Planar Shape Interpolation Based On Teichmüller Mapping

dc.contributor.authorNian, Xianshunen_US
dc.contributor.authorChen, Falaien_US
dc.contributor.editorEitan Grinspun and Bernd Bickel and Yoshinori Dobashien_US
dc.date.accessioned2016-10-11T05:18:41Z
dc.date.available2016-10-11T05:18:41Z
dc.date.issued2016
dc.description.abstractShape interpolation is a classical problem in computer graphics and has been widely investigated in the past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold-overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps - a special type of maps in the class of quasi-conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start-of-the-art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.en_US
dc.description.number7
dc.description.sectionheadersMatching and Interpolation
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume35
dc.identifier.doi10.1111/cgf.13002
dc.identifier.issn1467-8659
dc.identifier.pages43-56
dc.identifier.urihttps://doi.org/10.1111/cgf.13002
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13002
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.3 [Computer Graphics]
dc.subjectPicture/Image Generation
dc.subjectDisplay Algorithms
dc.subjectI.3.7 [Computer Graphics]
dc.subjectThree Dimensional Graphics and Realism
dc.subjectAnimation Keywords
dc.subjectshape interpolation
dc.subjectTeichmüller mapping
dc.subjectconformal distortion
dc.subjectBeltrami coefficient.
dc.titlePlanar Shape Interpolation Based On Teichmüller Mappingen_US
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