TRIANGULATION_TRIANGLE_NEIGHBORS
Triangle Neighbors
in a Triangulation

TRIANGULATION_TRIANGLE_NEIGHBORS is a MATLAB 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.

Related Data and Programs:

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

RCM is a MATLAB library which uses the reverse Cuthill-McKee method for mesh renumbering.

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

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

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

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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

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

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

TRIANGULATION_REFINE is a MATLAB 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 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.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• triangulation_triangle_neighbors_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• triangulation_triangle_neighbors_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• triangulation_triangle_neighbors.m, the main program for TRIANGULATION_TRIANGLE_NEIGHBORS.
• ch_cap.m, capitalizes a single character.
• ch_eqi.m, is a case insensitive comparison of two characters for equality.
• ch_to_digit.m, returns the integer value of a base 10 digit.
• dtable_data_read.m, reads data from a double precision table file.
• dtable_header_read.m, reads the header from a double precision table file.
• file_column_count.m, counts the number of columns in the first line of a file.
• file_name_ext_get.m, determines the "extension" of a file name.
• file_name_ext_swap.m, replaces the current "extension" of a file name.
• file_row_count.m, counts the number of row records in a file.
• i4mat_transpose_print_some.m, prints some of the transpose of an I4MAT.
• i4row_compare.m, compares two rows of an I4ROW.
• i4row_sort_a.m, ascending sorts the rows of an I4ROW.
• i4row_swap.m, swaps two rows of an I4ROW.
• itable_data_read.m, reads data from an integer table file.
• itable_data_write.m, writes data to an integer table file.
• itable_header_read.m, reads the header from an integer table file.
• itable_header_write.m, writes the header to an integer table file.
• itable_write.m, writes an integer table file.
• r8_epsilon.m, returns the R8 roundoff unit.
• r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.
• s_blank_delete.m, removes blanks from a string, left justifying the remainder.
• s_index_last_c.m, finds the LAST occurrence of a given character.
• s_len_trim.m, returns the length of a string to the last nonblank.
• s_word_count.m, counts the number of "words" in a string.
• sort_heap_external.m, externally sorts a list of items into ascending order.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• timestring.m, writes the current YMDHMS date into a string.
• triangulation_order3_neighbor_triangles.m, determines triangle neighbors.
• triangulation_order6_neighbor_triangles.m, determines triangle neighbors.

Examples and Tests:

Files associated with a 3-node triangulation:

• test3.out, 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.out, 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.

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