triangulation_quality

triangulation_quality, a C++ code 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 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:

TET_MESH_QUALITY, a C++ code which computes quality measures of a tetrahedral mesh.

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

TRIANGULATION a C++ code which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_NODE_TO_ELEMENT, a C++ code which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an "order1" finite element model of the data.

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_quality_test

Reference:

1. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
   Computational Geometry,
   Springer, 2000,
   ISBN: 3-540-65620-0.
2. David Field,
   Qualitative Measures for Initial Meshes,
   International Journal of Numerical Methods in Engineering,
   Volume 47, 2000, pages 887-906.
3. Joseph ORourke,
   Computational Geometry,
   Second Edition,
   Cambridge, 1998,
   ISBN: 0521649765,
   LC: QA448.D38.
4. Per-Olof Persson, Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, pages 329-345, June 2004.

Source Code:

• triangulation_quality.cpp, the source code.
• triangulation_quality.sh, compiles the source code.