Surface Parametrization and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Estimation of the principle curvatures of approximated surfaces
Computer Aided Geometric Design
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
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
A General Sixth Order Geometric Flow and Its Applications in Surface Processing
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
A general framework for surface modeling using geometric partial differential equations
Computer Aided Geometric Design
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Curvature estimation scheme for triangle meshes using biquadratic Bézier patches
Computer-Aided Design
ACM SIGGRAPH ASIA 2009 Courses
Convergence analysis of discrete differential geometry operators over surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Minimal mean-curvature-variation surfaces and their applications in surface modeling
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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The numerical integration of geometric partial differential equations is used in many applications such as image processing, surface processing, computer graphics and computer-aided geometric design. Discrete approximations of several first- and second-order geometric differential operators, such as the tangential gradient operator, the second tangential operator, the Laplace-Beltrami operator and the Giaquinta-Hildebrandt operator, are utilized in the numerical integrations. In this paper, we consider consistent discretized approximations of these operators based on a quadratic fitting scheme. An asymptotic error analysis is conducted which shows that under very mild conditions the discrete approximations of the first- and second-order geometric differential operators have quadratic and linear convergence rates, respectively.