Discrete schemes for Gaussian curvature and their convergence

Computers and Mathematics with Applications

Volumn 57, Issue 7, 2009, Pages 1187-1195

  Xu, Zhiqiang ^a   Xu, Guoliang ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Angular defect schemes; Discrete curvature; Discrete surfaces; Gaussian curvature; Geometric modelling

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DEFECTS; GAUSSIAN DISTRIBUTION;

ANGULAR DEFECT SCHEMES; DISCRETE CURVATURE; DISCRETE SURFACES; GAUSSIAN CURVATURE; GEOMETRIC MODELLING;

TRELLIS CODES;

EID: 61749089698     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.01.024     Document Type: Article

References (16)

1. Cazals F., and Pouget M. Estimating differential quantities using polynomial fitting of osculating jets. Computer Aided Geometric Design 22 (2005) 767-784
2. I. Douros, B.F. Buxton, Three-dimensional surface curvature estimation using quadric surface patches, in: Scanning 2002 Proceedings, Paris, 2002
3. Martin R. Estimation of principal curvatures from range data. International Journal of Shape Modeling 4 (1998) 99-111
4. Meek D.S., and Walton D.J. On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Computer Aided Geometric Design 17 (2000) 521-543
5. Xu G. Discrete Laplace-Betrami operators and their convergence. Computer Aided Geometric Design 21 (2004) 767-784
6. Borrelli V., Cazals F., and Morvan J.M. On the angular defect of triangulations and the pointwise approximation of curvatures. Computer Aided Geometric Design 20 (2003) 319-341
7. Calladine C.R. Gaussian curvature and shell structures. In: Gregory J.A. (Ed). The Mathematics of Surfaces (1986), Clarendon Press, Oxford
8. M. Meyer, M. Desbrun, P. Schröder, A.H. Barr, Discrete differential-geometry operator for triangulated 2-manifolds, in: Proc. VisMath'02, Berlin, Germany, 2002
9. Xu G. Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces. Computer Aided Geometric Design 23 (2006) 193-207
10. 3 et applications, Ph.D. Thesis, Ecole polytechnique, 1995
11. V. Borrelli, Courbures discrètes, Master Thesis, Claude Bernard University, Lyon 1, 1993
12. Zhiqiang Xu, Guoliang Xu, Jiaguang Sun, Convergence analysis of discrete differential geometry operators over surfaces, IMA Conference on the Mathematics of Surfaces, 2005, pp. 448-457
13. T. Langer, A.G. Belyaev, H.P. Seidel, Analysis and design of discrete normals and curvatures, Technical Report, Max-Planck-Institut für Informatik, 2005
14. D. Cohen-Steiner, J.M. Morvan, Restricted Delaunay triangulations and normal cycle, in: Proceedings of the nineteenth annual symposium on Computational geometry, 2003
15. Hildebrandt K., Polthier K., and Wardetzky M. On the convergence of metric and geometric properties of polyhedral surfaces. Geometriae Dedicata 123 (2006) 89-122
16. Pinkall U., and Polthier K. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2 (1993) 15-36