triangulation_quality

triangulation_quality, a MATLAB code which computes and prints a variety of 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 triangulation.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT 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 code which carries out triangular or tetrahedral mesh generation, by per-olof persson and gilbert strang.

mesh2d, a MATLAB code which can automatically create a triangular mesh for a given polygonal region, by darren engwirda.

tet_mesh_quality, a MATLAB code which computes quality measures of a tetrahedral mesh.

triangulation, a MATLAB code 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 directory which contains a description and examples of order 6 triangulations.

triangulation_quality_test

Source Code:

• triangulation_quality.m, the source code.