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  Spherical Barycentric Coordinates

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.

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 Creators:
Langer, Torsten1, Author           
Belyaev, Alexander1, Author           
Seidel, Hans-Peter1, Author           
Fellner, Dieter W., Editor
Spencer, Stephen N., Editor
Sheffer, Alla, Editor
Polthier, Konrad, Editor
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1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 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.

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Language(s): eng - English
 Dates: 2007-03-032006
 Publication Status: Issued
 Pages: -
 Publishing info: Aire-la-Ville, Switzerland : Eurographics
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314588
Other: Local-ID: C125675300671F7B-9144C5FF262D3F9CC12571BE00348DDF-LangerSGP06
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Title: Untitled Event
Place of Event: Cagliari, Sardinia, Italy
Start-/End Date: 2006-06-26

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Title: SGP 2006 : Fourth Eurographics/ACM SIGGRAPH Symposium on Geometry Processing
Source Genre: Proceedings
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Publ. Info: Aire-la-Ville, Switzerland : Eurographics
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 81 - 88 Identifier: ISBN: 3-905673-36-3