On Transfinite Barycentric Coordinates
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2006Pay-Per-View via TIB Hannover:
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A general construction of transfinite 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 transfinite counterparts of discrete harmonic and Wachspress-Warren coordinates are studied as particular cases of that general construction. Motivated by finite element/volume applications, we study capabilities of transfinite barycentric interpolation schemes to approximate harmonic and quasi-harmonic functions. Finally we establish and analyze links between transfinite barycentric coordinates and certain inverse problems of differential and convex geometry.
BibTeX
@inproceedings {10.2312:SGP:SGP06:089-099,
booktitle = {Symposium on Geometry Processing},
editor = {Alla Sheffer and Konrad Polthier},
title = {{On Transfinite Barycentric Coordinates}},
author = {Belyaev, Alexander},
year = {2006},
publisher = {The Eurographics Association},
ISSN = {1727-8384},
ISBN = {3-905673-24-X},
DOI = {10.2312/SGP/SGP06/089-099}
}
booktitle = {Symposium on Geometry Processing},
editor = {Alla Sheffer and Konrad Polthier},
title = {{On Transfinite Barycentric Coordinates}},
author = {Belyaev, Alexander},
year = {2006},
publisher = {The Eurographics Association},
ISSN = {1727-8384},
ISBN = {3-905673-24-X},
DOI = {10.2312/SGP/SGP06/089-099}
}