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Fast Disk Conformal Parameterization of Simply-Connected Open Surfaces

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Abstract

Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit disk, which significantly speeds up the computation, enhances the conformality and stability, and guarantees the bijectivity. The conformality distortions at the inner region and on the boundary are corrected by two steps, with the aid of an iterative scheme using quasi-conformal theories. Experimental results demonstrate the effectiveness of our proposed method.

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Acknowledgments

Lok Ming Lui is supported by RGC GRF (CUHK Project ID: 404612) and CUHK FIS Grant (Project ID: 1902036).

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

    Pui Tung Choi & Lok Ming Lui

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  1. Pui Tung Choi
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  2. Lok Ming Lui
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Correspondence to Lok Ming Lui.

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Choi, P.T., Lui, L.M. Fast Disk Conformal Parameterization of Simply-Connected Open Surfaces. J Sci Comput 65, 1065–1090 (2015). https://doi.org/10.1007/s10915-015-9998-2

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