Efficient Conformal Parameterization of Multiply-Connected Surfaces Using Quasi-Conformal Theory
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10915_2021_1479_ReferencePDF.pdf
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13.17 MB
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b222e0645703e8ee946cfe8d8038a645
Author(s)
Choi, Gary P T
Date Issued
April 22, 2021
Publisher
Springer US
Citation
Journal of Scientific Computing. 2021 Apr 22;87(3):70
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10915-021-01479-y
