How to do this with Delaunay Triangulation?

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Levente Kis 2021-2-26

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回答： YISONG PENG 2021-7-18

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I have X_0, Y_0 coordinates as column vectors and they can be plotted like in the following figure:

I am trying to create a Delaunay Triangulation with

DT = delaunayTriangulation(X_0,Y_0);
figure(1)
triplot(DT,'.-',"LineWidth",2,"MarkerSize",20);

and the result is the following:

As you can see there are many unnecessary lines and triangles in the circled area. What can I do to not have triangles in that area?

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John D'Errico 2021-2-26

What can you do? Don't use a delaunay triangulation. A delaunaytriangulation will result in a triangulation of the convex hull of the data. Those extra edges you see are a consequence of that.

You might try using a polyshape to describe the boundary of the region, as a non-convex polygon. Now use the triangulation method to form a triangulation of the domain.

Or, you might decide to form a constrained triangulation, where you force delaunayTriangulation to use specific edges. The result will still be convex. But now you can go in and delete the triangles with long edges.

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Answer 1

Bjorn Gustavsson 2021-2-26

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You'll have to go through DT.ConnectivityList and remove the triangles you don't like. The function returns a convex set of triangles so the triangulation you got is what's to be expected. You might also automate this by checking the side-lengths of the triangles and discard those that have to long sides, if that's what you prefer.

HTH