This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three dimensional search to two dimensions.

. This paper describes a simple algorithm for the adaptive polygonization of implicit surfaces. It gives a practical way to construct optimal piecewise linear representations. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by reducing part of the full three dimensional search to two dimensions. 1 Introduction Implicit models constitute a powerful mathematical description of the geometry of three dimensional objects [10]. Under this framework, a surface is defined as the set of points which satisfy the equation f(x; y; z) = 0. Simple primitive implicit shapes can be specified by algebraic functions, such as quadrics, [5]. More complex implicit shapes can be specified by combining primitives using point set or blend operations that are the basis of, respectively, CSG, [13], and Blobby models, [4]. The implicit descriptio...