A coordinate system associated with points scattered on a surface

CAD Computer Aided Design

Volumn 36, Issue 2, 2004, Pages 161-174

  Boissonnat, Jean Daniel ^a   Flötotto, Julia ^a  

^a INRIA   (France)

Author keywords

Computational geometry; Sampled surfaces; Scattered data interpolation

Indexed keywords

ALGORITHMS; FUNCTIONS; INTERPOLATION; MULTIVARIABLE SYSTEMS; SET THEORY;

COORDINATE SYSTEMS;

COMPUTATIONAL GEOMETRY;

EID: 0242405870     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(03)00059-9     Document Type: Conference Paper

References (23)

1. Alexa M, Behr J, Cohen-Or D, Levin D, Fleishman S, Silva CT. Point set surfaces. Proceedings of 12th IEEE Visualization 2001, San Diego, CA in press.
2. Alfeld P, Neamtu M, Schumaker L. Fitting scattered data on sphere-like surfaces using spherical splines; J. Comput. Appl. Math 1996;73:5-43.
3. Alfeld P, Neamtu M, Schumaker LL. Bernstein-bézier polynomials on spheres and sphere-like surfaces; Comput. Aided Geom. Design, 1996; 13:333-49.
4. Amenta N., Bern M. Surface reconstruction by Voronoi filtering. Discrete Comput Geom. 22:(4):1999;481-504.
5. Barnhill R., Piper B., Rescorla K. Interpolation to arbitrary data on a surface. Farin G. Geometric modeling: algorithms and new trends. 1987;281-289 SIAM, Philadelphia.
6. Boissonnat J.-D., Cazals F. Natural neighbor coordinates of points on a surface. Comput Geom: Theory Appl. 19:(2/3):2001;155-173.
7. Boissonnat J-D, Flötotto J. Implementation of a surface coordinate system and its applications based on CGAL. Technical report in preparation.
8. Boissonnat J.-D. Algorithmic geometry. 1998;Cambridge University Press, UK. Translated by Hervé Brönnimann.
9. Brown J.L. Natural neighbor interpolation on the sphere. Laurent P.J., Le Méhauté A., Schumaker L.L. Wavelets, images, and surface fitting. 1994;67-74 A.K. Peters, Wellesley, MA.
10. Brown J.L. Systems of coordinates associated with points scattered in the plane. Comput Aided Des. 14:1997;547-559.
11. The CGAL reference manual, August 2002. Release 2.3. http://www.cgal.org.
12. Chew LP. Guaranteed-quality mesh generation for curved surfaces. Proceedings of the Ninth Annual ACM Symposium on Computational Geometry;1993. pp. 274-80.
13. Farin G. Surfaces over Dirichlet tesselations. Comput Aided Geom Des. 7:1990;281-292.
14. Fasshauer G., Schumaker L. Scattered data fitting on the sphere. Lyche T., Daehlen M., Schumaker L.L. Methods for curves and surfaces II. 1998;117-166 Vanderbilt University Press, Nashville, TN.
15. Foley T. Interpolation to scattered data on a spherical domain. Mason J.C., Cox M.G. Algorithms for approximation II. 1990;303-310 Chapman & Hall, London.
16. Foley T.A., Lane D.A., Nielson G.M., Franke R., Hagen H. Interpolation of scattered data on closed surfaces. Comput Aided Geom Des. 7:(1-4):1990;303-312.
17. Hiyoshi H, Sugihara K. Voronoi-based interpolation with higher continuity. Proceedings of the 16th Annual ACM Symposium on Computational Geometry; 2000. pp. 242-50.
18. Leibon G., Letscher D. Delaunay triangulations and Voronoi diagrams for Riemannian manifolds. Proceedings of the 16th Annual ACM Symposium on Computational Geometry. 2000;341-349.
19. Neamtu M. Handbook of Geometric Design. Splines on surfaces. Elsevier Science BV, 2002.
20. Piper B. Properties of local coordinates based on dirichlet tesselations. Comput Suppl. 8:1993;227-239.
21. Sibson R. A vector identity for the Dirichlet tesselation. Math Proc Camb Phil Soc. 87:1980;151-155.
22. Sibson R. A brief description of natural neighbour interpolation. Barnet V. Interpreting multivariate data. 1981;21-36 Wiley, Chichester.
23. Wolter F.E. Cut locus and medial axis in global shape interrogation and representation. Technical report 92-2. 1992;Design Lab, Department of Ocean Engineering, MIT, Cambridge, MA.