CSG Constructs for Free-Form Solids Bounded by Implicit Algebraic Patches

This chapter covers dual-representation (Brep, CSG) systems and summarizes algorithms for converting between Brep (Boundary representation) and CSG (Constructive Solid Geometry). Hard problems (such as separation) in Brep-to-CSG conversion, and the lack of exact CSG support for free-form solids are identified as the key limitations that led to the decline of dual [Brep, CSG] systems. The chapter then addresses these limitations and covers in details the topics of exact CSG and efficient Brep-to-CSG conversion for free-form solids bounded by implicit algebraic patches. A related CSG construct - Constructive Shell Representation (CSR) - provides an alternate complete representation scheme with potential applications that exploit CSR's hybrid Brep/CSG character. All CSG constructs can now be processed on massively parallel machines based on a CSG-architecture. In particular, several applications are run on the RayCasting Engine (RCE), including shading, Monte Carlo based realistic rendering, Booleans, sweeping, Minkowski operations, and Numerical Control (NC) machining.