A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
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
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Estimating normal vectors and curvatures by centroid weights
Computer Aided Geometric Design
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
A Choice of Weights for Convex Combination Methods in Estimating Partial Derivatives
CGIV '04 Proceedings of the International Conference on Computer Graphics, Imaging and Visualization
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
A Geometric Interpretation of Weighted Normal Vectors and Its Improvements
CGIV '05 Proceedings of the International Conference on Computer Graphics, Imaging and Visualization
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Anisotropic smoothing of point sets
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
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In this note we present a local tangential lifting (LTL) algorithm to compute differential quantities for triangular meshes obtained from regular surfaces. First, we introduce a new notation of the local tangential polygon and lift functions and vector fields on a triangular mesh to the local tangential polygon. Then we use the centroid weights proposed by Chen and Wu [4] to define the discrete gradient of a function on a triangular mesh. We also use our new method to define the discrete Laplacian operator acting on functions on triangular meshes. Higher order differential operators can also be computed successively. Our approach is conceptually simple and easy to compute. Indeed, our LTL method also provides a unified algorithm to estimate the shape operator and curvatures of a triangular mesh and derivatives of functions and vector fields. We also compare three different methods : our method, the least square method and Akima's method to compute the gradients of functions.