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：我们提出了一种创新方法，用于测量离散曲面每个三角形的总曲率。该方法利用了每个三角形总曲率与高斯映射狄利克雷能量之间的内在关联。这一新工具既可应用于三角网格也可应用于点云，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网格简化来证明该技术的有效性，并表明其优于Meshlab、Trimesh2和Libigl等主流库中现有的曲率估算方法。对于点云曲率估算，我们的方法同样优于流行的PCL和CGAL库。