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http://dx.doi.org/10.7315/CADCAM.2012.262

GPU Algorithm for Outer Boundaries of a Triangle Set  

Kyung, Min-Ho (Department of Digital Media, Ajou University)
Publication Information
Korean Journal of Computational Design and Engineering / v.17, no.4, 2012 , pp. 262-273 More about this Journal
Abstract
We present a novel GPU algorithm to compute outer cell boundaries of 3D arrangement subdivided by a given set of triangles. An outer cell boundary is defined as a 2-manifold surface consisting of subdivided polygons facing outward. Many geometric problems, such as Minkowski sum, sweep volume, lower/upper envelop, Bool operations, can be reduced to finding outer cell boundaries with specific properties. Computing outer cell boundaries, however, is a very time-consuming job and also is susceptible to numerical errors. To address these problems, we develop an algorithm based on GPU with a robust scheme combining interval arithmetic and multi-level precisions. The proposed algorithm is tested on Minkowski sum of several polygonal models, and shows 5-20 times speedup over an existing algorithm running on CPU.
Keywords
3D arrangement; GPU; Minkowski sum; Outer boundary; Robustness; Triangle set;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 de Berg, M., Dobrindt, K. and Schwarzkopf, O., 1994, On Lazy Randomized Incremental Construction, Discrete & Computational Geometry, 14(1), pp 261-286.
2 Agarwal, P. and Sharir, M., 1998, Arrangements and Their Applications, Handbook of Computational Geometry, Elsevier Sience Publishers, pp. 49-119.
3 Sharir, M., 2007, Arrangements in Geometry: Recent Advances and Challenges, Proc. the 15th annual European conference on Algorithms, Eilat, Isarael, pp. 12-16.
4 Krishnamurthy, Sara McMains, S. and Haller, K., 2009, Accelerating Geometric Queries using the GPU, Proc. 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 199-210.
5 Li, W. and McMains, S., 2011, Voxelized Minkowski Sum Computation on the GPU with Robust Culling, Computer-Aided Design, 43(10), pp 1270-1283.   DOI   ScienceOn
6 Halperin, D. and Shelton, C., 1998, A Perturbation Scheme for Spherical Arrangements with Application to Molecular Modeling, Computational Geometry: Theory and Applications, 10(4), pp. 273-288.   DOI   ScienceOn
7 Halperin, D. and Leiserowitz, E., 2004, Controlled Perturbation for Arrangements of Circles, International Journal of Computational Geometry and Applications, 14(4), pp. 277-310.   DOI   ScienceOn
8 Halperin, D. and Raab, S., 1999, Controlled Perturbation for Arrangements of Polyhedral Surfaces with Application to Swept Volumes, Proc. 15th Annual ACM Symposium on Computational Geometry, pp 163-172.
9 Milenkovic, V. and Sacks, E., 2012, Adaptive-Precision Controlled Perturbation, submitted to Symposium on Computational Geometry.
10 Kyung, M.-H., Keun, K.-J. and Choi, J.-J., 2011, Robust GPU-based Intersection Algorithm for a Large Triangle Set, Journal of Korea Computer Graphics, 17(3), pp. 9-20.
11 Lozano-Perez, T., 1983, Spatial Planning: A Configuration Space Approach, IEEE Transactions on Computers, C-32(2), pp. 108-120.   DOI   ScienceOn
12 Sacks, E., Milenkovic, V. and Kyung, M.-H., 2011, Controlled Linear Perturbation, Computer-Aided Design, 43(10), pp. 1250-1257.   DOI   ScienceOn
13 Abrams, S. and Allen, P., 2000, Computing Swept Volums, Journal of Visualization and Computer Animation, 11, pp. 69-82.   DOI
14 Tilove, R.B. and Requicha, A., 1980, Closure of Boolean Operations on Geometric Entities, Computer-Aided Design, 12(5), pp. 219-220.   DOI   ScienceOn
15 Requicha, A., 1985, Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms, Proc. IEEE, pp. 30-44.
16 Pach, J. and Sharir, M., 1989, The Upper Envelope of Piecewise Linear Functions and the Boundary of a Region Enclosed by Convex Plates: Combinatorial Analysis, Discrete & Computational Geometry, 4, pp. 291-309.   DOI
17 Arnovo, B. and Sharir, M., 1990, Triangles in Space or Building (and analyzing) Castles in the Air, Combinatorica, 10(2), pp. 137-173.   DOI
18 Halperin, D., 2002, Robust Geometric Computing in Motion", The Journal of Robotics Research, 21(3), pp. 219-232.   DOI
19 Pach, J. and Sharir, M., 2009, Combinatorial Geometry and Its Algorithmic Applications: The Alcala Lectures, AMS.
20 de Berg, M., Guibas, L.J. and Halperin, D., 1994, Vertical Decomposition for Triangles in 3-space, Proc. the 10th Annu. ACM Symposium on Computational Geometry.
21 Guibas, L.J., Ramshaw, L. and Stolfi, J., 1983, A Kinetic Framework for Computational Geometry, Proc. 24th Annu. IEEE Symposium on Foundation of Computer Science, pp. 100-111.
22 Kaul, A. and O'Connor, M.A., 1993, Computing Minkowski Sums of Regular Polyhedra, Technical Report RC 18891(82557), IBM T. J. Watson Research Center, Yorktown Heights, N. Y..
23 Laurent Fousse, Guillaume Hanrot, Vincent Lefevre, Patrick Pelissier, Paul Zimmermann, 2007, MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding, ACM Transactions on Mathematical Software, 33(2).