The construction method is based on the Delaunay tetrahedralization of points in three dimensions and uses the half-space constraints imposed by the visibility directions of boundary points. The simplification method is based on the concept of sphericity . Sphericity is a quantity that measures how well a set of spheres is approximated by a single sphere. This allows us to reduce the number of primitives in a controlled way, while keeping the union of spheres model. It can also be used to stabilize the union of spheres model, i.e., to make it independent of the noise in the samples or other small distortions in the data.
Several examples illustrate the algorithm.