Range Image Segmentation Based on Differential Geometry: A Hybrid Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curvature approximation for triangulated surfaces
Geometric modelling
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
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
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
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
Apparent ridges for line drawing
ACM SIGGRAPH 2007 papers
Computer Vision and Image Understanding
An incremental approach to feature aligned quad dominant remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Parametric triangular Bézier surface interpolation with approximate continuity
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Demarcating curves for shape illustration
ACM SIGGRAPH Asia 2008 papers
How well do line drawings depict shape?
ACM SIGGRAPH 2009 papers
Characterization of 3D shape parts for semantic annotation
Computer-Aided Design
Robust Voronoi-based curvature and feature estimation
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Anisotropic smoothing of point sets
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Curvature estimation scheme for triangle meshes using biquadratic Bézier patches
Computer-Aided Design
A new CAD mesh segmentation method, based on curvature tensor analysis
Computer-Aided Design
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
| Hi-index | 0.00 |
The estimation of surface curvature is essential for a variety of applications in computer graphics because of its invariance with respect to rigid transformations. In this article, we describe a curvature estimation method for meshes by converting each planar triangular facet into a curved patch using the vertex positions and the normals of three vertices of each triangle. Our method interpolates three end points and the corresponding normal vectors of each triangle to construct a curved patch. Then, we compute the per triangle curvature of the neighboring triangles of a mesh point of interest. Similar to estimating per vertex normal from the adjacent per triangle normal, we compute the per vertex curvature by taking a weighted average of per triangle curvature. Through some examples, we demonstrate that our method is efficient and its accuracy is comparable to that of the existing methods.