IBNC: Integrated Boundary and Natural CSG for Polyhedra (Review, Simplifications, and Integration of Prior Art)

To improve rendering performance or reduce implementation difficulty, when rendering, animating, or processing a solid with curved faces, its polyhedral approximation is often used. The polyhedron, R, and each one of its faces are usually modeled in Brep (i.e. Boundary representation). To improve numeric accuracy and processing performance, it may be useful to also have an NCrep (i.e. Natural Constructive representation) that models R as the regularized CSG combination of the natural halfspaces, which are bounded by planes that contain the faces referenced in the Brep. We review several BtoNC (Brep to NCrep) conversion schemes and propose a simplification, a reformulation, and a novel combination of some of them to define a new NCrep representation, which we named MAS (for Match Aggregate of Sectors), where each cell (i.e. face, edge, vertex), c, of R is associated with a sector, an NCrep of the localization of R to the neighborhood of c. R, each face of R, and the sector of each vertex of R are the regularization of their MAS or of its complement. The proposed IBNC (Integrated Boundary and Natural CSG) annotates the Brep corners with easily computed binary tags, making it possible to process each MAS directly (i.e. without BtoNC conversion).