A parametric solution to common tangents

Proceedings - International Conference on Shape Modeling and Applications, SMI 2001

Volumn , Issue , 2001, Pages 240-249

  Johnstone, J K ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEZIER CURVE; HIGHER-DIMENSIONAL; IMPLICIT CURVES; PARAMETRIC CURVE; PARAMETRIC SOLUTIONS; RATIONAL BEZIER CURVES; ROBOT MOTION; TANGENT SPACE;

ALGORITHMS; COMPUTER GRAPHICS; GEOMETRY;

INTERPOLATION;

EID: 0005783702     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMA.2001.923395     Document Type: Conference Paper

References (15)

1. Bajaj, C. and M.-S. Kim (1987) Convex hull of objects bounded by algebraic curves. Technical Report CSD-TR-697, Computer Science, Purdue University.
2. Edelsbrunner, H. (1987) Algorithms in Combinatorial Geometry. Springer Verlag (Heidelberg), Chapters 1 and 12.
3. Farin, G. (1997) Curves and Surfaces for CAGD: A Practical Guide (4th edition). Academic Press (New York).
4. Goldman, R. and T. DeRose (1986) Recursive subdivision without the convex hull property. Computer Aided Geometric Design 3, 247-265. (Pubitemid 17654377)
5. Hartshorne, R. (1977) Algebraic Geometry. Springer-Verlag (New York).
6. Hoschek, J. (1983) Dual Bezier curves and surfaces. In Surfaces in Computer Aided Geometric Design, R. Barnhill and W. Boehm, eds., North Holland (Amsterdam), 147-156.
7. Johnstone, J. (2001) Smooth visibility from a point. 39th Annual ACM Southeast Conference, to appear.
8. Lasser, D. (1989) Calculating the self-intersections of Bezier curves. Computers in Industry 12, 259-268.
9. Nishita, T. and T. Sederberg and M. Kakimoto (1990) Ray Tracing Trimmed Rational Surface Patches. SIGGRAPH '90, Computer Graphics 24(4), 337-345.
10. O'Rourke, J. (1994) Computational Geometry in C. Cambridge University Press (New York).
11. Parida, L. and S. Mudur (1995) Common tangents to planar parametric curves: a geometric solution. Computer-Aided Design 27(1), 41-47.
12. Pottmann, H. (1995) Studying NURBS Curves and Surfaces with Classical Geometry. In Mathematical Methods for Curves and Surfaces, edited by M. Daehlen, T. Lyche and L. Schumaker, 413-438.
13. Sederberg, T. and S. Parry (1986) Comparison of three curve intersection algorithms. Computer Aided Design 18, 58-63.
14. Sederberg, T. and T. Nishita (1990) Curve intersection using Bezier clipping. Computer Aided Design 22(9), 538-549.
15. Sherbrooke, E. and N. Patrikalakis (1993) Computation of the solutions of nonlinear polynomial systems. Computer Aided Geometric Design 10(5), 379-405.