Octtrees Meet Splines

摘要

In this paper, the smooth isosurface generation from a set of voxels representing either a volumetric model or a discretization of a given solid is addressed. It is assumed that a certain isosurface value has been already given and that the set of voxels stabbing this value has been extracted for the volumetric model. The goal is to obtain an smooth, C~2, piecewise algebraic surface representing the isosurface. The proposed approach adds one dimension to the problem and works by considering a scalar function with domain coinciding with the octtree (or voxels) universe. An iterative local filter- ing operator is derived and discussed through several examples.