Abstract
This paper presents an innovational unified algorithmic framework to compute the 3D Minkowski sum of polyhedral models. Our algorithm decomposes the non-convex polyhedral objects into convex pieces, generates pairwise convex Minkowski sum, and compute their union. The framework incorporates different decomposition policies for different polyhedral models that have different attributes. We also present a more efficient and exact algorithm to compute Minkowski sum of convex polyhedra, which can handle degenerate input, and produces exact results. When incorporating the resulting Minkowski sum of polyhedra, our algorithm improves the fast swept volume methods to obtain approximate the uniting of the isosurface. We compare our framework with another available method, and the result shows that our method outperforms the former method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ghosh, P.: A Unified Computational Framework for Minkowski Operations. Comp. Graph 17(4), 357–378 (1993)
Badlyans, D.: A Computational Approach to Fisher Information Geometry with Applications to Image Analysis. In: Proceedings of 5th International Workshop, pp. 18–33 (2005)
Yun, S.C., Byoung, C., Choi, K.: Contour-parallel Offset Machining Without Tool-Retractions. J. Computer-Aided Design 35(9), 841–849 (2003)
Lozano, T.: Spatial Planning: A Configuration Space Approach. IEEE Trans. Comput. C-32, 108–120 (1983)
Chazelle, B.: Convex Partitions of Polyhedra: A Lower Bound and Worst-case Optimal Algorithm. SIAM J.Comput. 13(7), 488–507 (1984)
Fogel, E., Halperin, D.: On the Exact Maximum Complexity of Minkowski Sums of Convex Polyhedra. In: Proceedings of 23rd Annual ACM Symposium on Computational Geometry, pp. 319–326 (2007)
Chazelle: Convex Decompositions of Polyhedra. In: ACM Symposium on Theory of Computing, pp. 70–79 (1981)
Scott, S., Tao, J., Joe, W.: Manifold Dual Contouring. J. IEEE Transctions on Visualization and Computer Graphics 13(3), 610–620 (2007)
Chazelle, B., Dobkin, D., Shouraboura, N.: Strategies for Polyhedral Surface Decomposition: An Experimental Study. J. Comput. Geom. Theory Appl., 327–342 (1997)
Varadhan, G.., Manocha, D.: Accurate Minkowski Sum Approximation of Polyhedral Models. In Proc. Comput. Graph and Appl, 12th Paci_c Conf. on (PG 2004). IEEE Comput.Sci. pp. 392-401 (2005)
Chazelle, B., Palios, L.: Triangulating a Non-convex Polytope. Discrete Comput. Geom. pp. 505-526 (1990)
Ehmann, S., Lin, M.C.: Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition. Comput. Graph. Forum.Proc. of Eurographics’200 20(3), 500–510 (2001)
Fogel, E., Halperin, D.: Exact and Efficient Construction of Minkowski Sums of Convex Polyhedra with Applications. Computer-Aided Design 39, 929–940 (2007)
Computer Geometry Algorithm Library. (Http://www.cgal.org)
Kim, K.: Nakhoon,: Fast Extraction of Polyhedral Model Silhouettes From Moving Viewpoint on Curved Trajectory. Computers & Graphics 29, 393–402 (2005)
Chiou, J., Clay, V.: An Enhanced Marching Cubes Algorithm for In-Process Geometry Modeling. Manufacturing Science and Engineering 129(3), 566–574 (2007)
Sohn, B.: Topology Preserving Tetrahedral Decomposition of Trilinear Cell. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4487, pp. 350–357. Springer, Heidelberg (2007)
Library of Efficient Data Types and Algorithms. (http://www.mpi-inf.mpg.de)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guo, X., Xie, L., Gao, Y. (2008). Optimal Accurate Minkowski Sum Approximation of Polyhedral Models. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues. ICIC 2008. Lecture Notes in Computer Science, vol 5226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87442-3_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-87442-3_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87440-9
Online ISBN: 978-3-540-87442-3
eBook Packages: Computer ScienceComputer Science (R0)