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Mean Value Coordinates for Arbitrary Spherical Polygons and Polyhedra in IR3

MPG-Autoren
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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Zitation

Langer, T., Belyaev, A., & Seidel, H.-P. (2007). Mean Value Coordinates for Arbitrary Spherical Polygons and Polyhedra in IR3. In P. Chenin, T. Lyche, & L. L. Schumaker (Eds.), Curve and Surface Design: Avignon 2006 (pp. 193-202). Brentwood, TN, USA: Nashboro Press.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-1FD4-A
Zusammenfassung
Since their introduction, mean value coordinates have enjoyed 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.