On Transfinite Barycentric Coordinates

Belyaev, Alexander

On Transfinite Barycentric Coordinates

Files

089-099.pdf (295.7 KB)

Date

2006

Authors

Belyaev, Alexander

Publisher

The Eurographics Association

Abstract

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.

        @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
}
}