# A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

arXiv: https://arxiv.org/abs/1708.07391 · HTML: https://mlsanity.com/paper/1708.07391/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [PartUV: Part-Based UV Unwrapping of 3D Meshes](https://mlsanity.com/paper/2511.16659/) (2025)
- [Adaptive area-preserving parameterization of open and closed anatomical surfaces](https://mlsanity.com/paper/2111.04265/) (2021)
- [SeamFlow: Structure-Aware Flow Matching on Edge Probabilities for Artist-Like UV Unwrapping](https://mlsanity.com/paper/2609.04751/) (2026)

## Abstract (arXiv)

Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of simply connected open surfaces with a very small area distortion and a highly improved computational efficiency. In addition, the existence of nontrivial limit points of the SEM algorithm is guaranteed under some mild assumptions of the mesh quality. Numerical experiments indicate that the efficiency, accuracy, and robustness of the proposed SEM algorithm outperform other state-of-the-art algorithms. Applications of the SEM on surface remeshing and surface registration for simply connected open surfaces are demonstrated thereafter. Thanks to the SEM algorithm, the computations for these applications can be carried out efficiently and robustly.