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Conference Paper

On Transfinite Barycentric Coordinates

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

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

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Citation

Belyaev, A. (2006). On Transfinite Barycentric Coordinates. In SGP 2006: Fourth Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (pp. 89-99). Aire-la-Ville, Switzerland: Eurographics.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-23A7-D
Abstract
A general construction of trans_nite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The Gordon-Wixom interpolation scheme [GW74] and trans_nite counterparts of discrete harmonic and Wachspress-Warren coordinates are studied as particular cases of that general construction. Motivated by _nite element/volume applications, we study capabilities of trans_nite barycentric interpolation schemes to approximate harmonic and quasi-harmonic functions. Finally we establish and analyze links between trans_nite barycentric coordinates and certain inverse problems of di_erential and convex geometry.