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Planar Shape Interpolation Based On Teichmüller Mapping
Author(s) -
Nian Xianshun,
Chen Falai
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13002
Subject(s) - conformal map , interpolation (computer graphics) , image stitching , distortion (music) , mathematics , extremal length , affine transformation , linear interpolation , geometry , mathematical analysis , computer science , image (mathematics) , computer vision , polynomial , conformal field theory , amplifier , computer network , bandwidth (computing)
Shape 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.