Recent development of computational conformal geometry
type: Item
instance of: scholarly article
zbMATH Open document ID: 1247.53017
author: Lok Ming Lui
author: Luo Feng
author: Wei Zeng
author: Shing-Tung Yau
author: David Xianfeng Gu
publication date: 2012-07-21T00:00:00Z
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 52C26
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 6059327
zbMATH Keywords: computational conformal geometry
zbMATH Keywords: conformal structure
zbMATH Keywords: conformal modulus
zbMATH Keywords: Ricci flow
zbMATH Keywords: holomorphic differential
zbMATH Keywords: harmonic map
zbMATH Keywords: quasi-conformal geometry
MaRDI profile type: Publication
title: Recent development of computational conformal geometry
review text: This survey article about numerical conformal geometry presents state-of-the-art techniques for computing conformal mappings and conformal structures with particular emphasis on surfaces of complicated topology.NEWLINENEWLINESection~2 describes relevant literature, Section~3 introduces the necessary theoretical background from algebraic topology, Riemannian geometry, (quasi)-conformal geometry, and Teichmüller theory. The main computational techniques for computing conformal maps are introduced in Section~4. They are harmonic maps, holomorphic differential, and discrete Ricci flow. Methods for computing conformal moduli and canonical conformal mappings are described in Section~5, quasi-conformal mappings are the topic of Section~6, and Section~7 presents applications from computer graphics, geometric modeling, medical imaging, computer vision, computational geometry, and wireless sensor networks.NEWLINENEWLINEThe text is interspersed with a 32 attractive figures and numerous references for further reading.NEWLINENEWLINEFor the entire collection see [Zbl 1235.00046].
reviewed by: Hans-Peter Schröcker
description: scientific article; zbMATH DE number 6059327