BRep-Index: a multidimensional space partitioning tree

In this paper we introduce the brep-index, a new multi-dimensional space partitioning data structure that provides quick access to the vertices, edges and faces of a boundary representation (brep), thus yielding a single unified representation for polyhedral solids. We d~cribe the cortStruction of the brep-index and show that its size is O(v +e + f), where VI €I and J are the number of vertices, edges, and faces of the hrep. The lower bound can be achieved for some breps by compressing the structure using simple rewrite rules. We apply the hrep-index to solve the point/solid and the line/solid classification problems, and outline an efficient collision detection algorithm as an example of its use.