Curvature approximation for triangulated surfaces
Geometric modelling
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Geometric accuracy analysis for discrete surface approximation
Computer Aided Geometric Design
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
Consistent computation of first- and second-order differential quantities for surface meshes
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer Aided Geometric Design
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Generalized shape operators on polyhedral 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
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
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The convergence property of the discrete Laplace-Beltrami operator is the foundationof convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. The aim of this paper is to review several already-used discrete Laplace-Beltrami operators over triangulated surface and study numerically, as well as theoretically, their convergent behavior. We show that none of them is convergent in general, but two of them, proposed by Desbrun et al. and Meyer et al., are convergent in a special case. We point out that this special case is very important in the numerical simulation of geometric partial differential equations.