TRIANGULATION_PLOT
Plot a Triangulation

TRIANGULATION_PLOT is a FORTRAN90 program which plots a triangulation.

TRIANGULATION_PLOT reads one file listing the nodes, and a second file consisting of groups of 3 or 6 nodes that make up triangles, and creates an Encapsulated PostScript image of the triangulation.

Usage:

triangulation_plot prefix node_vis triangle_vis

• prefix_nodes.txt, the node coordinates (input);
• prefix_elements.txt, the triangulation (input);
• prefix.eps, the plot file (output);

• 0, do not show the nodes;
• 1, show the nodes;
• 2, show the nodes and label them.

• 0, do not show the triangles;
• 1, show the triangles;
• 2, show the triangles and label them.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TRIANGULATION_PLOT is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

TABLE_DELAUNAY, a FORTRAN90 program which triangulates a set of nodes whose coordinates are stored in a file.

TRI_SURFACE_DISPLAY, a MATLAB program which reads data defining a triangular mesh of a 3D surface and displays it.

TRIANGLE, a C program which computes a triangulation of a geometric region.

TRIANGULATION, a FORTRAN90 library which is useful for working with triangulations.

TRIANGULATION_BOUNDARY_NODES, a FORTRAN90 program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

TRIANGULATION_CORNER, a FORTRAN90 program which patches triangulations so that no triangle has two sides on the boundary.

TRIANGULATION_DELAUNAY_DISCREPANCY, a FORTRAN90 program which measures the amount by which a triangulation fails the local Delaunay test;

TRIANGULATION_DISPLAY, a MATLAB program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_HISTOGRAM, a FORTRAN90 program which computes histograms of data over a triangulation.

TRIANGULATION_L2Q, a FORTRAN90 program which reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.

TRIANGULATION_MASK, a FORTRAN90 program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

TRIANGULATION_ORDER3, a data directory which contains a description and examples of order 3 triangulations.

TRIANGULATION_ORDER6, a data directory which contains a description and examples of order 6 triangulations.

TRIANGULATION_ORIENT, a FORTRAN90 program which reads data defining a triangulation, makes sure that every triangle has positive orientation, and if not, writes a corrected triangle file.

TRIANGULATION_Q2L, a FORTRAN90 program which reads data defining a 6-node triangulation, and subdivides each triangle into 4 3-node triangles, writing the resulting triangulation to a file.

TRIANGULATION_QUAD, a FORTRAN90 program which estimates the integral of a function over a triangulated region.

TRIANGULATION_QUALITY, a FORTRAN90 program which reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM, a FORTRAN90 program which reads data defining a triangulation, determines an ordering of the nodes that will reduce the bandwidth of the adjacency matrix, and writes the new triangulation information to a file.

TRIANGULATION_REFINE, a FORTRAN90 program which reads data defining a triangulation, replaces each triangle by four congruent smaller ones, and writes the new triangulation information to a file.

TRIANGULATION_TRIANGLE_NEIGHBORS, a FORTRAN90 program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.

Reference:

1. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
   Computational Geometry,
   Springer, 2000,
   ISBN: 3-540-65620-0,
   LC: QA448.D38.C65.
2. Joseph ORourke,
   Computational Geometry,
   Second Edition,
   Cambridge, 1998,
   ISBN: 0521649765,
   LC: QA448.D38.

Source Code:

• triangulation_plot.f90, the source code.
• triangulation_plot.sh, commands to compile the source code.

Examples and Tests:

ELBOW3 is an elbow-shaped region, triangulated using order 3 triangles.

• elbow3_nodes.txt the point coordinates.
• elbow3_elements.txt the triangulation.
• elbow3_triangulation.png is a PNG image of the triangulation.

ELL3 is an order 3 triangulation of a set of nodes in an L-shaped region.

• ell3_nodes.txt, the nodes.
• ell3_elements.txt, the triangulation.
• ell3_triangulation.png, a PNG image of the triangulation.

ELL6 is an order 6 triangulation of a set of nodes in an L-shaped region.

• ell6_nodes.txt, the nodes.
• ell6_elements.txt, the triangulation.
• ell6_triangulation.png, a PNG image of the triangulation.

HEX_HOLES3 puts a set of nodes into the double hexagonal hole region using CVT techniques, and creates an order 3 triangulation using TABLE_DELAUNAY.

• hex_holes3_nodes.txt, the nodes.
• hex_holes3_elements.txt, the triangulation.
• hex_holes3_triangulation.png, a PNG image of the triangulation.

LAKE3 uses constrained CVT methods to place nodes inside and on the boundary of the problem 14 triangulation region, a lake with an island. An order 3 triangulation is used.

• lake3_nodes.txt, the nodes;
• lake3_elements.txt, the triangles;
• lake3_triangulation.png, a PNG image of the triangulation.

List of Routines:

• MAIN is the main program for TRIANGULATION_PLOT.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads data from a double precision table file.
• DTABLE_HEADER_READ reads the header from a double precision table file.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_NAME_EXT_GET determines the "extension" of a file name.
• FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_WRAP forces an integer to lie between given limits by wrapping.
• I4MAT_PRINT prints an I4MAT.
• I4MAT_PRINT_SOME prints some of an I4MAT.
• ITABLE_DATA_READ reads data from an integer table file.
• ITABLE_HEADER_READ reads the header from an integer table file.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• S_INDEX_LAST finds the LAST occurrence of a given substring.
• S_TO_I4 reads an integer value from a string.
• S_TO_I4VEC reads an integer vector from a string.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.
• TRIANGULATION_ORDER3_PLOT plots a 3-node triangulation of a pointset.
• TRIANGULATION_ORDER6_PLOT plots a 6-node triangulation of a pointset.

You can go up one level to the FORTRAN90 source codes.