TRIANGULATION_QUALITY
Triangulation Quality Measures

TRIANGULATION_QUALITY is a FORTRAN90 program which computes and prints quality measures for a given triangulation of a set of points in 2D.

The triangulation is defined by a node file containing the coordinates of nodes, and a triangle file containing sets of 3 or 6 node indices.

The quality measures computed include:

• Alpha, the minimum angle divided by the maximum possible minimum angle.
• Area, the ratio of the minimum area to the maximum area;
• Q, the triangle shape uniformity measure, twice the radius of the inscribed circle divided by the radius of the circumscribed circle;

Each quality measure is defined as the minimum of its value over all the triangles; the maximum and best possible value is 1, and the minimum and worst possible value is 0.

Usage:

triangulation_quality prefix

• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the element definitions.

Licensing:

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

Languages:

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

Related Data and Programs:

DISTMESH, a MATLAB library which carries out triangular or tetrahedral mesh generation, by Per-Olof Persson and Gilbert Strang.

MESH2D, a MATLAB library which can automatically create a triangular mesh for a given polygonal region, by Darren Engwirda.

TET_MESH_QUALITY, a FORTRAN90 program which computes quality measures of a tetrahedral mesh.

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

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

TRIANGULATION_ORDER3, a 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.

Source Code:

• triangulation_quality.f90, the source code.

Examples and Tests:

ELL3 is a set of nodes in an L-shaped region, which have been arranged into an order 3 triangulation.

• ell3_nodes.txt, the node file.
• ell3_elements.txt, the element file.
• ell3_quality.txt, the report from the program.

HEX_HOLES6 is a set of nodes in an square region, with two hexagonal holes, which have been arranged into an order 6 triangulation.

• hex_holes6_nodes.txt, the node file.
• hex_holes6_elements.txt, the element file.
• hex_holes6_quality.txt, the report from the program.

List of Routines:

• MAIN is the main program for TRIANGULATION_QUALITY.
• ALPHA_MEASURE determines the triangulated pointset quality measure ALPHA.
• ARC_COSINE computes the arc cosine function, with argument truncation.
• AREA_MEASURE determines the area ratio quality measure.
• BANDWIDTH determines the bandwidth associated with the finite element mesh.
• 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_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• ITABLE_DATA_READ reads data from an integer table file.
• ITABLE_HEADER_READ reads the header from an integer table file.
• Q_MEASURE determines the triangulated pointset quality measure Q.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• 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.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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