A Complex View of Barycentric Mappings
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
Abstract
Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real-valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real-valued barycentric coordinates from a given weight function can be applied to generating complex-valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex-weighted combination of edge-to-edge similarity transformations, allowing the design of home-made barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.
Description
@article{10.1111:j.1467-8659.2011.02027.x,
journal = {Computer Graphics Forum},
title = {{A Complex View of Barycentric Mappings}},
author = {Weber, Ofir and Ben-Chen, Mirela and Gotsman, Craig and Hormann, Kai},
year = {2011},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2011.02027.x}
}