Abstract
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.
Abstract (translated)
我们引入了一种新方法，用于测量离散表面上每个三角形的总曲率。这种方法利用每个三角形的总曲率和高斯地图的狄利克雷能量之间的关系。这个新工具可以应用于三角形网格和点云，并有许多应用。在本研究中，我们利用这种方法展示了我们技术的有效性，通过使用它进行特征 aware 网格削减，并证明了它比流行的库如Meshlab、Trimesh2和Libigl现有的曲率估计方法更有效。在点云上进行曲率估计时，我们的方法比流行的库PCL和CGAL更有效。
URL
https://arxiv.org/abs/2305.12653
