Improvements to algorithms for computing the Minkowski sum of 3-polytopes

CAD Computer Aided Design

Volumn 35, Issue 13, 2003, Pages 1181-1192

  Wu, Yanyan ^a,b   Shah, Jami J ^a   Davidson, Joseph K ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

^b GE GLOBAL RESEARCH   (United States)

Author keywords

Convex hull; Geometric algorithms; Math modeling of geometric variations; Minkowski sum; Polytopes

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER GRAPHICS; GENETIC ALGORITHMS; IMAGE PROCESSING; MATHEMATICAL MODELS; ROBOTICS;

MINKOWSKI SUM;

COMPUTER AIDED DESIGN;

EID: 0041329646     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(03)00023-X     Document Type: Article

References (16)

1. Barber C.B., Dobkin D.P., Huhdanpaa H. Quickhull algorithm for convex hulls. ACM Trans Math Software. 22:(4):1996;469-483.
2. Bekker H., Roerdink J. An efficient algorithm to calculate the Minkowski sum of convex 3D polyhedra. Proc Comput Sci - ICCS. 2001.
3. de Berg M., Van Kreveld M., Overmars M., Schwarzkopf O. Computation geometry - algorithms and applications. 1997;Springer, Berlin/Heidelberg.
4. Chand D.R., Kapur S.S. An algorithm for convex polytopes. J Assoc Comput Mach. 17:1970;78-86.
5. Davidson JK, Mujezinovic A, Shah JJ. A new mathematical model for geometric tolerances as applied to round faces. DETC00/DAC-14249, Proceedings of the 2000 Design Engineering Technical Conferences, Baltimore, MD, Sept. 10-13, 2000.
6. Ghosh P.K. A unified computational framework for Minkowski operations. Comput Graphics. 17:(4):1993;357-378.
7. Gritzmann P., Sturmfels B. Minkowski addition of polytopes: computational complexity and applications to Grobner bases. SIAM J Disc Math. 6:(2):1993;246-269.
8. Guibas L., Ramshaw L., Stolfi J. A kinetic framework for computational geometry. IEEE 24th Symposium on the Foundations of Computer Science. 1983.
9. Guibas L., Seidel G. Computing convolutions by reciprocal search. Discrete Comput Geometry. 2:1987;175.
10. d. Inform Process Lett. 19:1984;197.
11. Kaul A., Rossignac J. Solid interpolating deformations: construction and animation of PIPs. Comput Graphics. 16:(1):1992;107.
12. Parry-Barwick SJ, Bowyer A. Minkowski sums of set-theoretic models. CSG94 Set-Theoretic Solid Modeling: Techniques and Applications Conference Proceedings, Winchester, April 1994. p. 101-16.
13. Preparata F.P., Hong S.J. Convex hulls of finite sets of points in two and three dimensions. Commun ACM. 20:1977;87-93.
14. Rourke J.O. Computational geometry in C. 2nd ed. 1998;Cambridge University Press, Cambridge.
15. Sedgewick R. Algorithms in C++. 1992;Addison-Wesley, Reading, MA.
16. Seidel R. Report TR 86-784. Report TR 86-784. 1986;Department of Computer Science, Cornell University, Ithaca, NY.