2005/10/31 by Jyh-Yang Wu, Wu, Jyh-Yang, Sheng-Gwo Chen +3
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computer Graphics and Visualization Techniques #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.cs/0510090
openalex publication_date 2005/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the differential of the Gauss map of the underlying surface. The Gauss map assigns to each point in the surface the unit normal vector of the tangent plane to the surface at this point. We follow the ideas developed in Chen and Wu \citeChen2(2004) and Wu, Chen and Chi\citeWu(2005) to describe a new and simple approach to estimate the differential of the Gauss map and curvatures from the viewpoint of the gradient and the centroid weights. This will give us a much better estimation of curvatures than Taubin's algorithm \citeTaubin (1995).