On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Discrete Laplace-Beltrami operators and their convergence
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Convergence analysis of discrete differential geometry operators over surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Direct spherical parameterization of 3D triangular meshes using local flattening operations
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
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The popular angular defect schemes for Gaussian curvature only converge at the regular vertex with valence 6. In this paper, we present a new discrete scheme for Gaussian curvature, which converges at the regular vertex with valence greater than 4. We show that it is impossible to build a discrete scheme for Gaussian curvature which converges at the regular vertex with valence 4 by a counterexample. We also study the convergence property of other discrete schemes for Gaussian curvature and compare their asymptotic errors by numerical experiments.