Common Volume/Intersection Volume between two Delaunay Triangulations
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Hello Everyone
I am creating a bunch of 3D Delaunay Triangulations from the different set of points and for any pair of 3D Delaunay Triangulations, I need to calculate the volume which is common to both 3D Delaunay Triangulations. There are number of pairs which share volume and I need to calculate the values of these shared volumes.
Does anyone have a quick and nice method to calculate this ?
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Answers (2)
Teja Muppirala
on 21 Feb 2013
Sounds like a difficult problem to do exactly/analytically. I think you can get a very good approximation using a much simpler method.
1. Make a regular 3d grid of points using NDGRID that spans the box containing both of your triangulations.
2. For each point in the 3d grid, see if it is inside both triangulations. (The file exchange has fast algorithms for testing this)
3. Count the number of points from step 2, divide by the total number of points in the grid, and scale it by the volume of the box.
4. Go back to #1, increase the number of points, repeat until you verify convergence.
You could also use random numbers instead of a regular grid.
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