TRIANGULATION_ORDER3 is a dataset directory which contains examples of triangulation data of order 3.
Defining a triangulation requires two files:
Other files that may be supplied include:
For details of this format, go to ../../data/triangulation_order3/triangulation_order3.html
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
FEM_BASIS_T3_DISPLAY, a MATLAB program which displays a basis function associated with a 3-node triangle "T3" 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.
TRIANGULATE, a C program which triangulates a (possibly nonconvex) polygon.
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 data directory which defines TRIANGULATION_ORDER3 files, a description of 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 examples of TRIANGULATION_ORDER4 files, a description of 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.
TRIANGULATION_ORDER6, a dataset directory which contains examples of TRIANGULATION_ORDER6 files, a description of 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_ORIENT, a C++ program which ensures that the triangles in an order 3 or order 6 triangulation have positive orientation;
TRIANGULATION_PLOT, a C++ program which makes a PostScript image of a triangulation of points.
TRIANGULATION_QUALITY, a C++ program which computes quality measures of a triangulation.
ANNULUS is an annulus, a circular region with a circular hole.
There are 208 nodes and 384 elements and 1 hole.
BIG_CAVITY is a triangulation using 8,185 nodes and 4,000 elements.
BOX3 is a rectangular region.
The smallest angle is 45 degrees.
There are 20 nodes and 24 elements.
BOX_HOLE is a square with a circular hole.
Some of the elements are degenerate, and could be discarded.
There are 40,516 nodes and 79,921 elements.
BOXY is a simple non-Delaunay triangulation of 13 nodes using 16 elements.
CHANNEL3 is a rectangular region 1 unit high and 3 units wide.
The smallest angle is 45 degrees.
There are 65 nodes and 96 elements.
CIRCLE_HOLE3 is from a mesh for fluid flow
past a circular obstacle. The triangulation of the nodes was
created by the TRIANGLE program. This data was supplied
by Professor Hyung-Chun Lee.
The smallest angle is 28.79 degrees.
There are 968 nodes and 1783 elements and 1 hole.
DEVILLERS3 is data provided by
Olivier Devillers for the demonstration of a 2D Delaunay triangulation
program.
The smallest angle is 0.07 degrees.
There are 1000 nodes and 1981 elements.
ELBOW3 is an elbow-shaped region.
The smallest angle is 39.06 degrees.
There are 320 nodes and 568 elements.
ELL3 is an L shaped region.
The smallest angle is 45 degrees.
There are 21 nodes and 24 elements.
EXAMPLE_DELAUNAY is an example in which 16 nodes are arranged in a Delaunay triangulation.
EXAMPLE_NONDELAUNAY is an example in which the same 16 nodes used in the EXAMPLE_DELAUNAY example are arranged in a non-Delaunay triangulation. Since almost all triangulation algorithms use a Delaunay approach, it is important to see an occasional example of what a non-Delaunay triangulation looks like. Simply by looking at this mesh and the Delaunay triangulation of the same set of points, you should have some intuitive feeling that the Delaunay triangulation has better properities, even if you can't say immediately what those properties might be exactly!
GREENLAND is a triangulation using 33,343 nodes and 64,125 elements.
HANG3 is a rectangular region 8 units high and 8 units wide.
This example is interesting because it is a triangulation which includes
"hanging nodes", that is, nodes which are shared by two triangles, but
which are only a vertex of one of them. Triangulations which allow
hanging nodes can cause problems for many meshing algorithms.
This is not a maximal triangulation, since more nodes could be connected
without crossing existing edges; therefore it is not a Delaunay
triangulation.
The smallest angle is 18.43 degrees.
There are 12 nodes and 11 elements.
HEX_HOLES3 is a region with two hexagonal holes.
The smallest angle is 31.78 degrees.
There are 142 nodes and 237 elements and 2 holes.
HOLEY_PIE is a polygonal shape suggesting a slice of pie with a circular hole and a triangular notch.
HOT_PIPE3 is a sample region for the MATLAB program
FEM_50_HEAT,
defined on a 13x13 grid in the unit square.
The smallest angle is 45 degrees.
There are 169 nodes and 288 elements.
HOUSE3 is a child's image of a house using an
order 3 triangulation.
The smallest angle is 45 degrees.
There are 5 nodes and 3 elements.
LAKE_COARSE is an irregular lake with an island.
There are 621 nodes and 974 elements and 1 hole.
LAKE3 is an irregular lake with an island.
The smallest angle is 23.46 degrees.
There are 1552 nodes and 2820 elements and 1 hole.
SHRINK3 is a 16x15 rectangle which uses a "shrinking" grid
in which the triangles get smaller as they rise.
The smallest angle is 45 degrees.
There are 36 nodes and 45 elements.
SLIVER3 is rectangle divided into triangles, some of which are
long and thin. Such a triangulation often causes numerical errors.
The smallest angle is 0.42 degrees.
There are 14 nodes and 12 elements.
SMALL3 is a square with a 5 by 5 grid of nodes.
The smallest angle is 45 degrees.
There are 25 nodes and 32 elements.
TED3 is a triangulation which is a Delaunay triangulation.
Compare this with TEN3 which is a non-Delaunay triangulation of the
same set of nodes.
The smallest angle is 26.99 degrees.
There are 10 nodes and 10 elements.
TEN3 is a triangulation which is NOT a Delaunay triangulation.
Compare this with TED3 which is a Delaunay triangulation of the same
set of nodes.
The smallest angle is 9.97 degrees.
There are 10 nodes and 10 elements.
TRIANGLE3 is a single triangle.
The smallest angle is 60 degrees.
There are 3 nodes and 1 element.
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