Decomposing trimmed surfaces using the Voronoï diagram and a scan line algorithm

Applied Mathematics and Computation

Volumn 89, Issue 1-3, 1998, Pages 327-344

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

^a Center for Image Processing and Integrated Computing (CIPIC)   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040095468     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)81666-9     Document Type: Article

References (22)

1. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, fourth edition, Academic Press, San Diego, CA, 1997.
2. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, A K Peters, Ltd., Wellesley, MA, 1993.
3. F. Aurenhammer, Power diagrams: properties, algorithms, and applications, SIAM Journal on Computing 16, pp. 78-96, (1987).
4. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, New York, NY, 1987.
5. F. P. Preparata and M. I. Shamos, Computational Geometry, third printing, Springer-Verlag, New York, NY, (1990).
6. R. T. Farouki and J. K. Johnstone, The bisector of a point and a plane parametric curve, Computer Aided Geometric Design 11(2), pp. 117-151, (1994).
7. R. Klein, K. Mehlhorn, and S. Meiser, Randomized incremental construction of abstract Voronoï diagrams, Computational Geometry. Theory and Applications 3, pp. 157-184, (1993).
8. D. T. Lee and R. L. Drysdale, Generalization of Voronoï diagrams in the plane, SIAM Journal on Computing 10(1), pp. 73-87, (1981).
9. D. Leven and M. Sharir, Intersection and proximity problems and Voronoï diagrams, in (Schwartz, J. and Yap, C. K., eds.), Advances in Robotics, Vol. I, Lawrence Erlbaum, London, U.K., pp. 187-228, (1986).
10. M. Sharir, Intersection and closest-pair problems for a set of discs, SIAM Journal on Computing 14(2), pp. 448-468, (1985).
11. V. Srinivasan and L. R. Nackman, Voronoï diagram for multiply-connected polygonal domains I: Algorithm, IBM J. Res. Develop. 31(3), pp. 361-372, (1987).
12. C. K. Yap, An O(n log n) algorithm for the Voronoï diagram of a set of simple curve segments, Discrete Computational Geometry 2, pp. 365-393, (1987).
13. A. P. Rockwood, K. Heaton, and T. Davis, Real time rendering of trimmed surfaces, ACM Transactions on Graphics 23, pp. 107-116, (1989).
14. P. L. Baehmann, S. L. Wittchen, M. S. Shephard, K. R. Grice, and M. A. Yerry, Robust, geometrically based, automatic two-dimensional mesh generation, International Journal for Numerical Methods in Engineering 24, pp. 1043-1078, (1987).
15. A. E. Vries-Baayens and C. H. Seebregts, 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, pp. 115-143, (1992).
16. J. Hoschek and F. J. Schneider, Spline conversion for trimmed rational Bézier and B-spline surfaces, Computer Aided Design 22, pp. 580-590, (1990).
17. W. Boehm and H. Prautzsch, Numerical Methods, A K Peters, Ltd., Wellesley, MA, 1994.
18. Patrikalakis, N. M. (1993), Surface-to-surface intersections, IEEE Computer Graphics and Applications 13(1), pp. 89-95.
19. R. E. Barnhill, Geometry Processing for Design and Manufacturing, SIAM, Philadelphia, PA, 1992.
20. L. A. Piegl, On NURBS: A survey, IEEE Computer Graphics and Applications 11(1), pp. 55-71, (1991a).
21. J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics, second edition, Addison Wesley, Reading, MA, (1990).
22. L. A. Piegl, 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, pp. 225-269, (1991b).