Multiresolution for Algebraic Curves and Surfaces Using Wavelets

Abstract

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero-valued algebraic isosurface of a tensor-product uniform cubic Bspline. A wavelet multiresolution method that deals with uniform cubic Bsplines on bounded domains has been constructed. Further, the report explains how to set the unknown coefficients to produce the most compact object, how to recover the initial object, a suitable data structure and, finally, points out several improvements that might produce better results. Keywords: geometric modeling, algebraic surfaces, wavelets, multiresolution, topological simplification, conversion algorithms. 2 1 Introduction In this paper a curve and surface multiresolution method that simplifies the topology is presented. We will work with algebraic curves and surfaces defined as the zero-valued algebraic isosurface of a tensor-product ..