Smoothing polyhedra using implicit algebraic splines

Polyhedron "smoothing" is an efficient construction scheme for generating complex boundary models of solid physical objects. This paper presents efficient algorithms for generating families of curved solid objects with boundaty topology related to an input polyhedron. Individual faces of a polyhedron are replaced by low degree implicit algebraic surface patches with local support. These quintic patches replace the @ contacts of planar facets with C' continuity along all irtterpatch boundaries. Selection of suitable instances of implicit surfaces as well as local control of the individual surface patches are achieved via simultaneouss interpolation and weighted least-squares approximation.