9,14,13,12,8 F5=5,6,1,7,10,15,14,9 16. CSOW - Cubic Solid Wedge E1=1,2,3,4 E4=16,17,18,19 E7=1,10,13,16 E2=4,5,6,7 E5=19,20,21,22 E8=4,11,14,19 E3=7,8,9,1 E6=22,23,24,16 E9=7,12,15,22 F1=1,2,3,4,5,6,7,8,9 F2=16,17,18,19,20,21,22,23,24 F3=1,2,3,4,11,14,19,18,17,16,13,10 F4=4,5,6,7,12,15,22,21,20,19,14,11 F5=7,8,9,1,10,13,16,24,23,22,15,12 Figure 37. Finite Element Topology Set (continued) 141 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 142 4.26 FINITE ELEMENT ENTITY (TYPE 136) 17. LSO - Linear Solid E1=1,2 E5=5,6 E9=1,5 F1=1,2,3,4 E2=2,3 E6=6,7 E10=2,6 F2=5,6,7,8 E3=3,4 E7=7,8 E11=3,7 F3=1,2,6,5 E4=4,1 E8=8,5 E12=4,8 F4=2,3,7,6 F5=3,4,8,7 F6=4,1,5,8 18. PSO - Parabolic Solid E1=1,2,3 E7=17,18,19 E2=3,4,5 E8=19,20,13 E3=5,6,7 E9=1,9,13 E4=7,8,1 E10=3,10,15 E5=13,14,15 E11=5,11,17 E6=15,16,17 E12=7,12,19 F1=1,2,3,4,5,6,7,8 F2=13,14,15,16,17,18,19,20 F3=1,2,3,10,15,14,13,9 F4=3,4,5,11,17,16,15,10 F5=5,6,7,12,19,18,17,11 F6=7,8,1,9,13,20,19,12 19. CSO - Cubic Solid E1=1,2,3,4 E7=27,28,29,30 E2=4,5,6,7 E8=30,31,32,21 E3=7,8,9,10 E9=1,13,17,21 E4=10,11,12,1 E10=4,14,18,24 E5=21,22,23,24 E11=7,15, 19, 27 E6=24,25,26,27 E12=10,16,20,30 F1=1,2,3,4,5,6,7,8,9,10,11,12 F2=21,22,23,24,25,26,27,28,29,30,31,32 F3=1,2,3,4,14,18,24,23,22,21,17,13 F4=4,5,6,7,15,19,27,26,25,24,18,14 F5=7,8,9,10,16,20,30,29,28,27,19,15 F6=10,11,12,1,13,17,21,32,31,30,20,16 Figure 37. Finite Element Topology Set (continued) 143 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 144 4.26 FINITE ELEMENT ENTITY (TYPE 136) 20. ALLIN - Axisymmetric Linear Line E1=1,2 No Faces 21. APLIN - Axisymmetric Parabolic Line E1=1,2,3 No Faces 22. ACLIN - Axisymmetric Cubic Line E1=1,2,3,4 No Faces 23. ALTRIA - Axisymmetric Linear Triangle E1=1,2 E2=2,3 No Faces E3=3,1 24. APTRIA - Axisymmetric Parabolic Triangle E1=1,2,3 E2=3,4,5 No Faces E3=5,6,1 25. ALQUAD - Axisymmetric Linear Quadrilateral E1=1,2 E2=2,3 E3=3,4 No Faces E4=4,1 26. APQUAD - Axisymmetric Parabolic Quadrilateral E1=1,2,3 E2=3,4,5 E3=5,6,7 No Faces E4=7,8,1 Figure 37. Finite Element Topology Set (continued) 145 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 146 4.26 FINITE ELEMENT ENTITY (TYPE 136) 27. SPR - Spring No edges or faces 28. GSPR - Grounded Spring 29. DAMP - Damper 30. GDAMP - Grounded damper 31. MASS - Mass 32. RBDY - Rigid Body 33. TBEAM - three noded beam (no faces) E1 = 1,2 Figure 37. Finite Element Topology Set (continued) 147 4.26 FINITE ELEMENT ENTITY (TYPE 136) Figure 37. Finite Element Topology Set (continued) 148 4.27 NODAL DISPLACEMENT AND ROTATION ENTITY (TYPE 138) 4.27 Nodal Displacement and Rotation Entity (Type 138) The Nodal Displacement and Rotation Entity is used to communicate finite element postprocessing data. It contains the incremental displacements and rotations (expressed in radians) for each load case and each node in the model. It also contains a pointer to a General Note Entity (Type 212) for a description of the load cases. For each node it contains the node number identifier and the node DE pointer. The node number identifier is equivalent to the node number in the Directory Entry subscript field of the Node Entity (Type 134). 149 4.27 NODAL DISPLACEMENT AND ROTATION ENTITY (TYPE 138) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 138 | ) |< n:a: > |< n:a: > |< n:a: > |< n:a: > |< n:a: > | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 138 |< n:a: > |< n:a: > | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 NC Integer Number of analysis cases 2 GP1 Pointer Pointer to the DE of the general note that describes the first analysis case .. . . . .. .. 1+NC GPNC Pointer Pointer to the DE of the general note that describes the last analysis case 2+NC NN Integer Number of nodes 3+NC NO1 Integer Node number identifier for first node 4+NC NP1 Pointer Pointer to the DE of the Node Directory Entry 5+NC X11 Real X-Incr. translation, first analysis case 6+NC Y11 Real Y-Incr. translation 7+NC Z11 Real Z-Incr. translation 8+NC RX11 Real RX-Incr. rotation 9+NC RY11 Real RY-Incr. rotation 10+NC RZ11 Real RZ-Incr. rotation .. . . . .. .. -1+7*NC X1NC Real X-Incr. translation, last analysis case 7*NC Y1NC Real Y-Incr. translation 1+7*NC Z1NC Real Z-Incr. translation 2+7*NC RX1NC Real RX-Incr. rotation .. . . . .. .. 3+NC+(-1+NN)*(2+6*NC) NONN Integer Node number identifier for NNth node 4+NC+(-1+NN)*(2+6*NC) NPNN Pointer Pointer to the DE of the Node Directory Entry 5+NC+(-1+NN)*(2+6*NC) XNN1 Real X-Incr. translation, first analysis case 6+NC+(-1+NN)*(2+6*NC) YNN1 Real Y- " " 7+NC+(-1+NN)*(2+6*NC) ZNN1 Real Z- " " 8+NC+(-1+NN)*(2+6*NC) RXNN1 Real RX-Incr. rotation, first analysis case 9+NC+(-1+NN)*(2+6*NC) RYNN1 Real RY- " " 10+NC+(-1+NN)*(2+6*NC) RZNN1 Real RZ- " " .. . . . .. .. -3+NC+NN*(2+6*NC) XNNNC Real X-Incr. translation, last analysis case -2+NC+NN*(2+6*NC) YNNNC Real Y- " " -1+NC+NN*(2+6*NC) ZNNNC Real Z- " " NC+NN*(2+6*NC) RXNNNC Real RX-Incr. rotation, last analysis case 150 4.27 NODAL DISPLACEMENT AND ROTATION ENTITY (TYPE 138) 1+NC+NN*(2+6*NC) RYNNNC Real RY- " " 2+NC+NN*(2+6*NC) RZNNNC Real RZ- " " Additional pointers as required (see Section 2.2.4.4.2). 151 4.28 OFFSET SURFACE ENTITY (TYPE 140) 4.28 Offset Surface Entity (Type 140) The offset surface is a surface defined in terms of an already existing surface. 1. Let S = S(u; v) be a regular surface defined by this specification parameterized and oriented by N (u; v), a differentiable field of unit normal vectors defined on the whole surface, and d a fixed nonzero real number. An offset surface to S is a parameterized surface S(u; v) given by: O(u; v) = S(u; v) + d * N (u; v); u1 u u2 v1 v v2: The base surface S(u; v) is referenced by a pointer in the parameter data section, while N (u; v) is found from S(u; v) as defined below. The value of d is provided as a parameter value in the parameter data section. 2. To determine which one of the two orientations of the orientable regular surface S(u; v) the offset surface will be used to define O, define N (u; v) = _@S=@u__x__@S=@v_____||@S=@u|:x @S=@v| In order to avoid confusion connecting the orientation of the base surface S(u; v), an additional offset indicator is included. That indicator, shown in Figure 38, consists of the vector (N x; N y; N z) defined by: (N x; N y; N z) = N (U m; V m)=||N (U m; V m)||: (This is the unit normal vector at the parameter values (U m; V m).) where, if the surface is bounded, U m = (u1 + u2)=2 and V m = (v1 + v2)=2 or, if the surface is unbounded, U m = 0:0 and V m = 0:0: This indicates the direction in which the offset distance, d, is measured positive at (U m; V m). CAUTION: The vector (N x; N y; N z) is just an indicator of the direction with respect to the base surface S(u; v) where the offset distance, d, is measured positively. This vector does not participate in the evaluation of the offset surface as is evident from the formula for O that defines the offset surface. 152 4.28 OFFSET SURFACE ENTITY (TYPE 140) Figure 38. Offset Surface in 3-D Euclidean Space 153 4.28 OFFSET SURFACE ENTITY (TYPE 140) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 140 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |??????** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 140 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 NX Real The x-coordinate of the offset indicator N (U m; V m) 2 NY Real The y-coordinate of the offset indicator N (U m; V m) 3 NZ Real The z-coordinate of the offset indicator N (U m; V m) 4 D Real The distance by which the surface is normally offset on the side of the offset indicator if d > 0 and on the opposite side if d < 0 5 DE Pointer Pointer to the DE of the surface entity to be offset Additional pointers as required (see Section 2.2.4.4.2). 154 4.29 BOUNDARY ENTITY (TYPE 141) 4.29 Boundary Entity (Type 141) ECO511 The definition of this entity can be found in Appendix G (see Section G.4). 155 4.30 CURVE ON A PARAMETRIC SURFACE ENTITY (TYPE 142) 4.30 Curve on a Parametric Surface Entity (Type 142) The Curve on a Parametric Surface Entity associates a given curve with a surface and identifies the curve as lying on the surface. Let S = S(u; v) = (x(u; v); y(u; v); z(u; v) ) be a regular parameterized surface whose domain is a rectangle defined by D = { (u; v) | u1 u u2 and v1 v v2}: Let B = B(t) be a curve defined by B(t) = (u(t); v(t)) for a t b taking its values in D. A curve C(t) on the surface S(u; v) is the composition of two mappings, S and B defined as follows: C(t) 4= S O B(t) 4= S(B(t)) 4= S(u(t); v(t)) 4= ( x(u(t); v(t)); y(u(t); v(t)); z(u(t); v(t)) ) a t b: The curve B lies in the two dimensional space which is the domain of the surface S. Therefore, the representation used for B which has been derived from a curve defined in this Specification must be two dimensional: the X and Y coordinates of this curve pointed to by BPTR are used. The Entity Use Flag (DE Field 9) of the entity B is set to 05, indicating that B is in the parameter space of the surface. Consequently, B cannot be scaled, and, if a transformation matrix is to be applied on B, it has to map it within the parameter space D in which it resides. A curve on a parametric surface is given by: (a) the mapping C and an indication that the curve lies on the surface S(u; v) (b) the mappings B and S whose composition gives the curve C. A curve on a surface may have been created in one of a number of various ways: (a) as the projection on the surface of a given curve in model space in a prescribed way, for example, parallel to a given fixed vector (b) as the intersection of two given surfaces (c) by a prescribed functional relation between the surface parameters "u" and "v" (d) by a special curve, such as a geodesic, emanating from a given point in a certain direction, a principal curve (line of curvature) emanating from a certain point, an asymptotic curve emanation from a certain point, an isoparametric curve for a given value, or any other kind of special curve. 156 4.30 CURVE ON A PARAMETRIC SURFACE ENTITY (TYPE 142) The Parameter Data section contains three pointers: (a) a pointer to the curve from which B(t) is derived (b) a pointer to the surface S(u; v) (c) a pointer to the mapping C(t). It also contains: (d) a flag to indicate how the curve was created (e) a flag to indicate which of the two alternate representations was preferred by the sending system. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 142 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????05** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 142 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 CRTN Integer Indicates the way the curve on the surface has been created: 0 = Unspecified 1 = Projection of a given curve on the surface 2 = Intersection of two surfaces 3 = Isoparametric curve, i.e., either a u-parametric or a v-parametric curve 2 SPTR Pointer Pointer to the DE of the surface on which the curve lies 3 BPTR Pointer Pointer to the DE of the entity that contains the definition of the curve B in the parametric space (u; v) of the surface S 4 CPTR Pointer Pointer to the DE of the curve C 5 PREF Integer Indicates preferred representation in the sending system: 0 = Unspecified 1 = S O B is preferred 2 = C is preferred 3 = C and S O B are equally preferred Additional pointers as required (see Section 2.2.4.4.2). 157 4.31 BOUNDED SURFACE ENTITY (TYPE 143) 4.31 Bounded Surface Entity (Type 143) ECO511 The definition of this entity can be found in Appendix G (see Section G.5). 158 4.32 TRIMMED (PARAMETRIC) SURFACE ENTITY (TYPE 144) 4.32 Trimmed (Parametric) Surface Entity (Type 144) A simple closed curve in the Euclidean plane divides the plane into two disjoint open connected components; one bounded and one unbounded. The bounded one is called the interior region to the curve (herein called `interior'). The unbounded component is called the exterior region to the curve (herein called `exterior'). The domain of the trimmed surface is defined as the common region of the interior of the outer boundary and the exterior of each of the inner boundaries and includes the boundary curves. Note that the trimmed surface has the same mapping S(u; v) as the original (untrimmed surface) but different domain. The curves that delineate either the outer or the inner boundary of the trimmed surface are curves on the surface S, and are to be exchanged by means of the Curve on a Parametric Surface Entity (Type 142). Let S(u; v) be a regular parameterized surface, whose untrimmed domain is a rectangle D consisting of those points (u; v) such that a u b and c v d for given constants a, b, c, and d with a < b and c < d. Assume that S takes its values in three dimensional Euclidean space so that it can be expressed as: 2 3 x(u; v) S = S(u; v) = 64 y(u; v) 75 for each ordered pair (u; v) in D. z(u; v) Also let the mapping S be subject to the following regularity conditions: - It has continuous normal vector in the interior of D. - It is one-to-one in D. - There are no singular points in D, i.e., the vectors of the first partial derivatives of S at any point in D are linearly independent. Two types of simple closed curves are utilized to define the domain of the trimmed (parametric) surface. 1. Outer boundary: there is exactly one. It lies in D, and in particular, it can be the boundary curve of D. 2. Inner boundary: there can be any number of them including zero. The set of inner boundaries satisfies two criteria: (a) The curves as well as their interiors are mutually disjoint. (b) Each curve lies in the interior of the outer boundary. If the outer boundary of the surface being defined is the boundary of D and there are no inner boundaries, the trimmed surface being defined is untrimmed. 159 4.32 TRIMMED (PARAMETRIC) SURFACE ENTITY (TYPE 144) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 144 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 144 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 PTS Pointer Pointer to the DE of the surface entity that is to be trimmed 2 N1 Integer 0 = the outer boundary is the boundary of D 1 = otherwise 3 N2 Integer This number indicates the number of simple closed curves which constitute the inner boundary of the trimmed surface. In case no inner boundary is introduced, this is set equal to zero. 4 PTO Pointer Pointer to the DE of the simple closed curve entity (Curve on a Parametric Surface Entity), that constitutes the outer boundary of the trimmed surface or zero 5 PTI1 Pointer Pointer to the DE of the first simple closed inner boundary curve entity (Curve on a Parametric Surface Entity) according to some arbitrary ordering of these entities .. . . . .. .. 4+N2 PTIN2 Pointer Pointer to the DE of the last simple closed inner boundary curve entity (Curve on a Parametric Surface Entity) Additional pointers as required (see Section 2.2.4.4.2). 160 4.33 NODAL RESULTS ENTITY (TYPE 146) 4.33 Nodal Results Entity (Type 146) The definition of this entity can be found in Appendix G (see Section G.6). 161 4.34 ELEMENT RESULTS ENTITY (TYPE 148) 4.34 Element Results Entity (Type 148) The definition of this entity can be found in Appendix G (see Section G.7). 162 4.35 BLOCK ENTITY (TYPE 150) 4.35 Block Entity (Type 150) The block is a rectangular parallelepiped, defined with one vertex at (X1,Y1,Z1) and three edges lying along the local +X, +Y, and +Z axes. The local X-axis is defined by the unit vector (I1,J1,K1) and the local Z-axis by (I2,J2,K2). The local Y-axis is derived by taking the cross product of Z into X. The resulting local system must be orthogonal, with (I1,J1,K1) values having the highest accuracy precedence. The block is specified by the positive lengths (LX,LY,LZ) along these axes as shown in Figure 39. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 150 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 150 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 LX Real Length in the local X-direction 2 LY Real Length in the local Y-direction 3 LZ Real Length in the local Z-direction 4 X1 Real Corner point coordinates (default (0,0,0)) 5 Y1 Real 6 Z1 Real 7 I1 Real Unit vector defining local X-axis (default (1,0,0)) 8 J1 Real 9 K1 Real 10 I2 Real Unit vector defining local Z-axis (default (0,0,1)) 11 J2 Real 12 K2 Real Must be orthogonal (see above) to (I1,J1,K1) Additional pointers as required (see Section 2.2.4.4.2). 163 4.35 BLOCK ENTITY (TYPE 150) Figure 39. Parameters of the CSG Block Entity 164 4.36 RIGHT ANGULAR WEDGE ENTITY (TYPE 152) 4.36 Right Angular Wedge Entity (Type 152) The right angular wedge is defined with one vertex at (X1,Y1,Z1) and three orthogonal edges lying along the local +X, +Y, and +Z axes. Figure 40 shows one example. A triangular/trapezoidal face lies in the local XY-plane. The local X-axis is defined by the unit vector (I1,J1,K1) and the local Z- axis by (I2,J2,K2). The local Y-axis is derived by taking the cross product of Z into X. The resulting local system must be orthogonal, with (I1,J1,K1) values having the highest accuracy precedence. The wedge is specified by the positive lengths LX, LY, LZ along these axes and the length LTX (where LTX | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 152 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 LX Real Length in the local X-direction at Y=0 2 LY Real Length in the local Y-direction 3 LZ Real Length in the local Z-direction 4 LTX Real Length in the local X-direction at distance LY from local X-axis 5 X1 Real Corner point coordinates (default (0,0,0)) 6 Y1 Real 7 Z1 Real 8 I1 Real Unit vector defining local X-axis (default (1,0,0)) 9 J1 Real 10 K1 Real 11 I2 Real Unit vector defining local Z-axis (default (0,0,1)) 12 J2 Real 13 K2 Real Must be orthogonal (see above) to (I1,J1,K1) Additional pointers as required (see Section 2.2.4.4.2). 165 4.36 RIGHT ANGULAR WEDGE ENTITY (TYPE 152) Figure 40. Parameters of the CSG Right Angular Wedge Entity 166 4.37 RIGHT CIRCULAR CYLINDER ENTITY (TYPE 154) 4.37 Right Circular Cylinder Entity (Type 154) The right circular cylinder is defined by the center of one circular cylinder face, a unit vector, a height, and a radius as shown in Figure 41. The faces are perpendicular to the unit vector in the axis direction (I1,J1,K1) and are circular discs with the specified radius R (where R>0). The height H (where H> 0) is the distance from the first circular face center in the positive direction of the unit vector to the second circular face center. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 154 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 154 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 H Real Cylinder height 2 R Real Cylinder radius 3 X1 Real First face center coordinates (default (0,0,0)) 4 Y1 Real 5 Z1 Real 6 I1 Real Unit vector in axis direction (default (0,0,1)) 7 J1 Real 8 K1 Real Additional pointers as required (see Section 2.2.4.4.2). 167 4.37 RIGHT CIRCULAR CYLINDER ENTITY (TYPE 154) Figure 41. Parameters of the CSG Right Circular Cylinder Entity 168 4.38 RIGHT CIRCULAR CONE FRUSTUM ENTITY (TYPE 156) 4.38 Right Circular Cone Frustum Entity (Type 156) The right circular cone frustum is defined by the center of the larger circular face of the frustum (X1,Y1,Z1), its radius R1, a unit vector in the axis direction (I1,J1,K1), a height H in this direction, and a second circular face with radius R2, where R1 > R2 0 and H > 0. As shown by Figure 42, the circular faces are perpendicular to the unit vector (I1,J1,K1). Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 156 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 156 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 H Real Height 2 R1 Real Larger face radius 3 R2 Real Smaller face radius (zero for cone apex - default) 4 X1 Real Larger face center coordinates (default (0,0,0)) 5 Y1 Real 6 Z1 Real 7 I1 Real Unit vector in axis direction (default (0,0,1)) 8 J1 Real 9 K1 Real Additional pointers as required (see Section 2.2.4.4.2). 169 4.38 RIGHT CIRCULAR CONE FRUSTUM ENTITY (TYPE 156) Figure 42. Parameters of the CSG Right Circular Cone Frustum Entity 170 4.39 SPHERE ENTITY (TYPE 158) 4.39 Sphere Entity (Type 158) The sphere is defined with its center coordinates at (X1,Y1,Z1) and a radius R, where R > 0. Figure 43 shows one example. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 158 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 158 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 R Real Radius 2 X1 Real Center coordinates (default (0,0,0)) 3 Y1 Real 4 Z1 Real Additional pointers as required (see Section 2.2.4.4.2). 171 4.39 SPHERE ENTITY (TYPE 158) Figure 43. Parameters of the CSG Sphere Entity 172 4.40 TORUS ENTITY (TYPE 160) 4.40 Torus Entity (Type 160) The torus is the solid formed by revolving a circular disc about a specified coplanar axis. R1 is the distance from the axis to the center of the defining disc, and R2 is the radius of the defining disc, where R1 > R2 > 0. The torus is located with its center at (X1, Y1,Z1), and its axis is oriented in the (I1,J1,K1) direction, as shown in Figure 44. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 160 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 160 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 R1 Real Distance from center of torus to center of circular disc to be revolved (perpendicular to axis) 2 R2 Real Radius of circular disc 3 X1 Real Torus center coordinates (default (0,0,0)) 4 Y1 Real 5 Z1 Real 6 I1 Real Unit vector in axis direction (default (0,0,1)) 7 J1 Real 8 K1 Real Additional pointers as required (see Section 2.2.4.4.2). 173 4.40 TORUS ENTITY (TYPE 160) Figure 44. Parameters of the CSG Torus Entity 174 4.41 SOLID OF REVOLUTION ENTITY (TYPE 162) 4.41 Solid of Revolution Entity (Type 162) The solid of revolution is defined by revolving the area determined by a planar curve about a specified axis (which must be in the same plane) through a given fraction of full rotation F (0 < F 1), using the right hand rule (counterclockwise when viewed from the positive direction). The curve must not intersect itself. It must not cross the axis but may touch it. Figure 45 shows one example. Two form numbers are used to indicate how the area is determined from the curve. If the curve is closed, the form number shall be set to 1, and the area enclosed by the curve is used. If the curve is not closed and the form number = 0, projections are made from the ends of the curve to the rotation axis and the area enclosed by the curve, the projections, and the axis is used. In this case, the curve must be such that it does not intersect the projections, except at the end points. If the curve is not closed and the form number = 1, the curve is closed by adding a line connecting its end points and the area enclosed by the curve and the added line is used. In this case, the curve must not intersect the added line, except at the end points. Field 15 of the Directory Entry accommodates a form number. For this entity, the options are as follows: __________________________________ |__Form__|_______Meaning_______|__ | 0 |Curve closed to axis | |____1____|Curve_closed_to_itself_ | 175 4.41 SOLID OF REVOLUTION ENTITY (TYPE 162) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 162 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 162 | # | #; ) | # | # | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: Valid values of the Form Number are 0, 1. Parameter Data Index__ Name____ Type___ Description___ 1 PTR Pointer Pointer to the DE of the curve entity to be revolved. The curve must be coplanar with rotation axis. 2 F Real Fraction of full rotation through which the curve entity will be revolved (0 < F 1) - counterclockwise when viewed from the positive direction; default 1 3 X1 Real Coordinates of point on axis (default (0,0,0)) 4 Y1 Real 5 Z1 Real 6 I1 Real Unit vector in axis direction (default (0,0,1)) 7 J1 Real 8 K1 Real Additional pointers as required (see Section 2.2.4.4.2). 176 4.41 SOLID OF REVOLUTION ENTITY (TYPE 162) Figure 45. Parameters of the CSG Solid of Revolution Entity 177 4.42 SOLID OF LINEAR EXTRUSION ENTITY (TYPE 164) 4.42 Solid of Linear Extrusion Entity (Type 164) The solid of linear extrusion is defined by translating an area determined by a planar curve. The curve as indicated by PTR in Figure 46 must be closed and nonintersecting. The direction of the translation is defined by a unit vector (I1,J1,K1) and the length of the translation is defined by L, where L > 0. The vector (I1,J1,K1) must not be coplanar with the closed curve. Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 164 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 164 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 PTR Pointer Pointer to the DE of the closed curve entity 2 L Real Length of extrusion along the vector positive direction 3 I1 Real Unit vector specifying direction of extrusion (default (0,0,1)) 4 J1 Real 5 K1 Real Additional pointers as required (see Section 2.2.4.4.2). 178 4.42 SOLID OF LINEAR EXTRUSION ENTITY (TYPE 164) Figure 46. Parameters of the CSG Solid of Linear Extrusion Entity 179 4.43 ELLIPSOID ENTITY (TYPE 168) 4.43 Ellipsoid Entity (Type 168) The ellipsoid is a solid bounded by the surface defined by: _X2__ + _Y_2_ + _Z2__ = 1 LX2 LY 2 LZ2 when centered at the origin and aligned with its major axis (LX) in the X direction and with the minor axis (LZ) in the Z direction. A major axis of an ellipsoid can be found by choosing a point on the surface farthest from the center and constructing the line from that point through the center. The plane through the center perpendicular to this major axis intersects the surface of the ellipsoid in an ellipse. The other two axes of the ellipsoid are the axes of this ellipse. The ellipsoid is defined with its center at (X1,Y1,Z1) and its three axes coincident with the local X, Y, Z axes, as shown in Figure 47. The local X-axis is defined by the unit vector (I1,J1,K1) and the local Z-axis by (I2,J2,K2). The local Y-axis is derived by taking the cross product of Z into X. The resulting local system must be orthogonal, with (I1,J1,K1) values having the highest accuracy precedence. The ellipsoid is specified by positive lengths (LX, LY, and LZ respectively, where LX LY LZ > 0) from the local origin to the surface along the local +X, +Y, +Z axes. Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 168 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00** | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 168 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 LX Real Length in the local X-direction 2 LY Real Length in the local Y-direction 3 LZ Real Length in the local Z-direction 4 X1 Real Coordinates of point in center of ellipsoid 5 Y1 Real (default (0,0,0)) 6 Z1 Real 7 I1 Real Unit vector defining local X-axis (Ellipsoid major axis) 8 J1 Real (default (1,0,0)) 9 K1 Real 10 I2 Real Unit vector defining local Z-axis (Ellipsoid minor axis) 11 J2 Real (default (0,0,1)) Must be orthogonal (see above) to (I1,J1,K1) 12 K2 Real Additional pointers as required (see Section 2.2.4.4.2). 180 4.43 ELLIPSOID ENTITY (TYPE 168) Figure 47. Parameters of the CSG Ellipsoid Entity 181 4.44 BOOLEAN TREE ENTITY (TYPE 180) 4.44 Boolean Tree Entity (Type 180) The Boolean tree describes a binary tree structure composed of regularized Boolean operations and operands, in postorder notation. A regularized Boolean operation is defined as the closure of the interior of the result_of a Boolean set operation. Specifically, denote the interior of a set X by Xo, the closure of X by X , and use [*; \*; and -* to denote the regularized Boolean operations union, intersection, and difference, respectively. Then: ___________ X [* Y = (X__[_Y_)o_ X \* Y = (X__\_Y_)o__ X -* Y = (X - Y )o Since the topological space under consideration is a 3-dimensional space, all lower dimensional enti- ties resulting from these operations will disappear. A discussion of regularized Boolean operations can be found in [TILO80]. All operations are assigned integers as follows: ___________________________ |__Integer__|Operation__|__ | 1 | Union | | 2 |Intersection | |_____3_____|_Difference___| Allowable operands are: o Primitive entities o Boolean Tree Entities o Solid Instance Entities The parameter data entries for the Boolean Tree Entity can be operation codes (integers) or pointers to operands. A positive (or unsigned) value in a parameter data entry implies an operation code; a negative value implies the absolute value is to be taken as a pointer to an operand. A transformation matrix may be pointed to by Field 7 of the DE to position the resulting solid in any desired manner. 182 4.44 BOOLEAN TREE ENTITY (TYPE 180) Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 180 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????00?? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 180 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Note: When the Hierarchy is set to Global Defer (01), all of the following are ignored and may be defaulted: Line Font Pattern, Line Weight, Color Number, Level, View, and Blank Status. Parameter Data Index__ Name____ Type___ Description___ 1 N Integer Length of post-order notation, including operations and operands (N > 2) 2 PTR(1) Pointer Negated pointer to the DE of the first operand 3 PTR(2) Pointer Negated pointer to the DE of the second operand 4 PTR(3) Pointer Negated pointer to the DE of the third operand or or or IOP(1) Integer Integer for the first operation .. . . . .. .. N PTR(M) Pointer Negated pointer to the DE of the last operand or or or IOP(L-1) Integer Integer for next-to-last operation N+1 IOP(L) Integer Integer for last operation Notes: Parameters 2 and 3 will always be operands and thus will be negative numbers. As L is the number of operations, and M is the number of operands, N = L+M. Additional pointers as required (see Section 2.2.4.4.2). 183 4.44 BOOLEAN TREE ENTITY (TYPE 180) The following is an example of a Boolean tree composed of five operands and four operations. [* j Q Ordinary infix notation: j Q -* \* (A -* (B [* C )) [* (D \* E) @ @ @ @ Postorder notation: A [* D E A B C [* -* D E \* [* J JJ B C Parameters: 9 A B C 1 3 D E 2 1 (A, B, C, D, & E are negative values representing pointers to operands.) For the preceding example, the values are: PARAMETER VALUE 1 9 2 PTRA (negative) 3 PTRB (negative) 4 PTRC (negative) 5 1 6 3 7 PTRD (negative) 8 PTRE (negative) 9 2 10 1 Additional pointers as required (see Section 2.2.4.4.2). 184 4.45 SELECTED COMPONENT ENTITY (TYPE 182) 4.45 Selected Component Entity (Type 182) ECO505 The definition of this entity may be found in Appendix G (see Section G.8). 185 4.46 SOLID ASSEMBLY ENTITY (TYPE 184) 4.46 Solid Assembly Entity (Type 184) A solid assembly is a collection of items which possess a shared fixed geometric relationship. It differs from a union of the items in that each item retains its own structure, even if the items touch. The transformation matrices are applied to the items individually before a matrix pointed to in Field 7 of the DE is applied to the collection. A value of zero in the pointer field indicates the identity matrix. Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 184 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????02?? | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 184 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Note: When the Hierarchy is set to Global Defer (01), all of the following are ignored and may be defaulted: Line Font Pattern, Line Weight, Color Number, Level, View, and Blank Status. Parameter Data Index__ Name____ Type___ Description___ 1 N Integer Number of items 2 PTR1 Pointer Pointer to the DE of the first item .. . . . .. .. 1+N PTRN Pointer Pointer to the DE of the last item 2+N PTRM1 Pointer Pointer to the DE of the Transformation Matrix Entity for the first item .. . . . .. .. 1+2*N PTRMN Pointer Pointer to the DE of the Transformation Matrix Entity for the last item Additional pointers as required (see Section 2.2.4.4.2). 186 4.47 MANIFOLD SOLID B-REP OBJECT ENTITY (TYPE 186) 4.47 Manifold Solid B-Rep Object Entity (Type 186) ECO603 The definition of this entity can be found in Appendix G (see Section G.9). 187 4.48 PLANE SURFACE ENTITY (TYPE 190) 4.48 Plane Surface Entity (Type 190) ECO603 The definition of this entity can be found in Appendix G (see Section G.10). 188 4.49 RIGHT CIRCULAR CYLINDRICAL SURFACE ENTITY (TYPE 192) 4.49 Right Circular Cylindrical Surface Entity (Type 192) ECO603 The definition of this entity can be found in Appendix G (see Section G.11). 189 4.50 RIGHT CIRCULAR CONICAL SURFACE ENTITY (TYPE 194) 4.50 Right Circular Conical Surface Entity (Type 194) ECO603 The definition of this entity can be found in Appendix G (see Section G.12). 190 4.51 SPHERICAL SURFACE ENTITY (TYPE 196) 4.51 Spherical Surface Entity (Type 196) ECO603 The definition of this entity can be found in Appendix G (see Section G.13). 191 4.52 TOROIDAL SURFACE ENTITY (TYPE 198) 4.52 Toroidal Surface Entity (Type 198) ECO603 The definition of this entity can be found in Appendix G (see Section G.14). 192 4.53 ANGULAR DIMENSION ENTITY (TYPE 202) 4.53 Angular Dimension Entity (Type 202) An Angular Dimension Entity consists of a general note; zero, one, or two witness lines; two leaders; and an angle vertex point. Figure 48 indicates the construction used. Refer to Figure 49 for examples of angular dimensions. If two witness lines are used, each is contained in its own Copious Data Entity. Each leader consists of at least one circular arc segment with an arrowhead at one end. The leader pointers are ordered such that the first circular arc segment of the first leader is defined in a counterclockwise manner from arrowhead to terminate point, and the first circular arc segment of the second leader is defined in a clockwise manner. (Refer to Section 3.2.4 for information relating to the use of the term counterclockwise). Section 4.60 contains a discussion of multi-segment leaders. For those leaders in Angular Dimension Entities consisting of more than one segment, the first two segments are circular arcs with a center at the vertex point. The second circular arc segment is defined in the opposite direction from the first circular arc segment. Remaining segments, if any, are straight lines. Any leader segment in which the start point is the same as the terminate point is to be ignored. This convention arises to facilitate the definition of the second circular arc segment such as in the bottom leader in Figure 48. The first example in Figure 49 illustrates a leader with three segments. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 202 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????01?? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 202 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 DENOTE Pointer Pointer to the DE of the General Note Entity 2 DEWIT1 Pointer Pointer to the DE of the first Witness Line Entity or zero 3 DEWIT2 Pointer Pointer to the DE of the second Witness Line Entity or zero 4 XT Real Coordinates of vertex point 5 YT Real 6 R Real Radius of Leader arcs 7 DEARRW1 Pointer Pointer to the DE of the first Leader Entity 8 DEARRW2 Pointer Pointer to the DE of the second Leader Entity Additional pointers as required (see Section 2.2.4.4.2). 193 4.53 ANGULAR DIMENSION ENTITY (TYPE 202) Figure 48. Construction of Leaders for the Angular Dimension Entity. The radius of the arc in the leader must be calculated between the vertex point and the start point of the leader. 194 4.53 ANGULAR DIMENSION ENTITY (TYPE 202) Figure 49. Examples Defined Using the Angular Dimension Entity 195 4.54 CURVE DIMENSION ENTITY (TYPE 204) 4.54 Curve Dimension Entity (Type 204) ECO566 The definition of this entity may be found in Appendix G (see Section G.15). 196 4.55 DIAMETER DIMENSION ENTITY (TYPE 206) 4.55 Diameter Dimension Entity (Type 206) A Diameter Dimension Entity consists of a general note, one or two leaders, and an arc center point. Refer to Figure 50 for examples of the Diameter Dimension Entity. The arc center coordinates are used as reference in constructing the diameter dimension but have no effect on the dimension components. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 206 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????01?? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 206 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 DENOTE Pointer Pointer to the DE of the General Note Entity 2 DEARRW1 Pointer Pointer to the DE of the first Leader Entity 3 DEARRW2 Pointer Pointer to the DE of the second Leader Entity or zero 4 XT Real Arc center coordinates 5 YT Real Additional pointers as required (see Section 2.2.4.4.2). 197 4.55 DIAMETER DIMENSION ENTITY (TYPE 206) Figure 50. Examples Defined Using the Diameter Dimension Entity 198 4.56 FLAG NOTE ENTITY (TYPE 208) 4.56 Flag Note Entity (Type 208) A Flag Note Entity is label information formatted as shown in Figure 51. The rotation angle and location of the lower left corner coordinate in the Flag Note Entity override the General Note Entity (Type 212) rotation angle and placement. The Flag Note Entity may be defined with or without leaders. The flag note is constructed from information defined in the General Note Entity. This data is the character box height and character box width. For this reason, no geometric definition is explicit within the definition of the Flag Note Entity. The box containing the text (as defined in the General Note Entity) shall be centered in the flag note box of size (H x L). The general note may consist of multiple text strings; however, they must share a common baseline. The number of characters shall not be greater than 10. Variables: H = Height CH = Character Height (from General Note) L = Length TW = Text Width (from General Note) T = Tip Length A = Rotation Angle (in radians) Formulas: H = 2 * CH L = TW + 0.4 * CH T = 0.5 * H / tan 350 Restrictions: H shall never be less than 0.3 in. L shall never be less than 0.6 in. Examples defined using the Flag Note Entity are shown in Figure 52. 199 4.56 FLAG NOTE ENTITY (TYPE 208) Directory Entry |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Typ|eParamete|rStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern| | | Matrix | Display | Number | Number | | | | | | | | | | | | | 208 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????01?? | D # | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Typ|e Line | Color | Paramete|r Form | Reserved| Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|t Number | | | Label | Subscrip|tNumber | | | | | | | | | | | | | 208 | # | #; ) | # | 0 | | | | # |D # + 1 | |__________|_________|_________|_________|__________|_________|_________|__________|_________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 XT Real Lower left corner coordinate of the Flag 2 YT Real 3 ZT Real 4 A Real Rotation angle in radians 5 DENOTE Pointer Pointer to the DE of the General Note Entity 6 N Integer Number of Arrows (Leaders) or zero 7 DEARRW1 Pointer Pointer to the DE of the first associated Leader Entity .. . . . .. .. 6+N DEARRWN Pointer Pointer to the DE of the last associated Leader Entity Additional pointers as required (see Section 2.2.4.4.2). 200 4.56 FLAG NOTE ENTITY (TYPE 208) Figure 51. Parameters of the Flag Note Entity. Note that the box outlined within the flag illustrates the bounds of the text and is not a subsymbol. 201 4.56 FLAG NOTE ENTITY (TYPE 208) Figure 52. Examples Defined Using the Flag Note Entity 202 4.57 GENERAL LABEL ENTITY (TYPE 210) 4.57 General Label Entity (Type 210) A General Label Entity consists of a general note with one or more associated leaders. Examples of general labels are shown in Figure 53. Directory Entry |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |Entity Ty|peParamet|erStructur|eLine Fon|t Level | View |Xformatio|n Label | Status | Sequence| | Number | Data | | Pattern | | | Matrix | Display| Number | Number | | | | | | | | | | | | | 210 | ) |< n:a: > | #; ) | #; ) | 0; ) | 0; ) | 0; ) |????01?? | D # | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ | | | | | | | | | | | | (11) | (12) | (13) | (14) | (15) | (16) | (17) | (18) | (19) | (20) | |Entity Ty|pe Line | Color |Parameter| Form | Reserved | Reserved| Entity | Entity | Sequence| | Number | Weight | Number |Line Coun|tNumber | | | Label | Subscript| Number | | | | | | | | | | | | | 210 | # | #; ) | # | 0 | | | | # |D # + 1 | |_________|_________|__________|_________|_________|__________|_________|_________|__________|_________|_ Parameter Data Index__ Name____ Type___ Description___ 1 DENOTE Pointer Pointer to the DE of the associated General Note Entity 2 N Integer Number of Leaders 3 DEARRW1 Pointer Pointer to the DE of the first associated Leader Entity .. . . . .. .. 2+N DEARRWN Pointer Pointer to the DE of the last associated Leader Entity Additional pointers as required (see Section 2.2.4.4.2). 203 4.57 GENERAL LABEL ENTITY (TYPE 210) Figure 53. Examples Defined Using the General Label Entity 204 4.58 GENERAL NOTE ENTITY (TYPE 212) 4.58 General Note Entity (Type 212) A General Note Entity consists of one or more text strings. Each text string contains text, a starting point, a text size, and an angle of rotation of the text. Examples of general notes are shown in Figure 58. The font code (FC) is an integer specifying the desired character set and its associated display characteristics. Positive values are predefined fonts. Negative values point to implementor-defined fonts or modifications to a predefined font, through the use of the Text Font ECO532 Definition Entity (Type 310). The following font codes are defined: ____________________________________________________ |__FC__||_______________Description_______________|_ | 0 |Symbol Font (no longer recommended) | | 1 |Default Style for ASCII Character Set | | 2 |LeRoy | | 3 |Futura | | 6 |Comp 80 | | 12 |News Gothic | | 13 |Lightline Gothic | | 14 |Simplex Roman | | 17 |Century Schoolbook | | 18 |Helvetica | | 19 |OCR-B [ISO1073] (see Appendix G) | | 1001 |Symbol Font 1 | | 1002 |Symbol Font 2 | | 1003 |Drafting Font | |__2001__|Kanji_[JIS6226]_(see_Appendix_G)_______|__ FC 0 specifies an old symbol font and should no longer be used. Figure F1 in Appendix F is a mapping symbol definition for FC 0. FC 1 does not specify a defined display. Use of Font 1 implies that the receiving system may use any font which displays the appropriate ASCII format characters. The intent of this font is for usage when the actual display of the characters is not critical for the application. FC 19 specifies a symbol font shown in Figure 54 and is defined in Appendix G (see Section G.16). Display symbols must be represented using 7-bit ASCII codes with FC-values in the 1000 series as ECO531 shown in Figures 55, 56 and 57. The 7-bit ASCII control characters, i.e., hexadecimal 00 through 1F and hexadecimal 7F, may not be used to represent display symbols. They do not specify a character display font. FC 2001 specifies a symbol font defined in Appendix G (see Section G.16). ECO547 If the predefined font codes are not sufficient to describe a desired character set or display charac- teristic, a Text Font Definition Entity (Type 310) may be used to define the font. If a text font definition is being used, the negative of the pointer value for the directory entry of the Text Font Definition Entity is placed in the font code (FC) parameter. The use of the values WT, HT, SL, A, and text start point are shown in Figure 59. Table 5 provides names for the graphical characters generated for each valid FC. 205 4.58 GENERAL NOTE ENTITY (TYPE 212) Within definition space, the parameters for the text block are applied in the following order (see Figure 60): 1. Define the box height (HT) and box width (WT). The rotate internal text flag indicates whether the text box is filled with horizontal text or vertical text. The box width is measured from the start of the left-most (first) text charac- ter/symbol in the positive XT direction along the text base line, and extends to the end of the right-most (last) character/symbol, extending N characters/symbols and N-1 intercharacter spaces. The box height is measured in the positive YT direction and is the height of capital letters. It is equivalent to the symbol "h" used in Appendix C of [ANSI82]. Special symbols, such as those appearing in Appendix C of [ANSI82], which exceed "h" in height are centered vertically. Descenders and portions of symbols exceeding "h" extend outside the lower and/or ECO549 upper borders of the box (see Figure 61). The box height and width are measured before the rotation angle (A) is applied. The text start point is defined as the lower left corner of the ECO579 first character/symbol box. 2. The slant angle is then applied to each individual character. For horizontal text, it is measured from the XT axis in a counterclockwise direction. For vertical text, the slant angle is measured from the YT axis. 3. The rotation angle is then applied to the text block. This rotation is applied in a counter- clockwise direction about the text start point. The plane of rotation is the XT, YT plane at the depth ZSn (where ZSn is the value given for the text start point). 4. The mirror operation is performed next. The value 1 indicates the mirror axis is the (rotated) line perpendicular to the text base line and through the text start point. The value 2 indicates the mirror axis is the (rotated) text base line. Finally, the Transformation Matrix Entity is used to specify the relative position of definition space within model space. The number of characters (NCn) must always be equal to the character count in its corresponding text string (TEXTn). 206 4.58 GENERAL NOTE ENTITY (TYPE 212) ________________________________________________________|| | | | | | | | The definition of this font can be found | | | | in Appendix G (see Section G.16). | | | | | |_______________________________________________________| Figure 54. General Note Font Specified by FC 19 207 4.58 GENERAL NOTE ENTITY (TYPE 212) ________________________________________________________________________________________________ | | BL | | |0 | 0 | | @ | @ | | P | P | | | | |p | iP | | |_|_________|____|_|_____|______|_|______|______|_|_____|_______|_|_____|_______|_|_____|______|_| | | ! |! | |1 | 1 | | A | A | | Q | Q | | a | ___ | |q | C|_ | | |_|________|_____|_|____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | " |" | | 2 | 2 | | B | B | | R | R | | b | _|_|_|||r | if | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_|_ | | # |# | | 3 | 3 | | C | C | | S | S | | c | ___ | |s | iS | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_|_ | | $ |$ | | 4 | 4 | | D | D | | T | T | | d | |_|_ | |t | ___||||| |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | % |% | | 5 | 5 | | E | E | | U | U | | e | i | |u | i| | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | & |& | | 6 | 6 | | F | F | | V | V | | f | | |v | ___|A| | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | | | | 7 | 7 | | G | G | | W | W | | g | f | |w | 3| | | |_|_______|____|_|______|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | ( |( | | 8 | 8 | | H | H | | X | X | | h | % | | x | 4| | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|______|_|_____|_______|_|_ | | ) |) | | 9 | 9 | | I | I | | Y | Y | | i | _____| |y | @@ | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | * |* | | : | : | |J | J | | Z | Z | | j | _f|_ | |z | Y | | |_|________|____|_|_____|________|_|____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | + |+ | | ; | ; | |K | K | | [ | [ | |k | |_| | |{ | { | | |_|________|____|_|_____|________|_|____|______|_|______|________|_|____|_______|_|____|_______|_| | | , | , | |< | < | | L | L | | " | " | | l | ? | | _ | I | | |_|________|______|_|____|______|_|_____|_______|_|_____|______|_|______|______|_|_____|________| | | | - |- | |= | = | | M | M | | ] | ] | |m | Mi | |} | } | | |_|________|_____|_|____|_______|_|_____|______|_|______|________|_|____|_______|_|____|_______|_| | | . | . | |> | > | | N | N | | ^ | ^ | | n | i | |" | " | | |_|________|______|_|____|______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | / |/ | | ? | ? | | O | O | | _ | _ | | o | O | | |_|________|____|_|_____|_______|_|_____|______|_|______|_______|_|_____|______|_| Figure 55. General Note Font Specified by FC 1001 208 4.58 GENERAL NOTE ENTITY (TYPE 212) ________________________________________________________________________________________________ | | BL | | |0 | 0 | | @ | @ | | P | P | | | | |p | " | | |_|_________|____|_|_____|______|_|______|______|_|_____|_______|_|_____|_______|_|_____|______|_|_ | | ! |! | |1 | 1 | | A | A | | Q | Q | | a | ___@@| |q | # | | |_|________|_____|_|____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | " |" | | 2 | 2 | | B | B | | R | R | | b | | | r | ! | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_____|_|______|______|_| | | # | | | 3 | 3 | | C | C | | S | S | | c | | | s | | | |_|________|___|_|______|_______|_|_____|______|_|______|______|_|______|_____|_|______|______|_| | | $ | | | 4 | 4 | | D | D | | T | T | | d | | | t | OE | | |_|________|___|_|______|_______|_|_____|______|_|______|______|_|______|_____|_|______|________| | | | % |% | | 5 | 5 | | E | E | | U | U | | e | 4 | | u | | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|______|_|_____|______|_| | | & |& | | 6 | 6 | | F | F | | V | V | | f | p | |v | fl | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|________| | | | | | | 7 | 7 | | G | G | | W | W | | g | x | | w | | | |_|_______|____|_|______|_______|_|_____|______|_|______|______|_|______|______|_|_____|_______|_| | | ( |( | | 8 | 8 | | H | H | | X | X | | h | | | x | ! | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_____|_|______|_______|_| | | ) |) | | 9 | 9 | | I | I | | Y | Y | | i | 6= | |y | | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|______|_|R | | * |* | | : | : | |J | J | | Z | Z | | j | | |z | ff | | |_|________|____|_|_____|________|_|____|_______|_|_____|______|_|______|_______|_|____|________| | | | + |+ | | ; | ; | |K | K | | [ | [ | |k | | | { | ffi | | |_|________|____|_|_____|________|_|____|______|_|______|________|_|____|_____|_|______|________ | | | | , | , | |< | < | | L | L | | " | " | | l | _ | | _ | | | |_|________|______|_|____|______|_|_____|_______|_|_____|______|_|______|______|_|_____|______|_| | | - |- | |= | = | | M | M | | ] | ] | |m | ^ | | } | ss | | |_|________|_____|_|____|_______|_|_____|______|_|______|________|_|____|______|_|_____|________| | | | . | . | |> | > | | N | N | | ^ | ^ | | n | | | " | ___ | | |_|________|______|_|____|______|_|_____|______|_|______|______|_|______|_____|_|______|_______|_|P | | / |/ | | ? | ? | | O | O | | _ | _ | | o | | | |_|________|____|_|_____|_______|_|_____|______|_|______|_______|_|_____|_______| | Figure 56. General Note Font Specified by FC 1002 209 4.58 GENERAL NOTE ENTITY (TYPE 212) ________________________________________________________________________________________________ | | BL | | |0 | 0 | | @ | @ | | P | P | | | | |p | iP | | |_|_________|____|_|_____|______|_|______|______|_|_____|_______|_|_____|_______|_|_____|______|_| | | ! |! | |1 | 1 | | A | A | | Q | Q | | a | ___ | |q | C|_ | | |_|________|_____|_|____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | " |" | | 2 | 2 | | B | B | | R | R | | b | ? | | r | if | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|______|_|_____|_______|_|_ | | # |# | | 3 | 3 | | C | C | | S | S | | c | ___ | |s | iS | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | $ |$ | | 4 | 4 | | D | D | | T | T | | d | |_|_ | |t | __ | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_| | | % |% | | 5 | 5 | | E | E | | U | U | | e | i | |u | ___ | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | & |& | | 6 | 6 | | F | F | | V | V | | f | | |v | ___||| | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | ' | | | 7 | 7 | | G | G | | W | W | | g | f | |w | _ | | |_|________|___|_|______|_______|_|_____|______|_|______|______|_|______|_______|_|____|_______|_|_ | | ( |( | | 8 | 8 | | H | H | | X | X | | h | % | | x | # | | |_|________|____|_|_____|_______|_|_____|______|_|______|______|_|______|______|_|_____|_______|_| | | ) |) | | 9 | 9 | | I | I | | Y | Y | | i | _____| |y | _|>_ | | |_|________|____|_|_____|_______|_|_____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | * |* | | : | : | |J | J | | Z | Z | | j | _f|_ | |z | ___|@@|| |_|________|____|_|_____|________|_|____|_______|_|_____|______|_|______|_______|_|____|_______|_| | | + |+ | | ; | ; | |K | K | | [ | [ | |k | |_| | |{ | { | | |_|________|____|_|_____|________|_|____|______|_|______|________|_|____|_______|_|____|_______|_| | | , | , | |< | < | | L | L | | " | " | | l | Li | |_ | I | | |_|________|______|_|____|______|_|_____|_______|_|_____|______|_|______|_______|_|____|________| | | | - |- | |= | = | | M | M | | ] | ] | |m | Mi | |} | } | | |_|________|_____|_|____|_______|_|_____|______|_|______|________|_|____|_______|_|____|_______|_| | | . | . | |> | > | | N | N | | ^ | _ | | n | i | |" | | | |_|________|______|_|____|______|_|_____|______|_|______|______|_|______|_______|_|____|______|_|_ | | / |/ | | ? | ? | | O | O | | _ | _ | | o | ___||| | |_|________|____|_|_____|_______|_|_____|______|_|______|_______|_|_____|_______| | Figure 57. General Note Font Specified by FC 1003 210 4.58 GENERAL NOTE ENTITY (TYPE 212) Table 5. Character Names for the Symbol and Drafting Fonts _______________________________________________________________ | | ||____________FCy____________| |_________Name_________||__Symbol_||__1_|_|1001_||_1002__|1003_ | | Space | | 20 | 20 | 20 | 20 | | Exclamation mark | ! |21 | 21 | 21 | 21 | | Quotation marks | " | 22 | 22 | 22 | 22 | | Pound sign | # | 23 | 23 | | 23 | | Plus/minus | | | | 23 | 60 | | Dollar sign | $O | 24 | 24 | | 24 | | Degree symbol | | | | 24 | 7E | | Percent sign | % | 25 | 25 | 25 | 25 | | Ampersand | & | 26 | 26 | 26 | 26 | | Apostrophe | | 27 | 27 | 27 | 27 | | Left parenthesis | ( | 28 | 28 | 28 | 28 | | Right parenthesis | ) | 29 | 29 | 29 | 29 | | Asterisk | * | 2A | 2A | 2A | 2A | | Plus sign | + | 2B | 2B | 2B | 2B | | Comma | , |2C | 2C | 2C | 2C | | Minus sign/hyphen | - |2D | 2D | 2D | 2D | | Period | . |2E | 2E | 2E | 2E | | Slash | / | 2F | 2F | 2F | 2F | | Numeric 0 | 0 | 30 | 30 | 30 | 30 | | Numeric 1 | 1 | 31 | 31 | 31 | 31 | | Numeric 2 | 2 | 32 | 32 | 32 | 32 | | Numeric 3 | 3 | 33 | 33 | 33 | 33 | | Numeric 4 | 4 | 34 | 34 | 34 | 34 | | Numeric 5 | 5 | 35 | 35 | 35 | 35 | | Numeric 6 | 6 | 36 | 36 | 36 | 36 | | Numeric 7 | 7 | 37 | 37 | 37 | 37 | | Numeric 8 | 8 | 38 | 38 | 38 | 38 | | Numeric 9 | 9 | 39 | 39 | 39 | 39 | | Colon | : |3A | 3A | 3A | 3A | | Semi-colon | ; |3B | 3B | 3B | 3B | | Less than | < | 3C | 3C | 3C | 3C | | Equal sign | = | 3D | 3D | 3D | 3D | | Greater than | > | 3E | 3E | 3E | 3E | | Question mark | ? | 3F | 3F | 3F | 3F | | Commercial at | @ | 40 | 40 | 40 | 40 | | Upper case letter A | A | 41 | 41 | 41 | 41 | | Upper case letter B | B | 42 | 42 | 42 | 42 | | Upper case letter C | C | 43 | 43 | 43 | 43 | | Upper case letter D | D | 44 | 44 | 44 | 44 | | Upper case letter E | E | 45 | 45 | 45 | 45 | | Upper case letter F | F | 46 | 46 | 46 | 46 | | Upper case letter G | G | 47 | 47 | 47 | 47 | |__Upper_case_letter_H__|___H_____|_48__|__48___|_48___|__48___| yEntries for each FC are hexadecimal ASCII equivalent 211 4.58 GENERAL NOTE ENTITY (TYPE 212) Table 5. Character Names for the Symbol and Drafting Fonts (continued) _________________________________________________________________ | | ||____________FCy____________| |__________Name__________||__Symbol_||__1_|_|1001_||_1002__|1003_ | | Upper case letter I | I |49 | 49 | 49 | 49 | | Upper case letter J | J |4A | 4A | 4A | 4A | | Upper case letter K | K | 4B | 4B | 4B | 4B | | Upper case letter L | L | 4C | 4C | 4C | 4C | | Upper case letter M | M | 4D | 4D | 4D | 4D | | Upper case letter N | N | 4E | 4E | 4E | 4E | | Upper case letter O | O | 4F | 4F | 4F | 4F | | Upper case letter P | P | 50 | 50 | 50 | 50 | | Upper case letter Q | Q | 51 | 51 | 51 | 51 | | Upper case letter R | R | 52 | 52 | 52 | 52 | | Upper case letter S | S | 53 | 53 | 53 | 53 | | Upper case letter T | T | 54 | 54 | 54 | 54 | | Upper case letter U | U | 55 | 55 | 55 | 55 | | Upper case letter V | V | 56 | 56 | 56 | 56 | | Upper case letter W | W | 57 | 57 | 57 | 57 | | Upper case letter X | X | 58 | 58 | 58 | 58 | | Upper case letter Y | Y | 59 | 59 | 59 | 59 | | Upper case letter Z | Z | 5A | 5A | 5A | 5A | | Left bracket | [ |5B | 5B | 5B | 5B | | Backward slash | \ |5C | 5C | 5C | 5C | | Right bracket | ] |5D | 5D | 5D | 5D | | Caret | ^ | 5E | 5E | 5E | | | Arc length | _ | | | | 5E | | Underscore | ___ | 5F | 5F | 5F | 5F | | Reverse quote | | 60 | 60 | 60 | | | Lower case letter a | a |61 | | | | | Angularity | ____ | | 61 | | 61 | | Marker/symbol | ___@@ | | | 61 | | | Lower case letter b | b_ | 62 | | | | | Marker/symbol | _|_|| | | 62 | | | | Division symbol | | | | 62 | | | Perpendicularity | ? | | | | 62 | | Lower case letter c | c__ |63 | | | | | Flatness | ___ | | 63 | | 63 | | Less than or equal | | | | 63 | | | Lower case letter d | d_ | 64 | | | | | Profile of a surface | |_|_ | | 64 | | 64 | | Greater than or equal | | | | 64 | | | Lower case letter e | ei |65 | | | | | Circularity | | | 65 | | 65 | |__Marker/symbol________|_____4____|______|_______|__65___|______| yEntries for each FC are hexadecimal ASCII equivalent 212 4.58 GENERAL NOTE ENTITY (TYPE 212) Table 5. Character Names for the Symbol and Drafting Fonts (continued) ECO605 _________________________________________________________________________ | | ||____________FCy____________| |______________Name______________||__Symbol_||__1_|_|1001|_|1002__|1003__| | Lower case letter f | f | 66 | | | | | Parallelism | p | | 66 | | 66 | | Radical | | | | 66 | | | Lower case letter g | gf | 67 | | | | | Cylindricity | | | 67 | | 67 | | Cross product | x | | | 67 | | | Lower case letter h | h | 68 | | | | | Circular Runout | % | | 68 | | 68 | | Congruence | | | | 68 | | | Lower case letter i | i___ | 69 | | | | | Symmetry | __ | | 69 | | 69 | | Not equal | 6= | | | 69 | | | Lower case letter j | jf_ |6A | | | | | Position | R| | | 6A | | 6A | | Integral | | | | 6A | | | Lower case letter k | k_ | 6B | | | | | Profile of a line | | | | | 6B | | 6B | | Implication | | | | 6B | | | Lower case letter l | l | 6C | | | | | Perpendicularity | ? | | 6C | | | | Union | _i | | | 6C | | | Least material condition | L | | | | 6C | | Lower case letter m | mi |6D | | | | | Maximum material condition | M | | 6D | | 6D | | Intersection | ^ | | | 6D | | | Lower case letter n | ni | 6E | | | | | Diameter | | | 6E | | 6E | | Approximately equal | | | | 6E | | | Lower case letter o | o | 6F | | | | | All around applicability | PO | | 6F | | | | Greek letter sigma (Sum) | | | | 6F | | | Square (shape) | 2 | | | | 6F | | Lower case letter p | pi | 70 | | | | | Projected tolerance zone | P | | 70 | | 70 | | Up arrow | " | | | 70 | | | Lower case letter q | q | 71 | | | | | Centerline | C|_ | | 71 | | 71 | | Down arrow | # | | | 71 | | | Lower case letter r | rif | 72 | | | | | Concentricity | | | 72 | | 72 | |__Right_arrow____________________|___!____|______|______|__72___|_______| yEntries for Each FC are hexadecimal ASCII equivalent 213 4.58 GENERAL NOTE ENTITY (TYPE 212) Table 5. Character Names for the Symbol and Drafting Fonts (continued) _____________________________________________________________________ | | ||____________FCy____________| |____________Name____________||__Symbol_||__1_|_|1001|_|1002__|1003__| | Lower case letter s | si | 73 | | | | | Regardless of feature size | S | | 73 | | 73 | | Left arrow | | | | 73 | | | Lower case letter t | _t_| | 74 | | | | | Marker/symbol | ___|| | | 74 | | | | Greek letter phi | OE | | | 74 | | | Total runout | __ | | | | 74 | | Lower case letter u | ui| | 75 | | | | | Marker/symbol | | | 75 | | | | Greek letter theta | ___ | | | 75 | | | Straightness | | | | | 75 | | Lower case letter v | v| | 76 | | | | | Marker/symbol | ___A | | 76 | | | | Greek letter gamma | fl | | | 76 | | | Counterbore | ___|| | | | | 76 | | Lower case letter w | w | 77 | | | | | Marker/symbol | 3| | | 77 | | | | Greek letter psi | | | | 77 | | | Countersink | _ | | | | 77 | | Lower case letter x | x | 78 | | | | | Marker/symbol | 4| | | 78 | | | | Greek letter omega | _!_ | | | 78 | | | Depth | # | | | | 78 | | Lower case letter y | _y_ | 79 | | | | | Marker/symbol | @@ | | 79 | | | | Greek letter lambda | | | | 79 | | | Conical taper | _|>_ | | | | 79 | | Lower case letter z | z |7A | | | | | Marker/symbol | Y | | 7A | | | | Greek letter alpha | ff | | | 7A | | | Slope | ___|@@ | | | | 7A | | Left brace | { |7B | 7B | | 7B | | Greek letter delta | ffi | | | 7B | | | Vertical bar | | |7C | 7C | | 7C | | Greek letter mu | | | | 7C | | | Right brace | } |7D | 7D | | 7D | | Greek letter pi | ss | | | 7D | | | Tilde | " |7E | 7E | | | |__Overscore__________________|_________|_____|______|__7E___|_______| yEntries for each FC are hexadecimal ASCII equivalent 214 4.58 GENERAL NOTE ENTITY (TYPE 212) Figure 58. Examples Defined Using the General Note Entity 215 4.58 GENERAL NOTE ENTITY (TYPE 212) Figure 59. General Note Text Construction 216 4.58 GENERAL NOTE ENTITY (TYPE 212) Figure 60. General Note Example of Text Operations 217 4.58 GENERAL NOTE ENTITY (TYPE 212) Figure 61. Examples of Drafting Symbols That Exceed Text Box Height 218 4.58 GENERAL NOTE ENTITY (TYPE 212) The graphical representation and recreation of notes with a special structure are handled by the use of the Form Number in Field 15 of the Directory Entry for this entity. A system to accommodate these notes is outlined below. Any strings after those specified by the form number are consid- ered additional, appended strings that are not related in any particular manner to the previously referenced strings. In the event that a string necessary for the defined structure is not present in the originating system's note, a null string (see NULL STRING in Appendix K) shall be inserted in the General Note Entity to take the place of the nonexistent string to maintain the structure of the data. Notes that contain fractional notation will be represented as mixed numerals. This is done through the use of four consecutive strings representing the whole number, the numerator, the denominator, and the divisor bar. These are examples of the divisor bar string: 1H/ 1H- 2H-- 1H_ The following form numbers for the general note are used to maintain the graphical representation of the originating system's note: Form 0: Simple Note (default) - A general note of one or more strings such that a text string is not related in any manner to another string in the same General Note Entity. Form 1: Dual Stack - A general note of two or more strings where the first two are related in a manner such that they are both left justified and the second string is displayed "below" the first. xxxxxx yyyyy Form 2: Imbedded Font Change - A general note of two or more strings that is intended as a single string but was divided to accommodate a font change in the string. xxxxxx xxxx Form 3: Superscript - A general note of two or more strings where the second string is a superscript of the first string. xxx yyy Form 4: Subscript - A general note of two or more strings where the second string is a subscript of the first string. xxx yyy 219 4.58 GENERAL NOTE ENTITY (TYPE 212) Form 5: Super-/Sub-script - A general note of three or more strings where the second string is a superscript of the first string and the third string is a subscript of the first string. xxx yyyzzz Form 6: Multiple Stack/Left Justified - A general note where all strings are left justified to a common margin. These strings originated as a "paragraphed" note. xxxxxxxxxx yyyyyyy zzzzzzzzzzz Form 7: Multiple Stack/Center Justified - A general note where all string