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.

[1]  M. Karasick.  On the representation and manipulation of rigid solids , 1989 .

[2]  John Amanatides,et al.  Merging BSP trees yields polyhedral set operations , 1990, SIGGRAPH.

[3]  Dana Nau,et al.  Set operations on polyhedra using decomposition methods , 1989 .

[4]  Bruce F. Naylor,et al.  Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.

[5]  Bruce G. Baumgart.  Winged edge polyhedron representation. , 1972 .

[6]  George Vanecek.  Protosolid: An inside look , 1989 .

[7]  Martti Mäntylä,et al.  Localized set operations for solid modeling , 1983, SIGGRAPH.

[8]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[9]  G. Vanecek.  A data structure for analyzing collisions of moving objects , 1991, Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences.

[10]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[11]  David P. Dobkin,et al.  Space Searching for Intersecting Objects , 1987, J. Algorithms.

[12]  Fujio Yamaguchi,et al.  Bridge Edge and Triangulation Approach in Solid Modeling , 1985 .

[13]  D. Ross.  Computer-aided design , 1961, CACM.

[14]  John E. Hopcroft,et al.  Simulation of physical systems from geometric models , 1987, IEEE J. Robotics Autom..

[15]  I. C. Braid,et al.  The synthesis of solids bounded by many faces , 1975, Commun. ACM.

[16]  C. M. Hoffmann,et al.  Model generation and modification for dynamic systems from geometric data , 1988 .

[17]  Bruce F. Naylor.  Binary space partitioning trees as an alternative representation of polytopes , 1990, Comput. Aided Des..

[18]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[19]  D. T. Lee,et al.  Location of a point in a planar subdivision and its applications , 1976, STOC '76.