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
Experiments in Curvature-Based Segmentation of Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 24th 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
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Conveying the 3D Shape of Smoothly Curving Transparent Surfaces via Texture
IEEE Transactions on Visualization and Computer Graphics
Normal vector voting: crease detection and curvature estimation on large, noisy meshes
Graphical Models - Special issue: Processing on large polygonal meshes
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Best Fit Surface Curvature at Vertices of Topologically Irregular Curve Networks
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
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
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Proceedings of the 4th international symposium on Non-photorealistic animation and rendering
Computer Vision and Image Understanding
Superquadrics and Angle-Preserving Transformations
IEEE Computer Graphics and 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
Technical Section: Pencil rendering on 3D meshes using convolution
Computers and Graphics
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In this paper, we estimate the principal curvatures of surfaces represented as triangular meshes using a generic model constructed from Euler Formula. Normal curvatures are sampled in the vertices on the direction of a 1- ring neighborhood of a target vertex. Our model is then fitted to a normal curvature graph that connects the pairs of sampled directions and normal curvatures. The principal properties of the surface at the target vertex are estimated from the parameters of the fitted model. We have tested our algorithm on triangular meshes generated from analytic surfaces and show that the errors in our technique are acceptable. We also apply the method to mesh models and discuss degenerate cases.