How to calculate the moment of inertia of a convex hull?

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Ricardo Vega Ayora
Ricardo Vega Ayora 2018-6-24
评论： Image Analyst 2018-6-25
I want to calculate the moment of inertia of the convex hull that surrounds points in a 3D space. Assuming, of course, that the mass and/or the density of the volume are known. I've seen the convhull function and the code by Michael Kleder to calculate the hull's volume and centroid, but how can I get the inertia matrix/tensor?
Additionally, I've ported the C code by Brian Mirtich into matlab, but it requires that the vertices of the faces to be ordered in a counterclock-wise direction. Is there a way to be independent form the clockwise or counterclock-wise faces?

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Anton Semechko
Anton Semechko 2018-6-24
Here is a link to a function on FEX that computes inertia tensors of objects represented by triangular surface meshes: https://www.mathworks.com/matlabcentral/fileexchange/48913-compute-exact-rigid-body-parameters-of-objects-represented-by-triangular-surface-meshes
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Anton Semechko
Anton Semechko 2018-6-25
No worries. Let me know if you have any problems using this function with your meshes.

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Image Analyst
Image Analyst 2018-6-25
For what it's worth, attached is my image moments demo. It's only 2-D though, not 3-D, but I think adapting it would be easy.
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Ricardo Vega Ayora
Ricardo Vega Ayora 2018-6-25
Given that you are working with pixels and not with position vectors for the points, how accurate is your method? Does it depend much on the image's resolution?
Image Analyst
Image Analyst 2018-6-25
Yes. It's a numerical solution, not an analytical one, so it will depend on the quantization (image resolution).

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