  We show how to compute the circular area invariant of planar curves, and the
spherical volume invariant of surfaces, in terms of line and surface integrals,
respectively. We use the Divergence Theorem to express the area and volume
integrals as line and surface integrals, respectively, against particular
kernels; our results also extend to higher dimensional hypersurfaces. The
resulting surface integrals are computable analytically on a triangulated mesh.
This gives a simple computational algorithm for computing the spherical volume
invariant for triangulated surfaces that does not involve discretizing the
ambient space. We discuss potential applications to feature detection on broken
bone fragments of interest in anthropology.
