Solid shape
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
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
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
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
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Suggestive contours for conveying shape
ACM SIGGRAPH 2003 Papers
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Efficiently combining positions and normals for precise 3D geometry
ACM SIGGRAPH 2005 Papers
Asymptotic analysis of discrete normals and curvatures of polylines
Proceedings of the 21st spring conference on Computer graphics
Curvature formulas for implicit curves and surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Laplacian Based Non-Linear Diffusion Filtering
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Graph Laplacians and their Convergence on Random Neighborhood Graphs
The Journal of Machine Learning Research
Convergence of discrete Laplace-Beltrami operators over surfaces
Computers & Mathematics with Applications
Estimating the principal curvatures and the Darboux frame from real 3-D range data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Computer Aided Geometric Design
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
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The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian curvature and the curvature tensor. The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact. Finally, we derive an approximation formula for the curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.