A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

TL;DR

This paper introduces a new stretch energy minimization algorithm that efficiently computes equiareal surface parameterizations with minimal area distortion, outperforming existing methods in accuracy and robustness.

Contribution

The paper presents a novel SEM algorithm that guarantees small area distortion and improved computational efficiency for equiareal parameterizations of surfaces.

Findings

Outperforms state-of-the-art algorithms in efficiency and accuracy.

Ensures the existence of nontrivial limit points under mild mesh quality assumptions.

Enables robust surface remeshing and registration applications.

Abstract

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.