The GAIA project on intersection and implicitization

Geometric Modeling and Algebraic Geometry

Volumn , Issue , 2008, Pages 5-25

  Dokken, Tor ^a  

^a SINTEF ICT   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38849133988     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-72185-7_1     Document Type: Chapter

References (60)

1. M. Aigner and B. Jüttler. Robust computation of foot points on implicitly defined curves. In M. Dæhlen, K. Mørken, and L. Schumaker, editors, Mathematical Methods for Curves and Surfaces: Tromsø 2004, pages 1-10. Nashboro Press, Brentwood, 2005.
2. M. Aigner, B. Jüttler, and Myung-Soo Kim. Analyzing and enhancing the robustness of implicit representations. In Geometric Modelling and Processing, pages 131-140. IEEE Press, 2004.
3. M. Aigner, I. Szilagyi, J. Schicho, and B. Jüttler. Implicitization and distance bounds. In M. Elkadi, B. Mourrain, and R. Piene, editors, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization. Springer, 2006.
4. J. G. Alćazar and J. R. Sendra. Computation of the topology of real algebraic space curves. J. Symbolic Comput., 39(6):719-744, 2005.
5. S. Briseid, T. Dokken, T. R. Hagen, and J. O. Nygaard. Spline surface intersections optimized for gpus. In V. N. Alexandrov, G. D. van Albada, P. M. A. Sloot, and J. Dongarra, editors, Computational Science ICCS 2006: 6th International Conference, Reading, UK, May 28-31, 2006, Proceedings, Part IV, volume 3994 of Lecture Notes in Computer Science, pages 204 - 211, Berlin / Heidelberg, 2006. ICCS, Springer.
6. L. Buśe and M. Chardin. Implicitizing rational hypersurfaces using approximation complexes. J. Symbolic Comput., 40(4-5):1150-1168, 2005.
7. L. Buśe and C. D'Andrea. Inversion of parameterized hypersurfaces by means of subresultants. In ISSAC 2004, pages 65-71. ACM, New York, 2004.
8. L. Buśe, M. Elkadi, and B. Mourrain. Using projection operators in computer aided geometric design. In Topics in algebraic geometry and geometric modeling, volume 334 of Contemp. Math., pages 321-342. Amer. Math. Soc., Providence, RI, 2003.
9. L. Buśe and A. Galligo. Using semi-implicit representation of algebraic surfaces. In Proceedings of IEEE International Conference on Shape Modeling and Applications 2004 (SMI'04), pages 342-345, Los Alamitos, CA, USA, 2004. IEEE Computer Society.
10. F. Carreras and L. Gonzalez-Vega. A bisection scheme for intersecting implicit curves. In Proceedings of the Encounters of Computer Algebra and its Applications EACA-2004, 77-82, Universidad de Cantabria, 2005, To appear.
11. P. Chalmoviansḱy and B. Jüttler. Filling holes in point clouds. In M. Wilson and R.R. Martin, editors, The Mathematics of Surfaces X, volume 2768 of Lecture Notes in Computer Science, pages 196-212, Berlin, 2003. Springer.
12. P. Chalmoviansḱy and B. Jüttler. Approximate parameterization by planar rational curves. In 20th Spring Conference on Computer Graphics, pages 27-35. Comenius University / ACM Siggraph, 2004.
13. P. Chalmoviansḱy and B. Jüttler. Fairness criteria for algebraic curves. Computing, 72:41-51, 2004.
14. S. Chau, M. Oberneder, A. Galligo, and B. Jüttler. Intersecting biquadratic B́ezier surface patches. In this volume.
15. R. M. Corless, L. Gonzalez-Vega, I: Necula, and A. Shakoori. Topology determination of implicitly defined real algebraic plane curves. An. Univ. Timişoara Ser. Mat.-Inform., 41(Special issue):83-96, 2003.
16. T. Dokken. Aspect of Intersection algorithms and Approximation, Thesis for the doctor philosophias degree. PhD thesis, University of Oslo, 1997.
17. T. Dokken. Approximate implicitization. In Mathematical methods for curves and surfaces (Oslo, 2000), Innov. Appl. Math., pages 81-102. Vanderbilt Univ. Press, Nashville, TN, 2001.
18. T. Dokken. Controlling the shape of the error in cubic ellipse approximation. In Curve and surface design (Saint-Malo, 2002), Mod. Methods Math., pages 113-122. Nashboro Press, Brentwood, TN, 2003.
19. T. Dokken and B. Jüttler, editors. Computational Methods for Algebraic Spline Surfaces. Springer, Heidelberg, 2005.
20. T. Dokken and V. Skytt. Intersection algorithms and cagd. In Applied Mathematics at SINTEF. Springer, To appear.
21. T. Dokken and J. B. Thomassen. Overview of approximate implicitization. In Topics in algebraic geometry and geometric modeling, volume 334 of Contemp. Math., pages 169-184. Amer. Math. Soc., Providence, RI, 2003.
22. T. Dokken and J. B. Thomassen. Weak approximate implicitization. In Proceedings of IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06), pages 204-214, Los Alamitos, CA, USA, 2006. IEEE Computer Society.
23. M. Elkadi, A. Galligo, and T.H. Le. Parametrized surfaces in P3 of bidegree (1, 2). In ISSAC 2004, pages 141-148. ACM, New York, 2004.
24. M. Elkadi and B. Mourrain. Residue and implicitization problem for rational surfaces. Appl. Algebra Engrg. Comm. Comput., 14(5):361-379, 2004.
25. F. Etayo, L. Gonzalez-Vega, and N. del Rio. A complete solution for the ellipses intersection problem. Comput. Aided Geom. Design, 23(4):324-350, 2006.
26. F. Etayo, L. Gonźalez-Vega, and C. T?an?asescu. Computing the intersection curve of two surfaces: The tangential case. An. Univ. Timişoara Ser. Mat.-Inform., 41(Special issue):111-121, 2003.
27. M. Fioravanti and L. Gonzalez-Vega. On the geometric extraneous components appearing when using implicitization. In Mathematical methods for curves and surfaces: Tromsø 2004, Mod. Methods Math., pages 157-168. Nashboro Press, Brentwood, TN, 2005.
28. M. Fioravanti, L. Gonzalez-Vega, and I. Necula. Computing the intersection of two ruled surfaces by using a new algebraic approach. J. Symbolic Comput.
29. M. Fioravanti, L. Gonzalez-Vega, and I. Necula. On the intersection with revolution and canal surfaces. In M. Elkadi, B. Mourrain, and R. Piene, editors, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization. Springer, 2006.
30. G. Gatellier, A. Labrouzy, B. Mourrain, and J. P. T́ecourt. Computing the topology of three-dimensional algebraic curves. In Computational methods for algebraic spline surfaces, pages 27-43. Springer, Berlin, 2005.
31. L. Gonźalez-Vega and I. Necula. Efficient topology determination of implicitly defined algebraic plane curves. Comput. Aided Geom. Design, 19(9):719-743, 2002.
32. L. Gonźalez-Vega, I. Necula, S. Ṕerez-Díaz, J. Sendra, and J. R. Sendra. Algebraic methods in computer aided geometric design: theoretical and practical applications. In F. Chen and D. Wang, editors, Geometric computation, volume 11 of Lecture Notes Series on Computing, pages 1-33. World Sci. Publishing, River Edge, NJ, 2004.
33. L. Gonźalez-Vega, I. Necula, and J. Puig-Pey. Manipulating 3d implicit surfaces by using differential equation solving and algebraic techniques. In F. Chen and D. Wang, editors, Geometric computation, volume 11 of Lecture Notes Series on Computing. World Scientific Publishing, River Edge, NJ, 2004.
34. P. H. Johansen. The geometry of the tangent developable. In Computational methods for algebraic spline surfaces, pages 95-106. Springer, Berlin, 2005.
35. P. H. Johansen, M. Løberg, and R. Piene. Monoid hypersurfaces. In this volume.
36. B. Jüttler, P. Chalmoviansḱy, M. Shalaby, and E. Wurm. Approximate algebraic methods for curves and surfaces and their applications. In 21st Spring Conference on Computer Graphics. Comenius University / ACM Siggraph, 2005.
37. B. Jüttler, J. Schicho, and M. Shalaby. Spline implicitization of planar curves. In Curve and surface design (Saint-Malo, 2002), Mod. Methods Math., pages 225-234. Nashboro Press, Brentwood, TN, 2003.
38. B. Jüttler, J. Schicho, and M. Shalaby. C1 spline implicitization of planar curves. In F. Winkler, editor, Automated deduction in geometry, Lecture Notes in Artificial Intelligence, pages 161-177, Heidelberg, 2004. Springer.
39. B. Jüttler and W. Wang. The shape of spherical quartics. Computer Aided Geometric Design, 20:621-636, 2003.
40. B. Jüttler and E. Wurm. Approximate implicitization via curve fitting. In L. Kobbelt, P. Schr̈oder, and H. Hoppe, editors, Symposium on Geometry Processing, pages 240-247, New York, 2003. Eurographics / ACM Siggraph.
41. T. H. Le and A. Galligo. General classification of (1,2) parametric surfaces in p3, 2006. In this volume.
42. B. Mourrain. Bezoutian and quotient ring structure. J. Symbolic Comput., 39(3-4):397-415, 2005.
43. S. Ṕerez-Díaz, J. Sendra, and J. R. Sendra. Parametrization of approximate algebraic curves by lines. Theoret. Comput. Sci., 315(2-3):627-650, 2004.
44. S. Ṕerez-Díaz, J. Sendra, and J. R. Sendra. Distance properties of points on algebraic curves. In Computational methods for algebraic spline surfaces, pages 45-61. Springer, Berlin, 2005.
45. S. Ṕerez-Díaz, J. Sendra, and J. R. Sendra. Parametrization of approximate algebraic surfaces by lines. Comput. Aided Geom. Design, 22(2):147-181, 2005.
46. S. Ṕerez-Díaz and J. R. Sendra. Computing all parametric solutions for blending parametric surfaces. J. Symbolic Comput., 36(6):925-964, 2003.
47. S. Ṕerez-Díaz and J. R. Sendra. Computation of the degree of rational surface parametrizations. J. Pure Appl. Algebra, 193(1-3):99-121, 2004.
48. R. Piene. Singularities of some projective rational surfaces. In Computational methods for algebraic spline surfaces, pages 171-182. Springer, Berlin, 2005.
49. J. R. Sendra. Rational curves and surfaces: algorithms and some applications. In F. Chen and D. Wang, editors, Geometric computation, volume 11 of Lecture Notes Series on Computing, pages 65-125. World Sci. Publishing, River Edge, NJ, 2004.
50. M. Shalaby and B. Jüttler. Approximate implicitization of space curves and of surfaces of revolution, 2006. In this volume.
51. M. Shalaby, B. Jüttler, and J. Schicho. Approximate implicitization of planar curves by piecewise rational approximation of the distance function. Appl. Algebra Eng. Comp., to appear.
52. M. Shalaby, J. Thomassen, E. Wurm, T. Dokken, and B. Jüttler. Piecewise approximate implicitization: Experiments using industrial data. In M. Elkadi, B. Mourrain, and R. Piene, editors, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization. Springer, 2006.
53. Z. Šír. Approximate parametrisation of confidence sets. In Computational methods for algebraic spline surfaces, pages 1-10. Springer, Berlin, 2005.
54. V. Skytt. Challenges in surface-surface intersections. In Computational methods for algebraic spline surfaces, pages 11-26. Springer, Berlin, 2005.
55. V. Skytt. A recursive approach to surface-surface intersections. In Mathematical methods for curves and surfaces: Tromsø 2004, Mod. Methods Math., pages 327-338. Nashboro Press, Brentwood, TN, 2005.
56. J. B. Thomassen. Self-intersection problems and approximate implicitization. In Computational methods for algebraic spline surfaces, pages 155-170. Springer, Berlin, 2005.
57. J. B. Thomassen, P. H. Johansen, and T. Dokken. Closest points, moving surfaces, and algebraic geometry. In Mathematical methods for curves and surfaces: Tromsø 2004, Mod. Methods Math., pages 351-362. Nashboro Press, Brentwood, TN, 2005.
58. E. Wings and B. Jüttler. Generating tool paths on surfaces for a numerically controlled calotte cutting system. Computer-Aided Design, 36:325-331, 2004.
59. E. Wurm, B. Jüttler, and M.-S. Kim. Approximate rational parameterization of implicitly defined surfaces. In R. Martin, H. Bez, and M. Sabin, editors, Mathematics of Surfaces XI, volume 3604 of LNCS, pages 434-447. Springer, 2005.
60. E. Wurm, J.B. Thomassen, B. Jüttler, and T. Dokken. Comparative benchmarking of methods for approximate parameterization. In M. Neamtu and M. Lucian, editors, Geometric Modeling and Computing: Seattle 2003, pages 537-548. Nashboro Press, Brentwood, 2004.