Hyperbolization of Euclidean ornaments
type: Item
instance of: scholarly article
title: Hyperbolization of Euclidean ornaments
zbMATH Open document ID: 1168.51310
author: Martin von Gagern
author: Jürgen Richter-Gebert
published in: The Electronic Journal of Combinatorics
publication date: 2009-07-08T00:00:00Z
full work available at URL: https://eudml.org/doc/130460
full work available at URL: v16i2r12.html
review text: Summary: We outline a method that automatically transforms an Euclidean ornament into a hyperbolic one. The necessary steps are pattern recognition, symmetry detection, extraction of a Euclidean fundamental region, conformal deformation to a hyperbolic fundamental region and tessellation of the hyperbolic plane with this patch. Each of these steps has its own mathematical subtleties that are discussed in this article. In particular, it is discussed which hyperbolic symmetry groups are suitable generalizations of Euclidean wallpaper groups. Furthermore it is shown how one can take advantage of methods from discrete differential geometry in order to perform the conformal deformation of the fundamental region. Finally it is demonstrated how a reverse pixel lookup strategy can be used to obtain hyperbolic images with optimal resolution.
Mathematics Subject Classification ID: 51M09
Mathematics Subject Classification ID: 52C26
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 68T10
zbMATH DE Number: 5576459
zbMATH Keywords: wallpaper groups
zbMATH Keywords: symmtry patterns, hyperbolic ornament
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5576459