Geometry, Imaging and Computing

Volume 3 (2016)

Number 1-2

Fast spherical quasiconformal parameterization of genus-$0$ closed surfaces with application to adaptive remeshing

Pages: 1 – 29

DOI: https://dx.doi.org/10.4310/GIC.2016.v3.n1.a1

Authors

Gary Pui-Tung Choi (John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, U.S.A.)

Mandy Hiu-Ying Man (Department of Mathematics, The Chinese University of Hong Kong)

Lok Ming Lui (Department of Mathematics, The Chinese University of Hong Kong)

Abstract

In this work, we are concerned with the spherical quasiconformal parameterization of genus-$0$ closed surfaces. Given a genus-$0$ closed triangulated surface and an arbitrary user-defined quasiconformal distortion, we propose a fast algorithm for computing a spherical parameterization of the surface that satisfies the prescribed distortion. The proposed algorithm can be effectively applied to adaptive surface remeshing for improving the visualization in computer graphics and animations. Experimental results are presented to demonstrate the effectiveness of our algorithm.

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Lok Ming Lui is supported by HKRGC GRF (Project ID: 3132707).

Received 10 January 2017

Published 19 April 2018