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

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?

Answer 1

[Anton Semechko]

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

[Ricardo Vega Ayora]

Thanks! I've seen that it is actually your code, so great work!

[Anton Semechko]

No worries. Let me know if you have any problems using this function with your meshes.

Answer 2

[Image Analyst]

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.

[Ricardo Vega Ayora]

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]

Yes. It's a numerical solution, not an analytical one, so it will depend on the quantization (image resolution).