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
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
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
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
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Convergence of discrete Laplace-Beltrami operators over surfaces
Computers & Mathematics with Applications
Parametric polynomial minimal surfaces of degree six with isothermal parameter
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Error term in pointwise approximation of the curvature of a curve
Computer Aided Geometric Design
Minimal mean-curvature-variation surfaces and their applications in surface modeling
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
| Hi-index | 0.00 |
In this paper, we study the convergence property of a well known discretized scheme for approximating Gaussian curvature, derived from Gauss-Bonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the approximation has quadratic convergence rate if the surface sampling satisfies the so-called parallelogram criterion. Numerical results which justify the theoretical analysis are also presented.