Regularizations of non-euclidean polygons

TL;DR

This paper explores simple geometric transformations designed to regularize polygons in non-Euclidean geometry, aiming for easy implementation and potential applications in non-Euclidean mesh processing.

Contribution

It introduces easy-to-implement transformations for regularizing polygons in non-Euclidean planes, extending prior Euclidean polygon regularization methods.

Findings

Transformations effectively regularize non-Euclidean polygons

Potential applications in non-Euclidean mesh processing

Provides algorithms suitable for practical implementation

Abstract

We are interested in easy geometric transformations which regularize n-polygons in the non-euclidean plane. A transformation is called easy if it can be easily implemented into an algorithm. This article is motivated by preceding work on geometric transformations on euclidean polygons and possible applications for non-euclidean meshes.