POLYGONIZATION OF NON-MANIFOLD IMPLICIT SURFACES

Abstract

We present a new method to define implicit surfaces, broadening the scope of implicit surface modeling. The implicit surfaces usually employed in Computer Graphics have been limited to two dimensional manifolds. These surfaces are defined by real valued functions that impose a binary partitioning of space (i.e., they represent solid models that define an inside and an outside). When tiled, these surfaces yield tessellations whose edges are all of multiplicity 2. The method presented here allows for the definition of implicit surfaces with borders (i.e., edges of multiplicity 1) and intersections (i.e., edges of multiplicity 3 or more). These non-manifold implicit surfaces are defined by a multiple (rather than binary) partitioning of space. The object definition includes a list of those pairs of regions whose separating surface is of interest. We also present an implementation for a polygonizer that converts a non-manifold implicit surface definition into a collection of polygons. Although following the basic steps of a conventional implicit surface polygonizer, there are several significant differences necessitated by the multiple partitioning of space.