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geometrycgaltriangulationdelaunay

Triangulating a polygon with one hole

I'm trying to triangulate a polygon with one hole using Triangle project.

Does anyone have an example of feeding this algorithm with a polygon with a hole?

Solution

  • Here is an example of of .poly file with a hole:

    14 2 0 0
1 1 -1
2 1 1
3 .25 1.25
4 0 1
5 -.25 1.25
6 -1 1
7 -1 -1
8 -.25 -1.25
9 0 -1
10 .25 -1.25
11 .33 0
12 0 .33
13 -.33 0
14 0 -.33
14 0
1 10 1
2 1 2
3 2 3
4 3 4
5 4 5
6 5 6
7 6 7
8 7 8
9 8 9
10 9 10
11 11 12
12 12 13
13 13 14
14 14 11
1
1 0.0 0.0

    There are three sections in the file: the polygon vertices, the polygon segments and the hole specification. The last line indicates that the point (0,0) lies in a hole in the geometry and triangles in those components will be removed by triangle.

    In showme, this .poly file looks like this:

    polygon geometry

    The small "x" in the center indicates the location specified for the hole.

    Meshing this with the command triangle simple.poly -a0.06 -q20 gives the following result:

    resulting mesh