Implicit Modeling

Abstract

Implicit modeling in computer graphics covers many different methods for defining models. These include skeletal implicit modeling, offset surfaces, level sets, variational surfaces, and algebraic surfaces. In this chapter, the authors briefly touch on these methods and describe how to build skeletal implicit models in more detail. Despite the computational overhead of finding the implicit surface, designing with implicit modeling techniques offers some advantages over other modeling methods. Many geometric operations are simplified using implicit methods including: the definition of blends; the standard set operations (union, intersection, difference, etc.) of constructive solid geometry (CSG); functional composition with other implicit functions (e.g., R-functions, Barthe blends, Ricci blends, and warping); and inside/outside tests, (e.g., for collision detection). The authors also describe the original space partitioning algorithm and explore the more advanced methods. This algorithm together with postprocessing for mesh refinement and caching provide a method for interactive viewing of implicit models on modern workstations.