Universit a Degli Studi Bijective Dimension-independent Boundary to Interior Mapping with Bsp Trees

In this paper we discuss two algorithms for performing both ways the conversion between the boundary and the interior of d-dimensional polyhedra. Both a d-polyhedron and its (d 1)-faces are represented as BSP trees. An algorithm for boundary to BSP conversion starting from a standard B-rep was given by Thibault and Naylor in [15]. In this paper we assume no structure, no ordering and even no orientation on the set of boundary BSP-trees. The resulting algorithm can be executed on a parallel computing architecture. Also, if the incidence relations between faces of various dimension are known, then the algorithm can be executed iteratively, so allowing for reconstructing a d-polyhedron from its (d k)-faces, 1 k d. The converse algorithm allows to compute the BSP of the intersection of a generic hyperplane in Ed with the BSP representation of a d-polyhedron. If such section hyperplane is the support of a (d 1)-face, then a BSP tree of the face is generated. This second algorithm may be used iteratively to compute the k-skeletons of a d-polyhedron. ii