Page 28 - Geometric Modeling and Algebraic Geometry

22 T. Dokken
• The combined approximate implicit and recursive intersection toolkit is planned
to be available second half of 2006 from http://www.sintef.no/math/.
Thus most of the results interesting to researchers will be available, and can be
a starting point for further research. As also software tools are/will be available re-
searchers can start directly from the GAIA II algorithms implemented and avoid
re-implementing the algorithms of GAIA II before their research starts.

References

1. M. Aigner and B. J¨uttler. 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. J¨uttler, 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. J¨uttler. 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. Alc´ azar 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 opti-
mized 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 Sci-
ence, pages 204 – 211, Berlin / Heidelberg, 2006. ICCS, Springer.
6. L. Bus´ e and M. Chardin. Implicitizing rational hypersurfaces using approximation com-
plexes. J. Symbolic Comput., 40(4-5):1150–1168, 2005.
7. L. Bus´ e and C. D’Andrea. Inversion of parameterized hypersurfaces by means of subre-
sultants. In ISSAC 2004, pages 65–71. ACM, New York, 2004.
8. L. Bus´ e, 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. Bus´ e 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. Chalmoviansk´y and B. J¨uttler. Filling holes in point clouds. In M. Wilson and R.R.
Martin, editors, The Mathematics of Surfaces X, volume 2768 of Lecture Notes in Com-
puter Science, pages 196–212, Berlin, 2003. Springer.
12. P. Chalmoviansk´y and B. J¨uttler. Approximate parameterization by planar rational curves.
In 20th Spring Conference on Computer Graphics, pages 27–35. Comenius University /
ACM Siggraph, 2004.
13. P. Chalmoviansk´y and B. J¨uttler. Fairness criteria for algebraic curves. Computing, 72:41–
51, 2004.