Indeed, you can compute the exact volume of a closed triangle mesh by summing signed volumes of tetrahedra. The tessellation doesn't even need to be any good, you can just use one tetrahedron for each triangle, constructed from the triangle vertices and one other fixed point (typically the origin). http://stackoverflow.com/questions/1406029/how-to-calculate-the-volume-of-a-3d-mesh-object-the-surface-of-which-is-made-up
By summing the centers of mass of these tetrahedra, weighted by the signed volume, then I guess you get the center of mass of the whole mesh too? I didn't check the math but intuitively it makes sense to me. This algorithm does require the mesh to be closed. For non-closed meshes the fixed point could perhaps be the center of mass as computed now, that might give a reasonable approximation. On Sun, Jun 16, 2013 at 5:07 AM, panjz <[email protected]> wrote: > How about tetrahedron tessellation algorithm? IMO it will produce *exact* > result (no mathematical proof because I think it's trivially true ;) Correct > me if I'm wrong ) if the density of material is constant. If we only need to > calculate center of mass we can allow 'negative' tetrahedron in tessellation, > i.e. tetrahedron with negative orientation, hence negative mass. You can look > at 2D case, it should be much simpler (triangle tessellation with 'negative' > triangle allowed) and the whole idea is same. > >> Date: Sat, 15 Jun 2013 23:26:43 +0100 >> From: [email protected] >> To: [email protected]; [email protected] >> Subject: Re: [Bf-committers] Blender Center of Mass - Voxel data better >> algorithm? >> >> Is the problem different vertex density? >> I don't know how it is currently implemented, but, if vertex density is the >> problem, the face's area can weight in with no need for voxel dataset. >> >> -- >> Inês Almeida >> _______________________________________________ >> Bf-committers mailing list >> [email protected] >> http://lists.blender.org/mailman/listinfo/bf-committers > > _______________________________________________ > Bf-committers mailing list > [email protected] > http://lists.blender.org/mailman/listinfo/bf-committers _______________________________________________ Bf-committers mailing list [email protected] http://lists.blender.org/mailman/listinfo/bf-committers
