Conversion of binary space partitioning trees to boundary representation

Abstract. 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.

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 difficulty 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 defined 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 reconstructio..