Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Intrinsic scale space for images on surfaces: The Geodesic Curvature Flow
Graphical Models and Image Processing
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic nonlinear diffusion in flow visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Proceedings of the 12th Eurographics Workshop on Rendering Techniques
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis
IEEE Transactions on Visualization and Computer Graphics
Fairing of Point Based Surfaces
CGI '04 Proceedings of the Computer Graphics International
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Finite elements on point based surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
Solving PDEs on manifolds with global conformal parametriazation
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Real-Time Fluid Effects on Surfaces using the Closest Point Method
Computer Graphics Forum
SMI 2013: Feature-aware filtering for point-set surface denoising
Computers and Graphics
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We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs on point surfaces. This discretization is based on the local assembly of PDE-specific mass and stiffness matrices, using a local point coupling computation. Point couplings are computed using a local tangent plane construction and a local Delaunay triangulation of point neighborhoods. The definition of tangent planes relies on moment-based computation with proven scaling and stability properties. Once local stiffness matrices are obtained, we are able to easily assemble global matrices and efficiently solve the corresponding linear systems by standard iterative solvers. We demonstrate our framework by several types of PDE-based surface processing applications, such as segmentation, texture synthesis, bump mapping, and geometric fairing.