triangulation_corner_test

triangulation_corner_test, a MATLAB code which calls triangulation_corner(), which corrects situations in which a triangulation includes corner triangles, that is, triangles which have two sides on boundary.

Licensing:

The information on this web page is distributed under the MIT license.

Related Data and Programs:

triangulation_corner, a MATLAB code which patches triangulations so that no triangle has two sides on the boundary.

Source Code:

• triangulation_corner_test.m, calls all the tests.
• triangulation_corner_test.sh, runs all the tests.
• triangulation_corner_test.txt, the output file.

P03 is the square with a hole. The initial mesh has 1 corner triangle.

• p03_nodes.txt the mesh nodes of the problem.
• p03_elements.txt the mesh triangles of the problem.
• p03.png a PNG image of the initial mesh.
• p02_corner_elements.txt the triangle file after corner triangles have been repaired.
• p02_corner.png a PNG image of the repaired mesh.

P05 is the horn. The initial mesh has 4 corner triangles.

• p05_nodes.txt the mesh nodes of the problem.
• p05_elements.txt the mesh triangles of the problem.
• p05.png a PNG image of the initial mesh.
• p05_corner_elements.txt the triangle file after corner triangles have been repaired.
• p05_corner.png a PNG image of the repaired mesh.

P08 is the holey pie slice. The initial mesh has 2 corner triangles.

• p08_nodes.txt the mesh nodes of the problem.
• p08_elements.txt the mesh triangles of the problem.
• p08.png, a PNG image of the initial mesh.
• p08_corner_elements.txt the triangle file after corner triangles have been repaired.
• p08_corner.png a PNG image of the repaired mesh.

P09 is Jeff Borggaard's square with two hexagonal holes. The initial mesh has 3 corner triangles.

• p09_nodes.txt the mesh nodes of the problem.
• p09_elements.txt the mesh triangles of the problem.
• p09.png a PNG image of the initial mesh.
• p09_corner_elements.txt the triangle file after corner triangles have been repaired.
• p09_corner.png a PNG image of the repaired mesh.

P10 is the unit square. The initial mesh has 4 corner triangles.

• p10_nodes.txt the mesh nodes of the problem.
• p10_elements.txt the mesh triangles of the problem.
• p10.png a PNG image of the initial mesh.
• p10_corner_elements.txt the triangle file after corner triangles have been repaired.
• p10_corner.png a PNG image of the repaired mesh.

P11 is the L-shaped region. The initial mesh has 4 corner triangles.

• p11_nodes.txt the mesh nodes of the problem.
• p11_elements.txt the mesh triangles of the problem.
• p11.png a PNG image of the initial mesh.
• p11_corner_elements.txt the triangle file after corner triangles have been repaired.
• p11_corner.png a PNG image of the repaired mesh.

Q11 is the L-shaped region, but with quadratric (6 node) triangles. The initial mesh has 4 corner triangles. Because we are using quadratic triangles, when we merge two triangles and swap the diagonal, the midside node on the common diagonal will no longer lie on a line, midway between the two vertices. TRIANGULATION_CORNER assumes this is undesirable, and recomputes the coordinates of such midside nodes, and outputs a modified node coordinate file as well as the new triangle file.

• q11_nodes.txt the mesh nodes of the problem.
• q11_elements.txt the mesh triangles of the problem.
• q11.png a PNG image of the initial mesh.
• q11_nodes.corner.txt the node coordinate file after corner triangles have been repaired, which, for quadratric triangles, requires adjusting some midside nodes.
• q11_corner_elements.txt the triangle file after corner triangles have been repaired.
• q11_corner.png a PNG image of the repaired mesh.

P12 is the John Shadid's H-shaped region. The initial mesh has 7 corner triangles.

• p12_nodes.txt the mesh nodes of the problem.
• p12_elements.txt the mesh triangles of the problem.
• p12.png a PNG image of the initial mesh.
• p12_corner_elements.txt the triangle file after corner triangles have been repaired.
• p12_corner.png a PNG image of the repaired mesh.

P13 is the Sandia fork. The initial mesh has 6 corner triangles.

• p13_nodes.txt the mesh nodes of the problem.
• p13_elements.txt the mesh triangles of the problem.
• p13.png a PNG image of the initial mesh.
• p13_corner_elements.txt the triangle file after corner triangles have been repaired.
• p13_corner.png a PNG image of the repaired mesh.

P14 is Marcus Garvie's Lake Alpha, with Beta Island. The initial mesh has 5 corner triangles. (Must be small!)

• p14_nodes.txt the mesh nodes of the problem.
• p14_elements.txt the mesh triangles of the problem.
• p14.png a PNG image of the initial mesh.
• p14_corner_elements.txt the triangle file after corner triangles have been repaired.
• p14_corner.png a PNG image of the repaired mesh.

P15 is Sangbum Kim's forward step region. The initial mesh has 6 corner triangles.

• p15_nodes.txt the mesh nodes of the problem.
• p15_elements.txt the mesh triangles of the problem.
• p15.png a PNG image of the initial mesh.
• p15_corner_elements.txt the triangle file after corner triangles have been repaired.
• p15_corner.png a PNG image of the repaired mesh.

P16 is Kevin Pond's elbow, a quarter of a circular annulus. The initial mesh has 1 corner triangle.

• p16_nodes.txt the mesh nodes of the problem.
• p16_elements.txt the mesh triangles of the problem.
• p16.png a PNG image of the initial mesh.
• p16_corner_elements.txt the triangle file after corner triangles have been repaired.
• p16_corner.png a PNG image of the repaired mesh.

P17 is the rectangular channel with a Reuleaux triangle obstacle. The initial mesh has 4 corner triangles.

• p17_nodes.txt the mesh nodes of the problem.
• p17_elements.txt the mesh triangles of the problem.
• p17.png a PNG image of the initial mesh.
• p17_corner_elements.txt the triangle file after corner triangles have been repaired.
• p17_corner.png a PNG image of the repaired mesh.