# Estimating Discrete Total Curvature with Per Triangle Normal Variation

arXiv: https://arxiv.org/abs/2305.12653 · HTML: https://mlsanity.com/paper/2305.12653/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 9 references that are in the map.
- First posted on arXiv 22 May 2023.

## Built on by (most cited first, 1 of 1)

- [GradientSurf: Gradient-Domain Neural Surface Reconstruction from RGB Video](https://mlsanity.com/paper/2310.05406/) (2023)

## Abstract (arXiv)

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.