On the angular defect of triangulations and the pointwise approximation of curvatures

Computer Aided Geometric Design

Volumn 20, Issue 6, 2003, Pages 319-341

  Borrelli, V ^a   Cazals, F ^b   Morvan, J M ^a,b  

^a UNIVERSITÉ LYON 1   (France)

^b INRIA   (France)

Author keywords

Approximations; Curvatures; Differential geometry; Meshes; Smooth surfaces

Indexed keywords

APPROXIMATION THEORY; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS; ERROR DETECTION; POLYNOMIALS; TRIANGULATION;

DIFFERENTIAL GEOMETRY;

CURVE FITTING;

EID: 0041859748     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(03)00077-3     Document Type: Article

References (15)

1. Amenta N., Bern M. Surface reconstruction by Voronoi filtering. Discrete Comput. Geom. 22:(4):1999;481-504.
2. Banchoff T.F. Critical points and curvature for embedded polyhedra. J. Differential Geom. 1:1967;245-256.
3. Calladine C.R. Gaussian curvature and shell structures. Gregory J.A. The Mathematics of Surfaces. 1986;Oxford Univ. Press.
4. Cheeger J., Müller W., Schrader R. On the curvature of piecewise flat spaces. Comm. Math. Phys. 92:1984.
5. Cskny P., Wallace A.M. Computation of local differential parameters on irregular meshes. Cipolla R., Martin R. Mathematics of Surfaces. 2000;Springer.
6. Dyn N., Hormann K., Kim S.-J., Levin D. Optimizing 3d triangulations using discrete curvature analysis. Lyche T., Shumaker L.L. Mathematical Methods for Curves and Surfaces. 2001;Vanderbild Univ. Press.
7. Lafontaine J. Mesures de courbures des varietes lisses et discretes. Sem. Bourbaki. 664:1986.
8. Meyer M., Desbrun M., Schröder P., Barr A.H. Discrete differential-geometry operators for triangulated 2-manifolds. VisMath. 2002.
9. Morvan J.-M., Thibert B. Smooth surface and triangular mesh: Comparison of the area, the normals and the unfolding. ACM Symposium on Solid Modeling and Applications. 2001.
10. Meek D.S., Walton D.J. On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Comput. Aided Geom. Design. 2000.
11. Polthier K., Schmies M. Straightest geodesics on polyhedral surfaces. Hege H.C., Polthier K. Mathematical Visualization. 1998.
12. Reshetnyak Y.G. Two-dimensional manifolds of bounded curvature. Reshetnyak Y.G. Geometry IV. Encyclopedia of Mathematical Sciences. 70:1993;Springer, Berlin.
13. Spivak M. A Comprehensive Introduction to Differential Geometry. 3rd edn :1999;Publish or Perish.
14. Taubin G. Estimating the tensor of curvature of a surface from a polyhedral approximation. 15th International Conference on Computer Vision. 1995.
15. Watanabe K., Belyaev A.G. Detection of salient curvature features on polygonal surfaces. Eurographics. 2001.