Geometric Boundary Modelling without Topological Data Structures

Abstract

The Boundary Representation (BR) scheme for solid modelling is reconsidered and generalized in the paper. It is pointed out that the topological data, though usually represented separately, is derivable from the geometric data, and that there are fundamental inconsistencies between these two. The topological data structures are unnecessary or even harmful in practice as they restrict the modelling domain. New BR methodology without explicit topology is demonstrated by algorithms, which manipulate a stream of separate polygons as a solid model.