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

Belyaev, Alexander; Langer, Torsten; Seidel, Hans-Peter

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

MPS-Authors

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

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

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

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フルテキスト (公開)

MPI-I-2006-4-010.pdf
(全文テキスト（全般）), 205KB

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引用

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.

引用: https://hdl.handle.net/11858/00-001M-0000-0014-671C-2

要旨

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.