Joining polyhedral objects using implicitly defined surfaces

Abstract

Complex polyhedral objects are often constructed from simpler polyhedral objects using CSG, booleans and various blend operations that produce fillets and chamfers. Skinning and shrink wrapping techniques provide alternatives to generating a smooth composite object from individual object parts. This paper presents an effective and general technique for incrementally building complex polyhedral objects from simpler parts. We provide a procedural implicit function definition for a region of a polyhedral object that is star-shaped with respect to a skeletal point, called a blend center. We extend this definition to provide a single implicit function definition for an arbitrary polyhedral object, where every region is star-shaped with respect to a proximal blend center, chosen from an arbitrary set of blend centers. This allows the application of implicit function based modeling techniques in constructing transition surfaces between arbitrary polyhedral object parts. Generalizations of our approach allow the algebraic combination of arbitrarily shaped and positioned, disjoint object parts, and is thus a significant superset of CSG, booleans, and other blending techniques. At the same time original detail and character of object parts are preserved in regions where they are not involved in constructing transition surfaces or do not interact with other object parts. A complete implemetation of the presented concepts show polyhedral implicit primitives to be a general and efficient technique for building complex polyhedral objects from a modular set of polyhedral object parts.