Delaunay on Surface

This is a useful tip both to solve some of the problems with custom surface subdivisions, and to explain the uses of parametric surface evaluations (the U,V,W thing) and the practical use of data lists.

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Step 1: Put your points inside 0,0,0 and 1,1,0 so that the resulting coordinates can easily be converted to U and Vs. In the example, we are putting some random points between 0,0 and 1,1 using Populate2d component.

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Step 2: Then make whatever you want with these points. For example we can create voronoi subdivision or delaunay triangulation, or just draw something with a polyline there. This will be the drawing that is to be mapped onto the surface.

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Step 3: Explode the curves generated at Step 2 so that we’ll have the vertex connectivity sequences as a data list (or tree).

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Step 4: Just evaluate surface using the vertex coordinates as U, V values. Now the points should be on the surface if you choose “reparameterize” for the S input.

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Step 5: Finally join these mapped points again as a polyline to see that the explode operation did a good job in maintaining the order of the vertices so that we could easily re-create the curves on the surface.

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