Constructing isothermal curvature line coordinates on surfaces which admit them

TL;DR

This paper presents a method to construct isothermic coordinate charts on surfaces that admit them, facilitating numerical algorithms for surface visualization.

Contribution

It introduces a novel approach to generate isothermic coordinates from arbitrary charts on surfaces that admit such parameterizations.

Findings

Method successfully constructs isothermic coordinates from arbitrary charts.

Applicable to surfaces in Euclidean spaces that admit isothermic parameterizations.

Enhances numerical algorithms for surface visualization.

Abstract

Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.