Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
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Conformal virtual colon flattening
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Proceedings of the 2006 ACM symposium on Solid and physical modeling
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Computers and Graphics
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Computer Aided Geometric Design
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Recent Advances in Computational Conformal Geometry
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Computer Aided Geometric Design
Bounded distortion mapping spaces for triangular meshes
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Simple formulas for quasiconformal plane deformations
ACM Transactions on Graphics (TOG)
Computing Extremal Quasiconformal Maps
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Planar shape interpolation with bounded distortion
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Surface- and volume-based techniques for shape modeling and analysis
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A simple and local method for computing quasi-conformal map on 3D surfaces
Computer-Aided Design
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We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient , which describes the deviation from conformality of the deformation at each point. We propose an effective algorithm to solve the quasi-conformal map from the Beltrami coefficient. The major strategy is to deform the conformal structure of the original surface to a new conformal structure by the Beltrami coefficient, such that the quasi-conformal map becomes a conformal map. By using holomorphic differential forms, conformal maps under the new conformal structure are calculated, which are the desired quasi-conformal maps. The efficiency and efficacy of the algorithms are demonstrated by experimental results. Furthermore, the algorithms are robust for surfaces scanned from real life, and general for surfaces with different topologies.