Nonsplitting Macro Patches for Implicit Cubic Spline Surfaces

Abstract

Macro patches are important for generating quadric or cubic implicit spline surfaces from the input of a polyhedron. All existing macro patches split the triangular facets of the polyhedron- this paper presents cubic nonsplitting macro patches (NMP) that do not split these facets. The NMP s are based on a necessary and sufficient condition for nonsplitting constructions of implicit cubic spline surfaces. This condition can be satisfied for most practical applications, so the NMP s lead to an efficient and powerful spline surface scheme using implicit cubics. The free parameters in an NMP are set using a new technique for excluding topological anomalies such as extraneous sheets, splits, unwanted holes, self-intersections, and unwanted handles. Each cubic patch obtained by this technique best approximates, in a least-squares sense, a quadric patch from a single algebraic component of a monotone polynomial derived from the input data.