Isotopic meshing of implicit surfaces

Visual Computer

Volumn 23, Issue 1, 2007, Pages 45-58

  Plantinga, Simon ^a   Vegter, Gert ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Approximation; Implicit surfaces; Isotopy; Meshing

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; LINEAR SYSTEMS;

IMPLICIT SURFACES; ISOTOPIC MESHING; LINEAR APPROXIMATION;

COMPUTER SCIENCE;

EID: 33845347408     PISSN: 01782789     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00371-006-0083-6     Document Type: Article

References (19)

1. Akkouche, S., Galin, E.: Adaptive implicit surface polygonization using marching triangles. In: D. Duke, R. Scopigno (eds.) Computer Graphics Forum, vol. 20(2), pp. 67-80. Blackwell, Berlin (2001)
2. Alberti, L., Comte, G., Mourrain, B.: Meshing implicit algebraic surfaces: the smooth case. In: L.L. Schumaker, M. Maehlen, K. Morken (eds.) Mathematical Methods for Curves and Surfaces: Tromso'04, pp. 11-26. Nashboro, Gatlinburg (2005)
3. Bloomenthal, J.: Polygonization of implicit surfaces. Comput. Aided Geom. Des. 5, 341-355 (1988)
4. Boissonnat, J., Cohen-Steiner, D., Vegter, G.: Isotopic implicit surface meshing. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 301-309, Chicago (2004)
5. Boissonnat, J., Oudot, S.: Provably good sampling and meshing of surfaces. Graph. Models 67, 405-451 (2005)
6. Boissonnat, J.D., Oudot, S.: Provably good sampling and meshing of Lipschitz surfaces. In: SCG '06: Proceedings of the 22nd Annual Symposium on Computational Geometry, pp. 337-346. ACM, New York (2006)
7. Bottino, A., Nuij, W., van Overveld, K.: How to shrinkwrap through a critical point: an algorithm for the adaptive triangulation of isosurfaces with arbitrary topology. In: Proceedings of Implicit Surfaces, pp. 55-72 (1996)
8. Bremer, D., Hughes, J.F.: Rapid approximate silhouette rendering of implicit surfaces. In: Proceedings of Implicit Surfaces, pp. 155-164 (1998)
9. Cheng, S., Dey, T., Ramos, E., Ray, T.: Sampling and meshing a surface with guaranteed topology and geometry. In: Proceedings of the Symposium on Computational Geometry, pp. 280-289 (2004)
10. Chernyaev, E.V.: Marching cubes 33: construction of topologically correct isosurfaces. Tech. Rep. CERN CN 95-17 (1995)
11. Hartmann, E.: A marching method for the triangulation of surfaces. Vis. Comput. 14(3), 95-108 (1998)
12. Lerch, M., Tischler, G., von Gudenberg, J.W., Hofschuster, W., Krämer, W.: Filib++ interval library, http://www.math.uni-wuppertal.de/ wrswt/software/fllib.html. Cited (2005)
13. Lopes, H., Oliveira, J.B., de Figueiredo, L.H.: Robust adaptive polygonal approximation of implicit curves. Comput. Graph. 26(6), 841-852 (2002)
14. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, pp. 163-169. ACM, New York (1987)
15. Plantinga, S., Vegter, G.: Contour generators of evolving implicit surfaces. In: Proceedings of the 8th ACM Symposium on Solid Modeling and Applications, pp. 23-32. ACM, New York (2003)
16. Plantinga, S., Vegter, G.: Isotopic approximation of implicit curves and surfaces. In: Proceedings of the Symposium on Geometry Processing, pp. 245-254 (2004)
17. Snyder, J.M.: Interval analysis for computer graphics. Comput. Graph. 26(2), 121-130 (1992)
18. Stander, B.T., Hart, J.C.: Guaranteeing the topology of an implicit surface polygonization for interactive modeling. In: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 279-286. ACM Press/Addison-Wesley, New York (1997)
19. van Overveld, C., Wywill, B.: Shrinkwrap: an adaptive algorithm for polygonizing an implicit surface. Tech. Rep. 93/514/19, University of Calgary (1993)