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.

翻译：我们提出了一种新颖的方法，用于测量离散曲面上每个三角形的总曲率。该方法利用了每个三角形的总曲率与高斯映射的狄利克雷能量之间的关系。这一新工具可同时应用于三角网格和点云，并具有广泛的应用前景。在本研究中，我们通过将其用于特征感知的网格简化来展示该技术的有效性，并证明其优于来自Meshlab、Trimesh2和Libigl等流行库的现有曲率估计方法。在点云曲率估计方面，我们的方法优于流行的PCL和CGAL库。