These are some examples of TRIANGULATION data of order 3; defining a triangulation requires two files:
This is the simplest form of a triangulation. It is sometimes called a linear triangulation.
The point sets are distinguished by the values of the following parameters:
At the moment, no facility is provided for allowing the specification of constrained edges, or the existence of holes in the region, both of which are of some interest.
The FEM format is used to store a finite element model. It includes a node and element file, as well as a node data file. The node and triangle files described here are an example of the first two of these files.
MESH_BANDWIDTH is an interactive executable FORTRAN90 program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.
The TABLE format is used for both the node and triangle files.
TRIANGULATION_ORDER6 describes the related idea of a quadratic triangulation in which each triangle is defined by 6 nodes.
TRIANGULATION_PLOT is an executable FORTRAN90 program which can create an Encapsulated PostScript image of a triangulation.
As a simple example, suppose we had the following set of points:
16 17 18
11 12 13 14 15
6 7 8 9 10
1 2 3 4 5
then the node file might look like this:
# Node file for simple example.
#
0.0 0.0
1.0 0.0
2.0 0.0
3.0 0.0
4.0 0.0
0.0 1.0
1.0 1.0
2.0 1.0
3.0 1.0
4.0 1.0
0.0 2.0
1.0 2.0
2.0 2.0
3.0 2.0
4.0 2.0
0.0 3.0
1.0 3.0
2.0 3.0
A possible order 3 triangulation of these nodes is:
16-17-18
|\ |\ |
| \| \|
11-12-13-14-15
|\ |\ |\ |\ |
| \| \| \| \|
6--7--8--9-10
|\ |\ |\ |\ |
| \| \| \| \|
1--2--3--4--5
in which case the triangle file would loook like this:
# Triangle file for simple example.
#
1 2 6
7 6 2
2 3 7
8 7 3
3 4 8
9 8 4
4 5 9
10 9 5
6 7 11
12 11 7
7 8 12
13 12 8
8 9 13
14 13 9
9 10 14
15 14 10
11 12 16
17 16 12
12 13 17
18 17 13
The triangles could be listed in any order. The three nodes
of the triangle could be listed in any counterclockwise
order.
A node file can come from anywhere. In most cases, you generate this data by observation or the characteristics of a particular problem or set of data you are working on.
Once you have generated a node file, it is possible to generate a triangulation of the nodes. Programs and routines to create a triangulation include
BOX_ORDER3 is a rectangular region.
CHANNEL_ORDER3 is a rectangular region 1 unit high and 3 units wide.
CIRCLE_HOLE_ORDER3 is a set of 968 points, making 1783 triangles. The resulting mesh was used to study the problem of 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.
DEVILLERS_ORDER3 is a set of 1000 points in 2D provided by Olivier Devillers for the demonstration of a 2D Delaunay triangulation program.
DOUBLE_HEX2 is a region with two hexagonal holes, and a set of 48 points specified along the boundary and the holes. An unconstrained Delaunay triangulation program will not recognize that we do not want to triangulate the hexagonal holes, so in that case we will need to manually delete such triangles.
ELL_ORDER3 is an L shaped region, triangulated using order 3 triangles.
HEX_CVT_ORDER3 is a region with a pair of hexagonal holes, which was meshed by a CVT code.
HEX_TRIANGLE_ORDER3 is a region with a pair of hexagonal holes, which was meshed by TRIANGLE.
HOT_PIPE_ORDER3 is a sample region for the MATLAB program FEM_50_HEAT, defined on a 13x13 grid in the unit square.
HOUSE_ORDER3 is a child's image of a house using an order 3 triangulation.
LAKE_ORDER3 is an irregular lake with an island. (Data supplied by Marcus Garvie.).
SMALL_ORDER3 is a square with a 5 by 5 grid of nodes, creating 32 elements of 3-node triangles.
TRIANGLE_ORDER3 is a single order 3 triangle.
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