Weber, OfirBen-Chen, MirelaGotsman, CraigHormann, KaiMario Botsch and Scott Schaefer2015-02-272015-02-2720111467-8659https://doi.org/10.1111/j.1467-8659.2011.02027.xBarycentric 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.I.3.3 [Computer Graphics]Picture/Image GenerationLine and curve generationG.1.1 [Numerical Analysis]InterpolationInterpolation formulas