Conversion of Binary Space Partitioning Trees to Boundary Representation

Binary Space Partitioning Trees (BSP-Trees) have been proposed as an alternative way to represent polytopes based on the spatial subdivision paradigm. Algorithms that convert from Boundary Representation (BRep) to BSP-Trees have been proposed, but none is known to perform the opposite conversion. In this paper we present such an algorithm, that takes as input a BSP-Tree representation for a polytope and produces a BRep as output. The di culty in designing such algorithm comes from the fact that the information about the boundary is not explicitly represented in the BSP-Tree. The solution we present involves a recursive traversal of the tree to compute lower dimensional information, along with a gluing algorithm that combine the convex regions de ned by the BSP-Tree, removing internal features. A new data structure is proposed (a Topological BSP-Tree), that augments the traditional BSPtree with topological pointers and is used to store intermediate results used in the reconstruction of the BRep.