While adding physics support to my voxel engine I needed a reasonable accurate & fast method to calculate the moment of inertia, volume, and center of mass for an arbitrary distance field.
I've written this C++ code to do so.
Feed it a regularly spaced grid of points and distances.
The points must fully bound the negative space of the field to be accurate.
The common primitives, such as a sphere, there are established formulas that we can compare against.
For a 10^3 distance field of a sphere, the estimate is off by about 1%, close enough for me.
If more accuracy is needed, the sample rate can be increased.