triangulation_q2l, a C++ code which reads information describing a triangulation of a set of points using 6-node ("quadratic") triangles, and creates a 3-node ("linear") triangulation.
The same nodes are used, but each 6-node triangle is broken up into four smaller 3-node triangles.
Thus, the program might be given the following 4 triangles:
11-12-13-14-15
|\ |\ |
| \ | \ |
6 7 8 9 10
| \ | \ |
| \| \|
1--2--3--4--5
It would make a new triangulation involving 16 triangles:
11-12-13-14-15
|\ |\ |\ |\ |
| \| \| \| \|
6--7--8--9-10
|\ |\ |\ |\ |
| \| \| \| \|
1--2--3--4--5
The input and output files use the simple TABLE format; comment lines begin with a "#" character. Otherwise, each line of the file contains one set of information, either the coordinates of a node (for a node file), or the indices of nodes that make up a triangle, (for a triangle file).
The input file prefix_elements.txt contains the triangle information for the 6-node triangulation. Each line contains the indices of six nodes that form a triangle, in counterclockwise order. The first three indices are the vertices, in counterclockwise order. The fourth index is the midside node between vertices 1 and 2, the fifth the midside between vertices 2 and 3, and the sixth the midside between vertices 3 and 1.
The output file prefix_q2l_elements.txt contains the triangle information for the 3-node triangulation. The vertices for each triangle are listed in counterclockwise order. There are 4 times as many triangles in this triangulation.
triangulation_q2l prefixwhere prefix is the common filename prefix:
The computer code and data files described and made available on this web page are distributed under the MIT license
triangulation_q2l is available in a C++ version and a FORTRAN90 version and a MATLAB version.
TRIANGLE, 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_BOUNDARY_NODES, a C++ code which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.
TRIANGULATION_CORNER, a C++ code which patches triangulations so that no triangle has two sides on the boundary.
TRIANGULATION_DELAUNAY_DISCREPANCY, a C++ code which measures the amount by which a triangulation fails the local Delaunay test;
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TRIANGULATION_HISTOGRAM, a C++ code which computes histograms of data over a triangulation.
TRIANGULATION_L2Q, a C++ code which reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.
TRIANGULATION_MASK, a C++ code which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.
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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.
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TRIANGULATION_PLOT, a C++ code which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.
TRIANGULATION_QUAD, a C++ code which estimates the integral of a function over a triangulated region.
TRIANGULATION_QUALITY, a C++ code which reads data defining a triangulation and computes a number of quality measures.
TRIANGULATION_RCM, a C++ code which reads data defining a triangulation, determines an ordering of the nodes that will reduce the bandwidth of the adjacency matrix, and writes the new triangulation information to a file.
TRIANGULATION_REFINE, a C++ code 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, a C++ code which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.