A simple and local method for computing quasi-conformal map on 3D surfaces
Quasi-conformal maps have bounded conformal distortion, and are the natural extension of the conformal maps. The existing techniques to compute the quasi-conformal map require a global coordinate system; thus, they are limited to models of simple topological types, such as genus-0 or 1 surfaces, for...
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sg-ntu-dr.10356-1072302020-05-28T07:19:05Z A simple and local method for computing quasi-conformal map on 3D surfaces Zhang, Minqi He, Ying School of Computer Engineering DRNTU::Engineering::Computer science and engineering::Computer applications::Computer-aided engineering Quasi-conformal maps have bounded conformal distortion, and are the natural extension of the conformal maps. The existing techniques to compute the quasi-conformal map require a global coordinate system; thus, they are limited to models of simple topological types, such as genus-0 or 1 surfaces, for which one can obtain the global coordinates by the global parameterization. This paper presents a simple yet effective technique for computing a quasi-conformal map on surfaces of non-trivial topology. Our method extends the quasi-conformal iteration method (Lui et al., 2012) [8] from the complex plane to the manifold setting. It requires neither numerical solver nor the global coordinate system, thus, is easy to implement. Moreover, thanks to its simple and parallel structure, our method is well suited for parallel computing. Experimental results on 3D models of various topological types demonstrate the efficacy of our technique. 2013-11-21T07:04:03Z 2019-12-06T22:27:07Z 2013-11-21T07:04:03Z 2019-12-06T22:27:07Z 2013 2013 Journal Article Zhang, M., & He, Y. (2013). A simple and local method for computing quasi-conformal map on 3D surfaces. Computer-Aided Design, in press. 0010-4485 https://hdl.handle.net/10356/107230 http://hdl.handle.net/10220/17810 10.1016/j.cad.2013.08.031 en Computer-aided design |
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DRNTU::Engineering::Computer science and engineering::Computer applications::Computer-aided engineering Zhang, Minqi He, Ying A simple and local method for computing quasi-conformal map on 3D surfaces |
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Quasi-conformal maps have bounded conformal distortion, and are the natural extension of the conformal maps. The existing techniques to compute the quasi-conformal map require a global coordinate system; thus, they are limited to models of simple topological types, such as genus-0 or 1 surfaces, for which one can obtain the global coordinates by the global parameterization. This paper presents a simple yet effective technique for computing a quasi-conformal map on surfaces of non-trivial topology. Our method extends the quasi-conformal iteration method (Lui et al., 2012) [8] from the complex plane to the manifold setting. It requires neither numerical solver nor the global coordinate system, thus, is easy to implement. Moreover, thanks to its simple and parallel structure, our method is well suited for parallel computing. Experimental results on 3D models of various topological types demonstrate the efficacy of our technique. |
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School of Computer Engineering |
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School of Computer Engineering Zhang, Minqi He, Ying |
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Article |
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Zhang, Minqi He, Ying |
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Zhang, Minqi |
title |
A simple and local method for computing quasi-conformal map on 3D surfaces |
title_short |
A simple and local method for computing quasi-conformal map on 3D surfaces |
title_full |
A simple and local method for computing quasi-conformal map on 3D surfaces |
title_fullStr |
A simple and local method for computing quasi-conformal map on 3D surfaces |
title_full_unstemmed |
A simple and local method for computing quasi-conformal map on 3D surfaces |
title_sort |
simple and local method for computing quasi-conformal map on 3d surfaces |
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2013 |
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https://hdl.handle.net/10356/107230 http://hdl.handle.net/10220/17810 |
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1681059228865789952 |