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  Spherical Barycentric Coordinates

Langer, T., Belyaev, A., & Seidel, H.-P. (2006). Spherical Barycentric Coordinates. In D. W. Fellner, S. N. Spencer, A. Sheffer, & K. Polthier (Eds.), SGP 2006 : Fourth Eurographics Symposium on Geometry Processing (pp. 81-88). Aire-la-Ville, Switzerland: Eurographics.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-23FD-B Version Permalink: https://hdl.handle.net/21.11116/0000-000F-44A0-F
Genre: Conference Paper

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 Creators:
Langer, Torsten1, Author           
Belyaev, Alexander1, Author           
Seidel, Hans-Peter1, Author                 
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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Free keywords: -
 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: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314588
Other: Local-ID: C125675300671F7B-9144C5FF262D3F9CC12571BE00348DDF-LangerSGP06
BibTex Citekey: Langer-et-al_SGP06
DOI: 10.2312/SGP/SGP06/081-088
 Degree: -

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Title: Fourth Eurographics Symposium on Geometry Processing
Place of Event: Cagliari, Sardinia, Italy
Start-/End Date: 2006-06-26 - 2006-06-28

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Title: SGP 2006 : Fourth Eurographics Symposium on Geometry Processing
  Abbreviation : SGP 2006
Source Genre: Proceedings
 Creator(s):
Fellner, Dieter W.1, Editor
Spencer, Stephen N.1, Editor
Sheffer, Alla1, Editor
Polthier, Konrad1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Aire-la-Ville, Switzerland : Eurographics
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 81 - 88 Identifier: ISBN: 3-905673-36-3