Minimum distance between the faces of two convex polyhedra: A sufficient condition

Journal of Global Optimization

Volumn 26, Issue 4, 2003, Pages 361-385

  Llanas, B ^a,b   Fernandez De Sevilla, M ^a,b   Feliu, V ^a,b  

^a Canales y Puertos   (Spain)

^b ETSI Industriales   (Spain)

Author keywords

Distance between convex polyhedra; Local descent; Projection algorithms; Sufficient condition of global minimum

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DISTANCE MEASUREMENT; OPTIMIZATION;

CONVEX POLYHEDRA;

VIRTUAL REALITY;

EID: 0042307363     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024755315702     Document Type: Article

References (21)

1. Balakrishnan, A. V. (1981), Applied Functional Analysis, Springer, New York, Heidelberg, Berlin.
2. Bobrow, J.E. (1989), A direct minimization approach for obtaining the distance between convex polyhedra, The International Journal of Robotics Research 8, 65-76.
3. Cameron, S. (1997), A comparison of two fast algorithms for computing the distance between convex polyhedra, IEEE Transactions on Robotics and Automation 13, 915-920
4. Dobkin, D.P. and Kirkpatrick, D.G. (1990), Determining the separation of preprocessed polyhedra-a unified approach, In: Paterson, M.S. (ed.) Proc. 17th Internat. Colloq. Automata Lang. Program., Lecture Notes in Computer Science Vol 443, Springer, New York, Heidelberg, Berlin, pp. 400-413
5. Fujishige, S. and Zhan, P. (1990), A dual algorithm for finding the minimum-norm point in a polytope, J. of the Operations Research Society of Japan 33, 188-195.
6. Fujishige, S. and Zhan, P. (1992), A dual algorithm for finding a nearest pair of points in two polytopes, J. of the Operations Research Society of Japan 35, 353-365.
7. Gilbert, E., Johnson, D.W. and Keerthi, S.S. (1988), A fast procedure for computing the distance between complex objects in three-dimensional space, I.E.E.E. Journal of Robotics and Automation 4, 193-203.
8. Glaeser, G. (1994), Fast Algorithms for 30-Graphics, Springer, New York, Heidelberg, Berlin.
9. Halperin, D., Kavraki, L. and Latombe, J.C (1997), Robotics, In: Goodman, J.E. and O'Rourke, J.(eds.), Handbook of Discrete and Computational Geometry, CRC Press, Boca Ratón-New York, pp. 755-778.
10. Hurteau, G. and Stewart, P. (1988), A distance calculation for imminent collision indication in a robot system simulation, Robotica 6, 47-51.
11. Khatib, O. (1986), Real-time obstacle avoidance for manipulators and mobile robots, International Journal of Robotics Research 5, 90-98.
12. Lin, M. (1993), Efficient Collision Detection for Animation and Robotics, Ph. D. Thesis, University of California at Berkeley.
13. Lianas, B. and Moreno, C. (1996), Finding the projection on a polytope: An iterative method, Computers Math. Applic. 32, 33-39.
14. n, Computers Math. Applic. 40, 971-983.
15. Lumelsky, V. J. (1985), On fast computation of distance between line segments, Information Processing Letters 21, 55-61.
16. Red, W. E. (1983), Minimum distances for robot task simulation, Robotica 1, 231-238.
17. Rockafellar, R. T. (1970), Convex Analysis, Princeton University Press, Princeton, NJ.
18. Sekitani, K. and Yamamoto, Y. (1993), A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes, Mathematical Programming 61, 233-249.
19. Vince, J. (1995), Virtual Reality Systems, Addison-Wesley, Reading MA.
20. Wolfe, P. (1976), Finding the nearest point in a polytope, Mathematical Programming 11, 128-149.
21. Zeghloul, S., Rambeaud, P. and Lallemand, J. P. (1992), A fast distance calculation between convex objects by optimization approach, Proc. of the 1992 IEEE International Conference on Robotics and Automation, (Nice, France-May 1992) pp. 2520-2525