Fast and robust 2D Minkowski sum using reduced convolution

IEEE International Conference on Intelligent Robots and Systems

Volumn , Issue , 2011, Pages 1573-1578

  Behar, Evan ^a   Lien, Jyh Ming ^a  

^a Krasnow Institute for Advanced Study   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MINKOWSKI SUM; NONCONVEX POLYGONS; TOPOLOGICAL PROPERTIES;

INTELLIGENT ROBOTS; ROBOTICS; TOPOLOGY;

CONVOLUTION;

EID: 84455205150     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IROS.2011.6048091     Document Type: Conference Paper

References (23)

1. P. K. Ghosh, "A unified computational framework for Minkowski operations," Computers and Graphics, vol. 17, no. 4, pp. 357-378, 1993.
2. G. Varadhan and D. Manocha, "Accurate Minkowski sum approximation of polyhedral models," Graph. Models, vol. 68, no. 4, pp. 343-355, 2006. (Pubitemid 44037501)
3. E. Fogel and D. Halperin, "Exact and efficient construction of Minkowski sums of convex polyhedra with applications," in Proc. 8th Wrkshp. Alg. Eng. Exper. (Alenex'06), 2006, pp. 3-15.
4. A. Kaul and J. Rossignac, "Solid-interpolating deformations: construction and animation of PIPs," in Proc. Eurographics '91, 1991, pp. 493-505.
5. P. Gritzmann and B. Sturmfels, "Minkowski addition of polytopes: computational complexity and applications to Gröbner bases," SIAM J. Discret. Math., vol. 6, no. 2, pp. 246-269, 1993.
6. K. Fukuda, "From the zonotope construction to the minkowski addition of convex polytopes," Journal of Symbolic Computation, vol. 38, no. 4, pp. 1261-1272, 2004. (Pubitemid 39150704)
7. L. J. Guibas, L. Ramshaw, and J. Stolfi, "A kinetic framework for computational geometry," in Proc. 24th Annu. IEEE Sympos. Found. Comput. Sci., 1983, pp. 100-111.
8. E. Behar and J.-M. Lien, "Project Webpage for Fast and Robust 2D Minkowski Sum Using Reduced Convolution,"http://masc.cs.gmu.edu/wiki/ ReducedConvolution/, 2011.
9. J.-M. Lien, "A simple method for computing Minkowski sum boundary in 3d using collision detection," in The Eighth International Workshop on the Algorithmic Foundations of Robotics (WAFR), Guanajuato, Mexico, Dec 2008.
10. T. Lozano-Pérez, "Spatial planning: A configuration space approach,"IEEE Trans. Comput., vol. C-32, pp. 108-120, 1983.
11. P. K. Agarwal, E. Flato, and D. Halperin, "Polygon decomposition for efficient construction of minkowski sums," in European Symposium on Algorithms, 2000, pp. 20-31.
12. E. Flato, "Robuts and efficient construction of planar minkowski sums," M.Sc. Thesis, Dept. Comput. Sci., Tel-Aviv Univ., Isael, 2000.
13. L. J. Guibas and R. Seidel, "Computing convolutions by reciprocal search," Discrete Comput. Geom., vol. 2, pp. 175-193, 1987.
14. H. Barki, F. Denis, and F. Dupont, "Contributing vertices-based minkowski sum computation of convex polyhedra," Comput. Aided Des., vol. 41, no. 7, pp. 525-538, 2009.
15. -, "Contributing vertices-based minkowski sum of a non-convex polyhedron without fold and a convex polyhedron," in Shape Modeling and Applications, 2009. SMI 2009. IEEE International Conference on, june 2009, pp. 73 -80.
16. G. D. Ramkumar, "An algorithm to compute the minkowski sum outer-face of two simple polygons," in Polygons, Proc. ACM Symposium on Computational Geometry. Press, 1996, pp. 234-241.
17. R. Wein, "Exact and efficient construction of planar Minkowski sums using the convolution method," in Proc. 14th Annual European Symposium on Algorithms, 2006, pp. 829-840.
18. R. T. Farouki and J. Hass, "Evaluating the boundary and covering degree of planar minkowski sums and other geometrical convolutions," J. Comput. Appl. Math., vol. 209, pp. 246-266, December 2007. [Online]. Available: http://portal.acm.org/citation.cfm?id=1287834.1287914
19. D. Halperin, "Robust geometric computing in motion," The International Journal of Robotics Research, vol. 21, no. 3, pp. 219-232, 2002.
20. E. Behar and J.-M. Lien, "A new method for mapping the configuration space obstacles of polygons," George Mason University, Tech. Rep. GMU-CS-TR-2010-11, 2010.
21. C. Bajaj and T. K. Dey, "Polygon nesting and robustness," Inform. Process. Lett., vol. 35, pp. 23-32, 1990.
22. L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, "MPFR: A multiple-precision binary floating-point library with correct rounding," ACM Transactions on Mathematical Software (TOMS), vol. 33, no. 2, p. 13, 2007.
23. A. Fabri, G. Giezeman, L. Kettner, S. Schirra, and S. Sch "onherr, "On the design of CGAL a computational geometry algorithms library," Software Practice and Experience, vol. 30, no. 11, pp. 1167-1202, 2000.