Medial Spheres for Shape Approximation

Abstract

We study the problem of approximating a solid with a union of overlapping spheres. We introduce a method based on medial spheres which, when compared to a state-of-the-art approach, offers more than an order of magnitude speedup and achieves a tighter volumetric approximation of the original mesh, while using fewer spheres. The spheres generated by our method are internal to the object, which permits an exact error analysis and comparison with other sphere approximations. We demonstrate that a tight bounding volume hierarchy of our set of spheres may be constructed using rectangle-swept spheres as bounding volumes. Further, once our spheres are dilated, we show that this hierarchy generally offers superior performance in approximate separation distance tests.