Bijective Composite Mean Value Mappings |
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| Authors: | T Schneider K Hormann MS Floater |
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| Affiliation: | 1. Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland;2. Department of Mathematics, University of Oslo, Norway |
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| Abstract: | We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU‐assisted implementation for interactively designing composite mean value mappings which are bijective up to pixel resolution. We provide a number of examples of 2D image deformation and an example of 3D shape deformation based on a natural extension of the concept to spatial mappings. |
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| Keywords: | I 3 3 [Computer Graphics]: Picture/Image Generation— Line and curve generation G 1 1 [Numerical Analysis]: Interpolation— Interpolation formulas |
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