Boundary to Constructive Solid Geometry: A Step Towards 3D Conversion

Abstract

Several solid representation schemes exist today in solid modeling. As none of them has properties that are uniformly better than any other, the need for modeling systems working on two or more different schemes which perform every operation in the most suitable scheme, became evident. Then it is necessary to provide geometric modeling systems with the ability of converting from one scheme into another scheme. As most solid modellers use either, a boundary representation (BR) or a constructive solid geometry representation (CSG), conversion from one into the other appears to be of capital importance. Conversion from CSG into BR has been carefully studied but a few attention has been deserved to the conversion from BR to CSG. This paper presents an algorithm which generates CSG binary trees from BR representations over a restricted class of polyhedra. The tree is optimal in the output size. Unfortunately, the algorithm does not in general warrant a correct conversion and, consequently some open questions and ideas for further research are presented.