Adaptive polygonalization of implicitly defined surfaces

Abstract

A method for finding an adaptive polygonal approximation of an implicitly defined surface is presented. For algebraic surfaces, the method yields an approximation guaranteed accurate to within some user-specified tolerance of the actual surface. This polygonalization can then be rendered using standard shaded polygon drawing techniques. A method for eliminating or improving the aspect ratios of the 'skinny' polygons that often arise in traditional polygonalization methods is also presented. This method has proved particularly useful in the creation of polygonalization for finite-element analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>