Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
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
Image Processing via the Beltrami Operator
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Acoustics Scattering on Arbitrary Manifold Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
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
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology
Journal of Computational Physics
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
A general framework for surface modeling using geometric partial differential equations
Computer Aided Geometric Design
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
On the parametric finite element approximation of evolving hypersurfaces in R3
Journal of Computational Physics
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Constructing Laplace operator from point clouds in Rd
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Discrete schemes for Gaussian curvature and their convergence
Computers & Mathematics with Applications
Mixed finite element methods for geometric modeling using general fourth order geometric flows
Computer Aided Geometric Design
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
G1 surface modelling using fourth order geometric flows
Computer-Aided Design
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The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for these discrete Laplace-Beltrami operators are established under various conditions. Numerical results that support the theoretical analysis are given. Application examples of the proposed discrete Laplace-Beltrami operators in surface processing and modelling are also presented.