Volume of 3D polyhedron

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slaiyer on 24 Aug 2014
Commented: Iila on 25 Feb 2016
Given a set of 3D coordinates, how can one find the volume of the polyhedron that is not necessarily convex?
Iila on 25 Feb 2016
Thank you. But it doesn't. My polyhedra are concave. I also want to calculate the self intersecting volume, if any.

Mike Garrity on 24 Feb 2016
One option you might look at is alphaShape. It's similar to convhull, but more general. It will create non-convex shapes.
You use it like this. First I need a simple cloud of points.
npts = 75;
pts = randn(npts,3);
scatter3(pts(:,1),pts(:,2),pts(:,3),'filled')
Then I create my alphaShape, and plot it.
shp = alphaShape(pts);
h = plot(shp);
But the reason this might be useful for you, is that it has a method that will return the volume of the shape:
volume(shp)
ans =
27.3914
And another method which will tell you whether other points are inside the shape.
testpts = randn(150,3);
h.FaceColor = [.75 .75 .75];
h.FaceAlpha = .25;
hold on
slaiyer on 24 Feb 2016
This seems to be exactly what I was looking for back then. Thanks a lot for your input; cheers!

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