Estimating Discrete Total Curvature with Per Triangle Normal Variation
This provides a more accurate tool for curvature estimation in computer graphics and geometry processing, though it appears incremental as it builds on known relationships.
The paper tackles the problem of measuring total curvature on discrete surfaces by introducing a method based on the Dirichlet energy of the Gauss map, which outperforms existing libraries like Meshlab and PCL in feature-aware mesh decimation and point cloud curvature estimation.
We introduce a novel approach for measuring the total curvature at every triangle of a discrete surface. This method takes advantage of the relationship between per triangle total curvature and the Dirichlet energy of the Gauss map. This new tool can be used on both triangle meshes and point clouds and has numerous applications. In this study, we demonstrate the effectiveness of our technique by using it for feature-aware mesh decimation, and show that it outperforms existing curvature-estimation methods from popular libraries such as Meshlab, Trimesh2, and Libigl. When estimating curvature on point clouds, our method outperforms popular libraries PCL and CGAL.