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Efficient Conformal Parameterization of Multiply-Connected Surfaces Using Quasi-Conformal Theory
- Source :
- Journal of Scientific Computing. 87
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering. However, most of the existing conformal parameterization algorithms only focus on simply-connected surfaces and cannot be directly applied to surfaces with holes. In this work, we propose two novel algorithms for computing the conformal parameterization of multiply-connected surfaces. We first develop an efficient method for conformally parameterizing an open surface with one hole to an annulus on the plane. Based on this method, we then develop an efficient method for conformally parameterizing an open surface with $k$ holes onto a unit disk with $k$ circular holes. The conformality and bijectivity of the mappings are ensured by quasi-conformal theory. Numerical experiments and applications are presented to demonstrate the effectiveness of the proposed methods.
- Subjects :
- Computational Geometry (cs.CG)
FOS: Computer and information sciences
Mathematics - Differential Geometry
Surface (mathematics)
Work (thermodynamics)
Conformal map
01 natural sciences
Theoretical Computer Science
Computer Science - Graphics
FOS: Mathematics
Complex Variables (math.CV)
0101 mathematics
Mathematics
Numerical Analysis
Mathematics - Complex Variables
Plane (geometry)
Applied Mathematics
Mathematical analysis
General Engineering
Annulus (mathematics)
Unit disk
Graphics (cs.GR)
010101 applied mathematics
Computational Mathematics
Differential Geometry (math.DG)
Computational Theory and Mathematics
Differential geometry
Computer Science - Computational Geometry
Focus (optics)
Software
Subjects
Details
- ISSN :
- 15737691 and 08857474
- Volume :
- 87
- Database :
- OpenAIRE
- Journal :
- Journal of Scientific Computing
- Accession number :
- edsair.doi.dedup.....9b4d832ec1048ae03a5c399740797657