Geometric computations in parameter space

Spring Conference on Computer Graphics, SCCG 2005 - Conference Proceedings

Volumn , Issue , 2005, Pages 27-32

  Kim, Myung Soo ^a   Elber, Gershon ^b   Seong, Joon Kyung ^a  

^a Seoul National University   (South Korea)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Freeform curves and surfaces; Geometric constraints; Parameter space; System of polynomial equations

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; FUNCTIONS; LINEAR ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING;

FREEFORM CURVES AND SURFACES; GEOMETRIC CONSTRAINTS; PARAMETER SPACE; SYSTEM OF POLYNOMIAL EQUATIONS;

COMPUTER GRAPHICS;

EID: 33749008232     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1090122.1090127     Document Type: Conference Paper

References (28)

1. COHEN, E., RIESENFELD, R., AND ELBER, G. 2001. Geometric Modeling with Splines: An Introduction, A.K. Peters, Natick, USA.
2. DO CARMO, M. 1976. Differential Geometry of Curves and Surfaces, Prentice-Hall, Upper Saddle River, USA. http://www.cs.technion.ac.il/~irit.
3. ELBER, G. 1996. IRIT 7.0 User's Manual, Technion, http://www.es.technion. ac.il/~irit.
4. ELBER, G., BAREQUET, G., KIM, M.-S. 2001. Bisectors and α-sectors of rational varieties. Computing, 65.
5. ELBER, G., KIM, M.-S. 1998. Bisector curves of planar rational curves. Computer-Aided Design 30, 1089-1096.
6. ELBER, G., KIM, M.-S. 2000. A computational model for nonrational bisector surfaces: curve-surface and surface-surface bisectors. Proc. of Geometric Modeling and Processing 2000, Hong Kong, April 10-12, 2000.
7. ELBER, G., KIM, M.-S. 2001. Geometric constraint solver using multivariate rational spline functions. Proc. of ACM Symposium on Solid Modeling and Applications, Ann Arbor, MI, June 4-8, 2001.
8. ELBER, G., KIM, M.-S., HEO, H.-S. 2001. The convex hull of rational plane curves. Graphical Models, 2001.
9. ELBER, G., SAYEGH, R., BAREQUET, G., MARTIN, R. 2005. Two-dimensional visibility charts for continuous curves. Proc. of Shape Modeling International, 2005.
10. FARIN, G. 1997. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Fourth Ed., Academic Press, San Diego.
11. FAROUKI, R., JOHNSTONE, J. 1994. Computing point/curve and curve/curve bisectors. Design and Application of Curves and Surfaces: Mathematics of Surfaces V, R.B. Fisher (Ed.), Oxford Univ. Press, New York, 327-354.
12. FAROUKI, R., RAMAMURTHY, R. 1998. Specified-precision computation of curve/curve bisectors. Int'l J. of Computational Geometry & Applications 8, 599-617.
13. HANNIEL, I., MUTHUGANAPATHY, R., ELBER, G., KIM, M.-S. 2005. Precise Voronoi cell extraction of free-form rational planar closed curves. Proc. of ACM Symposium on Solid and Physical Modeling, Cambridge, USA.
14. HEO, H.-S., KIM, M.-S., ELBER, G. 1999. The intersection of two ruled surfaces. Computer-Aided Design 31, 33-50.
15. HEO, H.-S., HONG, S., SEONG, J.-K., KIM, M.-S., ELBER, G. 1999. The intersection of two ringed surfaces and some related problems, Graphical Models, 63(4). 228-244.
16. HOFFMANN, C., VERMEER, P. 1991. Eliminating extraneous solutions in curve and surface operation. Int'l J. of Comp. Geom. and Appl. 1, 47-66.
17. HOSCHEK, J., LASSER, D. 1993. Fundamentals of Computer Aided Geometric Design, A.K. Peters, Wellesley, USA.
18. KIM, M.-S., ELBER, G. 2000. Problem reduction to parameter space. The Mathematics of Surfaces IX (Proc. of the Ninth IMA Conference), R. Cipolla and R. Martin (Eds), Springer, London, 2000. pp 82-98.
19. LEE, I.-K., KIM, M.-S., ELBER, G. 1998. Polynomial/rational approximation of Minkowski sum boundary curves. Graphical Models and Image Processing 60, 136-165
20. MARTIN, R., STEPHENSON, P. 1990. Sweeping of three-dimensional objects. Computer-Aided Design 22, 223-234.
21. PATRIKALAKIS, N., MAEKAWA, T. 2002. Shape Interrogation for Computer Aided Design and Manufacturing, Springer-Verlag, Berlin.
22. PIEGL, L., TILLER, W. 1995. The NURBS Book, Springer, Berlin.
23. SEONG, J.-K., KIM, M.-S., AND ELBER, G. 2001. The convex hull of rational surfaces. Proc. of Third Israel-Korea Binational Conf. on Geometric Modeling and Computer Graphics, Seoul, Korea, 171-175.
24. SEONG, J.-K., KIM, K.-J., KIM, M.-S., ELBER, G., MARTIN, R. 2005. Intersecting a freeform surface with a general swept surface. Computer-Aided Design, 37(5), 473-483.
25. SEONG, J.-K., KIM, K.-J., KIM, M.-S., ELBER, G. 2005. Perspective silhouette of a general swept volume. To appear in The Visual Computer.
26. SEONG, J.-K., ELBER, G., KIM, M.-S. 2005. Trimming local and global self-intersections in offset curves/surfaces using distance maps Submitted to Computer-Aided Design.
27. SHERBROOKE, E., PATRIKALAKIS, N. 1993. Computation of the solutions of nonlinear polynomial systems. Computer Aided Geometric Design 10, 379-405.
28. WANG, W., WANG, J., KIM, M.-S. 2001. An algebraic condition for the separation of two ellipsoids. Computer Aided Geometric Design, 18(6), pp. 531-539.