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ADCM
2006

A general construction of barycentric coordinates over convex polygons

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A general construction of barycentric coordinates over convex polygons
Barycentric coordinates are unique for triangles, but there are many possible generalizations to convex polygons. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such coordinates have the same continuous extension to the boundary. We then present a general approach for constructing such coordinates and use it to show that the Wachspress, mean value, and discrete harmonic coordinates all belong to a unifying one-parameter family of smooth three-point coordinates. We show that the only members of this family that are positive, and therefore barycentric, are the Wachspress and mean value ones. However, our general approach allows us to construct several sets of smooth five-point coordinates, which are positive and therefore barycentric.
Michael S. Floater, Kai Hormann, Géza K&oac
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where ADCM
Authors Michael S. Floater, Kai Hormann, Géza Kós
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