TRIANGULATION_ORDER6
Examples of Order 6 Triangulations

TRIANGULATION_ORDER6 is a dataset directory which contains examples of triangulation data of order 6.

Defining a triangulation requires two files:

• the node file lists the coordinates of a set of points.
• the element file lists sets of six node indices, which are the vertices and side nodes.

For details of this format, go to ../../data/triangulation_order6/triangulation_order6.html

Licensing:

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

Related Data and Programs:

FEM, a data directory which contains examples of FEM files, three text files that can be used to describe many finite element models;

FEM_BASIS_T6_DISPLAY, a MATLAB program which displays a basis function associated with a 6-node triangle "T6" mesh.

MESH_BANDWIDTH, a C++ program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

TRIANGULATION, a C++ library which performs various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_BOUNDARY_NODES, a C++ program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a 2D triangulation and displays an image using OpenGL.

TRIANGULATION_ORDER3, a dataset directory which contains examples of TRIANGULATION_ORDER3 files, a linear triangulation of a set of 2D points, using a pair of files to list the node coordinates and the 3 nodes that make up each triangle;

TRIANGULATION_ORDER4, a dataset directory which contains TRIANGULATION_ORDER4 files, a triangulation of a set of 2D points, using a pair of files to list the node coordinates and the 4 nodes that make up each triangle (3 vertices and the centroid);

TRIANGULATION_ORDER6, a data directory which defines TRIANGULATION_ORDER6 files, a quadratic triangulation of a set of 2D points, using a pair of files to list the node coordinates and the 6 nodes that make up each triangle.

TRIANGULATION_PLOT, a C++ program which makes a PostScript image of a triangulation of points.

Sample Files:

BOX6 is a rectangular region.
The smallest angle is 45 degrees.
There are 63 nodes and 24 elements.

• box6_nodes.txt, the node coordinates.
• box6_elements.txt, the triangulation;
• box6_triangulation.png, a PNG image of the triangulation;
• box6_element_neighbors.txt, the neighbor triangles.
• box6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

CAVITY6 is a square region 1 unit high and 1 unit long, This data was supplied by Professor Hyung-Chun Lee.
There are 8,185 nodes and 4000 elements.

• cavity6_nodes.txt, the node coordinates.
• cavity6_elements.txt, the triangles.
• cavity6_triangulation.png, a PNG image of the triangulation.
• cavity6_element_neighbors.txt, the neighbor triangles.
• cavity6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

CHANNEL6 is a rectangular region 1 unit high and 3 units long.
There are 65 nodes and 24 elements.

• channel6_nodes.txt, the node coordinates.
• channel6_elements.txt, the triangles.
• channel6_triangulation.png, a PNG image of the triangulation.
• channel6_element_neighbors.txt, the neighbor triangles.
• channel6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

ELL6 is an L shaped region.
There are 21 nodes and 6 triangles.

• ell6_nodes.txt the node coordinates.
• ell6_elements.txt the triangles.
• ell6_triangulation.png is a PNG image of the triangulation.
• ell6_element_neighbors.txt, the neighbor triangles.
• ell6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

HEX_HOLES6 is a region with two hexagonal holes.
There are 142 nodes and 237 elements and 2 holes.

• hex_holes6_nodes.txt, the node coordinates.
• hex_holes6_elements.txt, the triangles.
• hex_holes6_triangulation.png, a PNG image of the triangulation.
• hex_holes6_element_neighbors.txt, the neighbor triangles.
• hex_holes6_boundary_nodes.txt, the nodes that lie on the boundary;
• hex_holes6_boundary_nodes.png, a PNG image of the boundary nodes.
• hex_holes6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

HOUSE6 is a child's image of a house.
There are 5 nodes and 3 elements.

• house6_nodes.txt, the node coordinates.
• house6_elements.txt, the triangles.
• house6_triangulation.png, a PNG image of the triangulation;
• house6_element_neighbors.txt, the neighbor triangles.
• house6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

IRREG6 is an irregular boxy region surrounding a hole.
There are 37 nodes and 10 elements and 1 hole.

• irreg6_nodes.txt, the node coordinates.
• irreg6_elements.txt, the triangles.
• irreg6_triangulation.png, a PNG image of the triangulation;
• irreg6_element_neighbors.txt, the neighbor triangles.
• irreg6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

SMALL6 is a square with a 5 by 5 grid of nodes.
There are 25 nodes and 8 elements.

• small6_nodes.txt, the node coordinates.
• small6_elements.txt, the triangles.
• small6_triangulation.png, a PNG image of the triangulation.
• small6_element_neighbors.txt, the neighbor triangles.
• small6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

TRIANGLE6 is a single order 6 triangle.
There are 6 nodes and 1 element.

• triangle6_nodes.txt, the node coordinates.
• triangle6_elements.txt, the triangles.
• triangle6_triangulation.png, a PNG image of the triangulation.
• triangle6_element_neighbors.txt, the neighbor triangles.
• triangle6_boundarynodes.txt, contains 0 for interior nodes, 1 for boundary nodes.

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