The convex hull of freeform surfaces

Computing (Vienna/New York)

Volumn 72, Issue 1-2, 2004, Pages 171-183

  Seong, J K ^a   Elber, G ^b   Johnstone, J K ^c   Kim, M S ^a  

^a Seoul National University   (South Korea)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

B spline; Common tangent; Convex hull; Freeform rational surface; Symbolic computation; Zero set finding

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; SURFACE PHENOMENA;

B-SPLINE; COMMON TANGENT; CONVEX HULL; FREEFORM RATIONAL SURFACE; SYMBOLIC COMPUTATION; ZERO-SET FINDING;

COMPUTATIONAL GEOMETRY;

EID: 2542454834     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-003-0055-x     Document Type: Conference Paper

References (17)

1. Aumann, G.: Interpolation with developable Bézier patches. Computer Aided Geometric Design 8, 409-420 (1991).
2. Bajaj, C. Kim, M.-S.: Convex hulls of objects bounded by algebraic curves. Algorithmica 6, 533-553 (1991).
3. Dobkin, D., Souvaine, D.: Computational geometry in a curved world. Algorithmica 5, 421-457 (1990).
4. do Carmo, M. P.: Differential geometry of curves and surfaces. New Jersey: Prentice Hall 1976.
5. Elber, G., Cohen, E.: Second-order surface analysis using hybrid symbolic and numeric operators. ACM Transactions on Graphics, 12, 160-178 (1993).
6. Elber, G., Kim, M.-S.: Geometric constraint solver using multivariate rational spline functions. Proc. of ACM Symposium on Solid Modeling and Applications, pp. 1-10. Ann Arbor, Michigan, USA June 4-8, 2001.
7. Elber, G., Kim, M.-S., Heo, H.-S.: The convex hull of rational plane curves. Graphical Models 63, 151-162 (2001).
8. Geismann, N., Hemmer, M., Schömer, E.: The convex hull of ellipsoids. Proc. of ACM Symposium on Computational Geometry, pp. 321-322. Medford, Massachusetts. June 3-5, 2001.
9. Graham, R., Yao, F.: Finding the convex hull of a simple polygon. J. of Algorithms 4, 324-331 (1983).
10. Johnstone, J.: A parametric solution to common tangents. Proc. of Int'l Conf. on Shape Modeling and Applications, pp. 240-249. Genova, Italy, May 7-11, 2001.
11. Jüttler, B., Wagner, M.: Rational motion-based surface generation. Computer-Aided Design 31, 203-214 (1999).
12. Lee, D. T.: On finding the convex hull of a simple polygon. Int'l J. Computer and Information Sciences 12, 87-98 (1983).
13. Lozano-Pérez, T., Wesley, M. A.: An algorithm for planning collision free paths among polyhedral obstacles. Comm. of the ACM 22, 560-570 (1979).
14. Lozano-Pérez, T.: Spatial planning: a configuration space approach. IEEE Trans, on Computers 32, 108-120 (1983).
15. Pottmann, H., Wallner, J.: Computational line geometry. Berlin: Springer-Verlag 2001.
16. Preparata, F., Shamos, M.: Computational geometry: an introduction. New York: Springer-Verlag 1985.
17. Schäffer, A., Wan Wyk, C.: Convex hulls of piecewise-smooth Jordan curves. J. of Algorithms 8, 66-94 (1987).