Problem statement
An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V, corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.
V = [1 0 0;
cos(2*pi/5) sin(2*pi/5) 0;
cos(4*pi/5) sin(4*pi/5) 0;
cos(4*pi/5) sin(-4*pi/5) 0;
cos(2*pi/5) sin(-2*pi/5) 0];
A triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles.
Your task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, F. The row order of the triangles in the list doesn't matter.
Example
The first triangle here can be [1, 2, 3] if counterclockwise oriented.
Tip
Beware to avoid self intersecting triangles.
Forbidden functions / expressions
- regexp
- assignin
- str2num
- echo
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To visualize and check your result you can do for instance :
trisurf(T,V(:,1),V(:,2),V(:,3));
colormap([0 1 1]);
axis equal, alpha(0.5);
Hi, I was wondering should the following mesh pass the test:
T = [1, 2, 3; 5, 1, 3; 4, 5, 3]
There should not be intersecting triangles, and the triangle vertices should be enumerated counter-clockwise.
Hi Pauli. You are right of course. Actually it corresponds to the test case #4,
T_correct4 = [3 4 5; 3 5 1; 3 1 2];
but while improving the tests, I forgot to put back the circular shift possibilities. I am going to do it now. Thanks again.
There was a little bug in the tests. I just fixed them. Thanks again for this feedback Pauli.