Page 178 - Geometric Modeling and Algebraic Geometry

180 S. Chau et al.
13. T. Dokken and J.B. Thomassen, Overview of Approximate Implicitization, Topics in Al-
gebraic Geometry and Geometric modeling, ed. Ron Goldman and Rimvydas Krasauskas,
AMS series on Contemporary Mathematics CONM 334, 2003, pp. 169–184.
14. G. Elber and M-S. Kim, Geometric Constraint Solver using Multivariate Rational Spline
Functions, The Sixth ACM/IEEE Symposium on Solid Modeling and Applications, 2001,
pp. 1–10.
15. M. Elkadi and B. Mourrain, Some applications of Bezoutians in Effective Algebraic
Geometry, Rapport de Recherche 3572, INRIA, Sophia Antipolis, 1998.
16. G. Farin, J. Hoschek and M-S. Kim, Handbook of Computer Aided Geometric Design,
Elsevier, 2002.
17. L. Gonz´ alez-Vega and I. Necula, Efficient topology determination of implicitly defined
algebraic plane curves, Comput. Aided Geom. Design, 19(9) (2002), pp. 719–743.
18. C. M. Hoffmann, Implicit Curves and Surfaces in CAGD, Comp. Graphics and Appl.
(1993), pp. 79–88.
19. M. E. Hohmeyer, A Surface Intersection Algorithm Based on Loop Detection, ACM Sym-
posium on Solid Modeling Foundations and CAD/CAM Applications, 1991, pp. 197–207.
20. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, A.K.
Peters, 1993.
21. S. Chau and M. Oberneder, http://www.ag.jku.at/˜margot/biquad
22. A. Khetan, The resultant of an unmixed bivariate system, J. of Symbolic Computation, 36
(2003), pp. 425–442. http://www.math.umass.edu/∼khetan/software.html
23. S. Krishnan and D. Manocha, An Efficient Surface Intersection Algorithm Based on
Lower-Dimensional Formulation, ACM Transactions on Graphics, 16(1) (1997), pp. 74–
106.
24. L. Kunwoo, Principles of CAD/CAM/CAE Systems, Addison-Wesley, 1999.
25. B. Mourrain and J.-P. Pavone, Subdivision methods for solving polynomial equations,
Technical Report 5658, INRIA Sophia-Antipolis, 2005.
26. T. Nishita, T.W. Sederberg and M. Kakimoto, Ray tracing trimmed rational surface
patches, Siggraph, 1990, pp. 337–345.
27. N.M. Patrikalakis, Surface-to-surface intersections, IEEE Computer Graphics and Appli-
cations, 13(1) (1993), pp. 89–95.
28. N. Patrikalakis and T. Maekawa, Chapter 25: Intersection problems, Handbook of Com-
puter Aided Geometric Design (G. Farin and J. Hoschek and M.-S. Kim, eds.), Elsevier,
2002.
29. J.-P. Pavone, Auto-intersection des surfaces param´ etr´ ees r´ eelles, Th`ese d’informatique de
l’Universit´e de Nice Sophia-Antipolis,D´ ecembre 2004.
30. J.P. T´ ecourt, Sur le calcul effectif de la topologie de courbes et surfaces implicites, PhD
thesis in Computer Science at INRIA Sophia-Antipolis,D´ ecembre 2005.
31. J.B. Thomassen, Self-Intersection Problems and Approximate Implicitization, Computa-
tional Methods for Algebraic Spline Surfaces, Springer, pp. 155–170, 2005.
32. A. Vlachos, J. Peters, C. Boyd and J. L. Mitchell, Curved PN Triangles, Symposium on
Interactive 3D Graphics, Bi-Annual Conference Series, ACM Press, 2001, 159–166.