Bijective Composite Mean Value Mappings
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Date
2013Author
Schneider, Teseo 
Hormann, Kai
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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.
BibTeX
@article {10.1111:cgf.12180,
journal = {Computer Graphics Forum},
title = {{Bijective Composite Mean Value Mappings}},
author = {Schneider, Teseo and Hormann, Kai and Floater, Michael S.},
year = {2013},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.12180}
}
journal = {Computer Graphics Forum},
title = {{Bijective Composite Mean Value Mappings}},
author = {Schneider, Teseo and Hormann, Kai and Floater, Michael S.},
year = {2013},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.12180}
}