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Conference Paper

Spherical Barycentric Coordinates

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44882

Langer,  Torsten
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

Langer, T., Belyaev, A., & Seidel, H.-P. (2006). Spherical Barycentric Coordinates. In SGP 2006 : Fourth Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (pp. 81-88). Aire-la-Ville, Switzerland: Eurographics.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-23FD-B
Abstract
We 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 B\'ezier surfaces, parameterization, free-form deformations, and interpolation of rotations.