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dc.contributor.authorChen, Renjieen_US
dc.contributor.authorGotsman, Craigen_US
dc.contributor.editorMaks Ovsjanikov and Daniele Panozzoen_US
dc.date.accessioned2016-06-17T14:11:47Z
dc.date.available2016-06-17T14:11:47Z
dc.date.issued2016en_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttp://dx.doi.org/10.1111/cgf.12962en_US
dc.description.abstractTransfinite barycentric kernels are the continuous version of traditional barycentric coordinates and are used to define inter-polants of values given on a smooth planar contour. When the data is two-dimensional, i.e. the boundary of a planar map, these kernels may be conveniently expressed using complex number algebra, simplifying much of the notation and results. In this paper we develop some of the basic complex-valued algebra needed to describe these planar maps, and use it to define similarity kernels, a natural alternative to the usual barycentric kernels. We develop the theory behind similarity kernels, explore their properties, and show that the transfinite versions of the popular three-point barycentric coordinates (Laplace, mean value and Wachspress) have surprisingly simple similarity kernels. We furthermore show how similarity kernels may be used to invert injective transfinite barycentric mappings using an iterative algorithm which converges quite rapidly. This is useful for rendering images deformed by planar barycentric mappings.en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputer Gemetry and Object Modelen_US
dc.subjectingen_US
dc.subjectBoundary representationsen_US
dc.subjectG.1.1 [Numerical Analysis]en_US
dc.subjectInterpolationen_US
dc.subjectInterpolation formulasen_US
dc.titleComplex Transfinite Barycentric Mappings with Similarity Kernelsen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.sectionheadersMappingsen_US
dc.description.volume35en_US
dc.description.number5en_US
dc.identifier.doi10.1111/cgf.12962en_US
dc.identifier.pages41-53en_US


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