Spherical Barycentric Coordinates

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dc.contributor.authorLanger, Torstenen_US
dc.contributor.authorBelyaev, Alexanderen_US
dc.contributor.authorSeidel, Hans-Peteren_US
dc.contributor.editorAlla Sheffer and Konrad Polthieren_US
dc.date.accessioned2014-01-29T08:14:02Z
dc.date.available2014-01-29T08:14:02Z
dc.date.issued2006en_US
dc.description.abstractWe develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect to the vertices of a given spherical polygon. In particular, we introduce spherical mean value coordinates that inherit many good properties of their planar counterparts. Furthermore, we present a construction that gives a simple and intuitive geometric interpretation for classical barycentric coordinates, like Wachspress coordinates, mean value coordinates, and discrete harmonic coordinates. One of the most interesting consequences is the possibility to construct mean value coordinates for arbitrary polygonal meshes. So far, this was only possible for triangular meshes. Furthermore, spherical barycentric coordinates can be used for all applications where only planar barycentric coordinates were available up to now. They include Bézier surfaces, parameterization, free-form deformations, and interpolation of rotations.en_US
dc.description.seriesinformationSymposium on Geometry Processingen_US
dc.identifier.isbn3-905673-24-Xen_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP06/081-088en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modelingen_US
dc.titleSpherical Barycentric Coordinatesen_US
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SGP06: Eurographics Symposium on Geometry Processing