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Mean value coordinates for arbitrary spherical polygons and polyhedra in $\mathbb{R}^{3}$

MPS-Authors
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/persons44882

Langer,  Torsten
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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Fulltext (public)

MPI-I-2006-4-010.pdf
(Any fulltext), 205KB

Supplementary Material (public)
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Citation

Belyaev, A., Langer, T., & Seidel, H.-P.(2006). Mean value coordinates for arbitrary spherical polygons and polyhedra in $\mathbb{R}^{3}$ (MPI-I-2006-4-010). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-671C-2
Abstract
Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to $\mathbb{R}^{3}$. We show that these spherical and 3D mean value coordinates are well-defined on the whole sphere and the whole space $\mathbb{R}^{3}$, respectively.