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Differential geometry


Introduction


Examples

Functions of two variables


Approximations

1 - Curve and surface fitting methods

Paper Fitting surface Neighborhood Gauss Mean Principal
curvatures
Principal
directions
Goldfeather & Interrante
Cazals & Pouget
Douros & Buxton
Meek & Walton
Hamann

References

A novel cubic-order algorithm for approximating principal direction vectors
Jack Goldfeather, Victoria Interrante
Transactions on Graphics, Volume 23, Issue 1, pp 45--63, January 2004



Estimating differential quantities using polynomial fitting of osculating jets
F. Cazals, M. Pouget
Eurographics symposium on Geometry processing, pp 177--187, 2003



Three-Dimensional Surface Curvature Estimation Using Quadric Surface Patches
I. Douros, B.F. Buxton
Scanning 2002 Proceedings



On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
D. S. Meek, D. J. Walton
Computer Aided Geometric Design, Volume 17, Issue 6, pp. 521--543, 2000



Curvature Approximation for Triangulated Surfaces
Bernd Hamann
In G. Farin et al.,editor,Geometric Modelling, pp 139--153. Springer Verlag, 1993
ist.psu


2 - Discrete methods


References

Exact and interpolatory quadratures for curvature tensor estimation
T. Langer, A. Belyaev, H. Seidel
Computer Aided Geometric Design, Volume 24, Issue 8-9, pp. 443-463, 2007



Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
M. Meyer, M. Desbrun, P. Schröder, A. H. Barr
In Visualization and Mathematics III, by Hans-Christian Hege, Konrad Polthier, pp 35--57, Springers-Verlag, Heidelberg, 2003
CiteSeer.IST


Restricted delaunay triangulations and normal cycle
David Cohen-Steiner, Jean-Marie Morvan
In Proceedings of the nineteenth annual symposium on Computational geometry, pp 312-321, 2003



Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes
D. L. Page, Y. Sun, A. F. Koschan, J. Paik, M. A. Abidi
Journal of Graphical Models 64(3/4):199-229, 2002
CiteSeer.IST


Robust Estimation of Curvature Information from Noisy 3D Data for Shape Description
Chi-Keung Tang, Gérard Medioni
In Proc. IEEE International Conference on Computer Vision, pp 426--433, 1999
CiteSeer.IST


Estimating The Tensor Of Curvature Of A Surface From A Polyhedral Approximation
Gabriel Taubin
In Fifth International Conference on Computer Vision, (ICCV'95), 1995
CiteSeer.IST


3 - Curvature tensor estimation


References

Robust statistical estimation of curvature on discretized surfaces
Evangelos Kalogerakis, Patricio Simari, Derek Nowrouzezahrai, Karan Singh
Eurographics Symposium on Geometry Processing 2007
Patricio Simari's webpage


Estimating curvatures and their derivatives on triangle meshes
S. Rusinkiewicz
3D Data Processing, Visualization, and Transmission, 2nd International Symposium on (3DPVT’04), pp 486–493, 2004
project's webpage



Misc


Spider: A robust curvature estimator for noisy, irregular meshes
Patricio Simari, Karan Singh, Hans Pedersen
Technical report CSRG-531, Dynamic Graphics Project, Department of Computer Science, University of Toronto, September 2005



Curvatures estimation on triangular mesh
Dong Chen-shi, Wang Guo-zhao
Journal of Zhejiang University, pp. 128-136, 2005



Generalized Barycentric Coordinates on Irregular Polygons
Mark Meyery, Haeyoung Leez, Alan Barry, Mathieu Desbrun
Journal of Graphics Tools 7, 1, 13--22, 2002



Optimizing 3D Triangulations Using Discrete Curvature Analysis
Nira Dyn, Kai Hormann, Sun-Jeong Kim, David Levin
Mathematical Methods for Curves and Surfaces, pp. 135--146, 2000



Surface parameterization and curvature measurement of arbitrary 3-D objects : five practical methods
E. M. Stockely, S. Y. Wu
IEEE transactions on pattern analysis and machine intelligence, vol. 14, no8, pp. 833-840, 1992



Second Fundamental Measure of Geometric Sets and Local Approximation of Curvatures
D. Cohen-Steiner, J.-M. Morvan
Journal of Differential Geometry, 2006

Programming
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