TRIANGULATION_TRIANGLE_NEIGHBORS
Triangle Neighbors
in a Triangulation

TRIANGULATION_TRIANGLE_NEIGHBORS is a FORTRAN90 program which computes the three neighboring triangles of each triangle in a triangulation.

The user supplies a node file and a triangle file, containing the coordinates of the nodes, and the indices of the nodes that make up each triangle. Either 3-node or 6-node triangles may be used.

The program reads the data, computes the triangle neighbor information, and writes out the information to a file. In cases where one side of a triangle has no triangle neighbor, a value of -1 is assigned.

The triangle neighbor array is useful if the triangulation has to be searched to find the triangle containing a given point. It is also useful when analyzing the bandwidth of the adjacency matrix, or of a finite element matrix derived from the triangulation.

Licensing:

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

Related Data and Programs:

MESH_BANDWIDTH is a FORTRAN90 program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

NEIGHBORS_TO_METIS_GRAPH is a FORTRAN90 program which reads a triangle mesh neighbor file created by TRIANGULATION_TRIANGLE_NEIGHBORS and writes a modified version of the same data suitable for input to the mesh partitioning program METIS.

RCM is a FORTRAN90 library of routines for reverse Cuthill-McKee computations.

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

TET_MESH_RCM is a FORTRAN90 library which applies the reverse Cuthill-McKee reordering to a tetrahedral mesh of nodes in 3D.

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

TRIANGULATION is a FORTRAN90 library which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_BOUNDARY_NODES is 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_DISPLAY_OPEN_GL is a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_L2Q is 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 is a FORTRAN90 program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

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

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

TRIANGULATION_ORIENT is 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_PLOT is a FORTRAN90 program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

TRIANGULATION_Q2L is 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_QUALITY is a FORTRAN90 program which reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM is a FORTRAN90 program which can reorder the nodes of a triangulation so that the bandwidth of the associated adjacency matrix is reduced.

TRIANGULATION_REFINE is a FORTRAN90 program which can be used to refine a triangulation.

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

Usage:

triangulation_triangle_neighbors node_file triangle_file

reads the triangulation whose nodal coordinates are given in node_file, and triangle indices in triangle_file, and produces a triangle neighbor file.

Reference:

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

Source Code:

• triangulation_triangle_neighbors.f90, the source code.
• triangulation_triangle_neighbors.csh, commands to compile the source code.

Examples and Tests:

Files associated with a 3-node triangulation:

• test3_output.txt, the printed output from the command
  "triangulation_triangle_neighbors nodes3.txt triangles3.txt"
• nodes3.txt, the node file.
• nodes3.png, a PNG image of the nodes.
• triangles3.txt, the triangle file.
• triangles3.png, a PNG image of the triangles.
• triangles3.tneighbor.txt, the triangle neighbor file.

Files associated with a 6-node triangulation:

• test6_output.txt, the printed output from the command
  "triangulation_triangle_neighbors nodes6.txt triangles6.txt"
• nodes6.txt, the node file.
• nodes6.png, a PNG image of the nodes.
• triangles6.txt, the triangle file.
• triangles6.png, a PNG image of the triangles.
• triangles6.tneighbor.txt, the triangle neighbor file.

List of Routines:

• MAIN is the main program for TRIANGULATION_TRIANGLE_NEIGHBORS.
• 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.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4ROW_COMPARE compares two rows of an I4ROW.
• I4ROW_SORT_A ascending sorts the rows of an I4ROW.
• I4ROW_SWAP swaps two rows of an I4ROW.
• ITABLE_DATA_READ reads data from an integer table file.
• ITABLE_DATA_WRITE writes data to an integer table file.
• ITABLE_HEADER_READ reads the header from an integer table file.
• ITABLE_HEADER_WRITE writes the header to an integer table file.
• ITABLE_WRITE writes an integer table file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• S_INDEX_LAST_C finds the LAST occurrence of a given character.
• S_TO_I4 reads an I4 from a string.
• S_TO_I4VEC reads an I4VEC 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.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.
• TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors.
• TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES determines triangle neighbors.

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