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
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Discrete Laplace-Beltrami operators and their convergence
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Large mesh deformation using the volumetric graph Laplacian
ACM SIGGRAPH 2005 Papers
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Towards a theoretical foundation for laplacian-based manifold methods
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Constructing Laplace operator from point clouds in Rd
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Laplacian lines for real-time shape illustration
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Integral estimation from point cloud in d-dimensional space: a geometric view
Proceedings of the twenty-fifth annual symposium on Computational geometry
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Approximating gradients for meshes and point clouds via diffusion metric
SGP '09 Proceedings of the Symposium on Geometry Processing
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shape comparison through mutual distances of real functions
Proceedings of the ACM workshop on 3D object retrieval
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
Curvature analysis of frequency modulated manifolds in dimensionality reduction
Calcolo: a quarterly on numerical analysis and theory of computation
SMI 2011: Full Paper: Harmonic point cloud orientation
Computers and Graphics
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
Photometric heat kernel signatures
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
Fragmented skull modeling using heat kernels
Graphical Models
SHREC'10 track: feature detection and description
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
Affine-invariant photometric heat kernel signatures
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
Extremum problems for eigenvalues of discrete Laplace operators
Computer Aided Geometric Design
SMI 2013: Grouping real functions defined on 3D surfaces
Computers and Graphics
Key-dependent 3D model hashing for authentication using heat kernel signature
Digital Signal Processing
The Visual Computer: International Journal of Computer Graphics
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Learning kernels on extended Reeb graphs for 3d shape classification and retrieval
3DOR '13 Proceedings of the Sixth Eurographics Workshop on 3D Object Retrieval
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In recent years a considerable amount of work in graphics and geometric optimization used tools based on the Laplace-Beltrami operator on a surface. The applications of the Laplacian include mesh editing, surface smoothing, and shape interpolations among others. However, it has been shown [13, 24, 26] that the popular cotangent approximation schemes do not provide convergent point-wise (or even L2) estimates, while many applications rely on point-wise estimation. Existence of such schemes has been an open question [13]. In this paper we propose the first algorithm for approximating the Laplace operator of a surface from a mesh with point-wise convergence guarantees applicable to arbitrary meshed surfaces. We show that for a sufficiently fine mesh over an arbitrary surface, our mesh Laplacian is close to the Laplace-Beltrami operator on the surface at every point of the surface. Moreover, the proposed algorithm is simple and easily implementable. Experimental evidence shows that our algorithm exhibits convergence empirically and compares favorably with cotangentbased methods in providing accurate approximation of the Laplace operator for various meshes.