Issue No. 01 - Jan. (2013 vol. 19)

ISSN: 1077-2626

pp: 16-29

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.104

D. Manocha , Dept. of Comput. Sci., Univ. of North Carolina, Chapel Hill, NC, USA

C. C. L. Wang , Dept. of Mech. & Autom. Eng., Chinese Univ. of Hong Kong, Hong Kong, China

ABSTRACT

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

INDEX TERMS

trees (mathematics), Boolean algebra, mesh generation, solid modelling, mesh reconstruction, efficient boundary extraction, BSP solids, clipping operations, manifold surface, binary space partition tree, polygonization algorithm, volumetric cells, spatial convex partition, point based representations, finite precision arithmetic, B-rep approximation, polygonization method, clipping algorithm, logical operations, floating point arithmetic, geometric processing, Boolean operations, model repair, Face, Solids, Computational modeling, Topology, Octrees, Robustness, Solid modeling, approximation, trees (mathematics), Boolean algebra, mesh generation, solid modelling, mesh reconstruction, efficient boundary extraction, BSP solids, clipping operations, manifold surface, binary space partition tree, polygonization algorithm, volumetric cells, spatial convex partition, point based representations, finite precision arithmetic, B-rep approximation, polygonization method, clipping algorithm, logical operations, floating point arithmetic, geometric processing, Boolean operations, model repair, Face, Solids, Computational modeling, Topology, Octrees, Robustness, Solid modeling, solid modeling, BSP to B-rep conversion, efficient, clipping

CITATION

D. Manocha, C. C. L. Wang, "Efficient Boundary Extraction of BSP Solids Based on Clipping Operations",

*IEEE Transactions on Visualization & Computer Graphics*, vol. 19, no. , pp. 16-29, Jan. 2013, doi:10.1109/TVCG.2012.104