Spherical Parameterization Balancing Angle and Area Distortions

TL;DR

This paper introduces a new framework for spherical mesh parameterization that balances angle and area distortions using innovative algorithms based on Yamabe flow, conformal welding, optimal mass transport, and polar decomposition, with demonstrated efficiency.

Contribution

It presents a novel spherical parameterization method that balances angle and area distortions, combining multiple advanced mathematical techniques.

Findings

Algorithms are efficient and effective on 3D geometric data.

The methods successfully balance angle and area distortions.

Experimental results demonstrate the practicality of the approaches.

Abstract

This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid theoretic foundation. An area-preserving spherical parameterization is also discussed, which is based on discrete optimal mass transport theory. Furthermore, a spherical parameterization algorithm, which is based on the polar decomposition method, balancing angle distortion and area distortion is presented. The algorithms are tested on 3D geometric data and the experiments demonstrate the efficiency and efficacy of the proposed methods.