It may be a stretch, but could these values be used in the solver? I saw someone using a different CAD use a volume constraint to set the height of a container. I doubt that's really feasible here, just wanted to share the thought.

The function of a volume from dimensions is not in general analytical, is it?

That's an interesting idea. But apart from the Volume(dimensions) function not being analytical, the volume is calculated on the triangle mesh - which is certain to cause "noise" in the value.

@whitequark That was a dumb question from me. Of course volume is computed numerically from the shell/mesh. While there may (theoretically) be a way to twiddle free parameters to get numeric derivatives, that isn't a thing in SS.

@ruevs Good point. A simple triangle mesh shouldn't be a problem but when the number of triangles changes there would be a discontinuity in the calculated volume.

Do the triangles have a consistent ordering? Meaning ABC is always CCW or CW when viewed from the outside? If so, the volume can be calculated by summing a.Cross(b).Dot(c)/6 for all the triangles. That would be a lot less code.

@phkahler look at the STriangle::SignedVolume used in GetCenterOfMass(). Code of @jwesthues leaved intentionally since I have no ability to test new volume calculation funtions.

BTW can someone explain me why I wrote div by 4 instead of div by 3 here:
https://github.com/solvespace/solvespace/blob/master/src/mesh.cpp#L352
I can't remember why, so this is probably a typo (since 3 and 4 close to each other).

@Evil-Spirit The division by 4 is because you're calculating the centre of a tetrahedron formed by the 3 triangle verticies and the origin. No need to add in the vector (0,0,0) but you still need to divide by 4 since there really are 4.

So to my point, you can just sum the STriangle::SignedVolume() of each triangle to get the total volume. Its implementation is exactly what I indicated in the previous comment.

This is explained in the following stack overflow question:
general-formula-to-calculate-polyhedron-volume

So to my point, you can just sum the STriangle::SignedVolume() of each triangle to get the total volume.
Its implementation is exactly what I indicated in the previous comment.

Yes this will be good. You are welcome to contribute!

@whitequark Does anything else need to be done for this to get in?

@phkahler Yes--SMesh::CalculateSurfaceArea shouldn't be a function on the mesh. As usual with commits that combine random refactoring that wasn't even necessary with adding a feature, it takes a while to review and merge.

@whitequark please, write more arguments why SMesh::CalculateSurfaceArea should be implemented in different way.
@phkahler it needs to be merged by hands because I used an old branch where some fixes about dimensions was not made. Sorry, I have no to time to rebase.

please, write more arguments why SMesh::CalculateSurfaceArea should be implemented in different way.

Sorry, I was wrong because I misread the code. I'll merge it soon.

@Evil-Spirit Thank you for this contribution. Merged as 915f55a and 7f9117b.