Robust interval algorithm for curve intersections

CAD Computer Aided Design

Volumn 28, Issue 6-7, 1996, Pages 495-506

  Hu, Chun Yi ^a   Maekawa, Takashi ^a   Sherbrooke, Evan C ^a   Patrikalakis, Nicholas M ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

CAD; CAGD; CAM; Curve intersection; Interval polynomial solver; Overlapping; Robustness; Rounded interval arithmetic; Tangency

Indexed keywords

EID: 0001406461     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/0010-4485(95)00063-1     Document Type: Article

References (22)

1. Patrikalakis, N M 'Surface-to-surface intersections' IEEE Comput. Graph. Appl. Vol 13 No 1 (1993) pp 89-95
2. Lasser, D 'Calculating the self-intersections of Bézier curves' Comput. Industry Vol 12 (1989) pp 259-268
3. Sederberg, T W and Parry, S R 'Comparison of three curve intersection algorithms' Comput.-Aided Des. Vol 18 No 1 (1986) pp 58-63
4. Lane, J M and Riesenfeld, R F 'A theoretical development for the computer display and generation of piecewise polynomial surfaces' IEEE Trans. PAMI Vol 2 No 1 (1980) pp 35-46
5. Koparkar, P A and Mudur, S P 'A new class of algorithms for processing of parametric curves' Comput.-Aided Des. Vol 15 No 1 (1983) pp 41-45
6. Sederberg, T W, Anderson, D C and Goldman, R N 'Implicit representation of parametric curves and surfaces' Comput. Vis. Graph. Image Proc. Vol 28 No 1 (1984) pp 72-84
7. Sederberg, T W and Nishita, T 'Curve intersection using Bézier clipping' Comput.-Aided Des. Vol 22 No 9 (1990) pp 538-549
8. Maekawa, T 'Robust computational methods for shape interrogation' PhD Thesis Massachusetts Institute of Technology, Cambridge, MA (June 1993)
9. Maekawa, T and Patrikalakis, N M 'Computation of singularities and intersections of offsets of planar curves' Comput. Aided Geom. Des Vol 10 No 5 (1993) pp 407-429
10. Sherbrooke, E C and Patrikalakis, N M 'Computation of the solutions of nonlinear polynomial systems' Comput. Aided Geom. Des Vol 10 No 5 (1993) pp 379-405
11. Sederberg, T W and Farouki, R T 'Approximation by interval Bézier curves' IEEE Comput. Graph. Appl. Vol 15 No 2 (1992) pp 87-95
12. Moore, R E Interval Analysis Prentice-Hall, Englewood Cliffs, NJ (1966)
13. Maekawa, T and Patrikalakis, N M 'Interrogation of differential geometry properties for design and manufacture' Visual Comput. Vol 10 No 4 (1994) pp 216-237
14. Lee, C, Ravani, B and Yang, A T 'A theory of contact for geometric continuity of parametric curves' Visual Comput. Vol 8 No 5-6 (1992) pp 338-350
15. Sherbrooke, E C 27Computation of the solutions of nonlinear polynomial systems' Master's Thesis Massachusetts Institute of Technology, Cambridge, MA (October 1993)
16. Patrikalakis, N M, Maekawa, T, Sherbrooke, E C and Zhou, J 'Computation ofsingularities for engineering design' in Kunii, T L and Shinagawa, Y (Eds.) Modern Geometric Computing for Visualization Springer-Verlag, Tokyo (1992) pp 167-191
17. Hu, C-Y 'Robust algorithms for sculptured shape visualization' Master's Thesis Massachusetts Institute of Technology, Cambridge, MA (July 1993)
18. Zhou, J, Sherbrooke, E C and Patrikalakis, N M 'Computation of stationary points of distance functions' Engng Comput. Vol 9 No 4 (1993) pp 231-246
19. Maekawa, T, Wolter, F-E and Patrikalakis, N M 'Umbilics and lines of curvature for shape interrogation' Comput. Aided Geom. Des. Vol 13 (to appear) (1996)
20. Hu, C-Y 'Towards robust interval solid modeling for curved objects' PhD Thesis Massachusetts Institute of Technology, Cambridge, MA (May 1995)
21. Hoschek, J and Lasser, D Fundamental of Computer Aided Geometric Design A K Peters, Wellesley, MA (1993) translated by Schumaker, L L
22. Wilkinson, J H Rounding Errors in Algebraic Processes H M Stationery Office, London, UK (1963)