A Complex View of Barycentric Mappings

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dc.contributor.authorWeber, Ofiren_US
dc.contributor.authorBen-Chen, Mirelaen_US
dc.contributor.authorGotsman, Craigen_US
dc.contributor.authorHormann, Kaien_US
dc.contributor.editorMario Botsch and Scott Schaeferen_US
dc.date.accessioned2015-02-27T15:03:11Z
dc.date.available2015-02-27T15:03:11Z
dc.date.issued2011en_US
dc.description.abstractBarycentric 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.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.doi10.1111/j.1467-8659.2011.02027.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2011.02027.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.3 [Computer Graphics]en_US
dc.subjectPicture/Image Generationen_US
dc.subjectLine and curve generationen_US
dc.subjectG.1.1 [Numerical Analysis]en_US
dc.subjectInterpolationen_US
dc.subjectInterpolation formulasen_US
dc.titleA Complex View of Barycentric Mappingsen_US
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SGP11: Eurographics Symposium on Geometry Processing