A tessellation algorithm for the representation of trimmed NURBS surfaces with arbitrary trimming curves

CAD Computer Aided Design

Volumn 28, Issue 6-7, 1996, Pages 461-472

  Hamann, Bernd ^b   Tsai, Po Yu ^a,b  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

^b University of California   (United States)

Author keywords

Bisector; NURBS; Scan line algorithm; Trimmed surface; Vorono diagram

Indexed keywords

EID: 0000715402     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/0010-4485(95)00043-7     Document Type: Article

References (35)

1. Farin, G Curves and Surfaces for Computer Aided Geometric Design (3rd Ed.) Academic Press, San Diego, CA (1993)
2. Hoschek, J and Lasser, D Fundamentals of Computer Aided Geometric Design A K Peters, Wellesley, MA (1993)
3. Aurenhammer, F 'Power diagrams: algorithms, and applications' SIAM J. Computing Vol 16 (1987) pp 78-96
4. Edelsbrunner, H Algorithms in Combinatorial Geometry Springer-Verlag, New York, NY (1987)
5. Facello, M A 'Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions' Comput. Aided Geom. Des. (1995) (to appear)
6. Preparata, F P and Shamos, M L Computational Geometry (3rd Ed.) Springer-Verlag, New York, NY (1990)
7. Farouki, R T and Johnstone, J K 'The bisector of a point and a plane parametric curve' Comput. Aided Geom. Des. Vol 11 No 2 (1994) pp 117-151
8. Lee, D T and Drysdale, R L 'Generalization of Voronoï diagrams in the plane' SIAM J. Computing Vol 10 No 1 pp 73-87
9. Leven, D and Sharir, M 'Intersection and proximity problems and Voronoï diagrams' in Schwartz, J and Yap, C K (Eds.) Advances in Robotics Vol I Lawrence Erlbaum, London, UK (1986) pp 187-228
10. Sharir, M 'Intersection and closest-pair problems for a set of discs' SIAM J. Computing Vol 14 No 2 (1985) pp 448-468
11. Srinivasan, V and Nackman, L R 'Voronoï diagram for multiply-connected polygonal domains I: Algorithm' IBM J. Res. Develop. Vol 31 No 3 (1987) pp 361-372
12. Srinivasan, V, Nackman, L R, Tang, J M and Meshkat, S N 'Automatic mesh generation using the symmetric axis transformation of polygonal domains' Proc. IEEE Vol 80 No 9 (1992) pp 1485-1501
13. Yap, C K 'An O (n log n) algorithm for the Voronoï diagram of a set of simple curve segments' Dis. Comput. Geom. Vol 2 (1987) pp 365-393
14. Rockwood, A P, Heaton, K and Davis, T 'Real time rendering of trimmed surfaces' ACM Trans. Graph. Vol 23 (1989) pp 107-116
15. Klein, R, Mehlhorn, K and Meiser, S 'Randomized incremental construction of abstract Voronoï diagrams' Comput. Geom. Theor. Appl. Vol 3 (1993) pp 157-184
16. Baehmann, P L, Wittchen, S L, Shephard, M S, Grice, K R and Yerry, M A 'Robust, geometrically based, automatic two-dimensional mesh generation' Int. J. Num. Meth. Eng. Vol 24 (1987) pp 1043-1078
17. Vries-Baayens, A E and Seebregts, C H 'Exact conversion of a trimmed nonrational Bézier surface into composite or basic nonrational Bézier surfaces' in Hagen, H (Ed.) Topics in Surface Modeling SIAM, Philadelphia, PA (1992) pp 115-143
18. Hoschek, J and Schneider, F J 'Spline conversion for trimmed rational Bézier and B-spline surfaces' Comput.-Aided Des. Vol 22 (1990) pp 580-590
19. Piegl, L A and Richard, A M 'Tessellating trimmed NURBS surfaces' Comput.-Aided Des. Vol 27 No 1 (1995) pp 16-26
20. Boehm, W and Prautzsch, H Numerical Methods A K Peters, Wellesley, MA (1994)
21. Barnhill, R E Geometry Processing for Design and Manufacturing SIAM, Philadelphia, PA (1992)
22. Patrikalakis, N M 'Surface-to-surface intersection' IEEE Comput. Graph. Appl. Vol 13 No 1 (1993) pp 89-95
23. Thompson, J F and Weatherill, N P 'Aspects of numerical grid generation: current science and art' Proc. 11th AIAA Applied Aerodynamics Conference Monterey, CA, August (1993)
24. Weatherill, N P, Hassan, O, Marcum, D L and Marchant, M J 'Grid generation by the Delaunay triangulation' von Karman Institute for Fluid Dynamics, 1993-1994 Lecture Series, January (1994)
25. Blum, H 'Biological shape and visual science (part I)' J. Theor. Biol. Vol 38 (1973) pp 205-287
26. Marr, D 'Representing visual information' AL Memo 415, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA (May 1977)
27. Pavlidis, T Structural Pattern Recognition Springer-Verlag, New York, NY (1977)
28. Rosenfeld, A and Kak, A C Digital Picture Processing Academic Press, New York, NY (1976)
29. Foley, J D, van Dam, A, Feiner, S K and Hughes, J F Computer Graphics (2nd Ed.) Addison Wesley, Reading, MA (1990)
30. Kunnii, T L and Shinagawa, Y 'Visualization: new concepts and techniques to integrate diverse application areas' in Patrikalakis, N M (Ed.) Scientific Visualization of Physical Phenomena Springer-Verlag, New York, NY (1991) pp 3-25
31. Piegl, L A 'On NURBS: a survey' IEEE Comput. Graph. Appl. Vol 11 No 1 (1991) pp 55-71
32. Piegl, L A 'Rational B-spline curves and surfaces for CAD and graphics' in Rogers, D F and Earnshaw, R A (Eds.) State of the Art in Computer Graphics Springer-Verlag, New York, NY (1991) pp 225-269
33. Thompson, J F, Warsi, Z U A and Mastin, C W Numerical Grid Generation North-Holland, New York, NY (1985)
34. George, P L Automatic Mesh Generation Wiley, New York, NY (1991)
35. Knupp, P M and Steinberg, S L Fundamentals of Grid Generation CRC Press, Boca Raton, FL (1993)