Convergence of Wachspress coordinates from polygo

Authors: Jiří Kosinka Michael Bartoň

Publish Date: 2014/08/08

Volume: 41, Issue: 3, Pages: 489-505

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Abstract

Given a smooth strictly convex planar domain we investigate pointwise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞h 2 for a sampling step size h of the boundary curve of the domain as h → 0 Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts Empirically the same convergence order is observed also for mean value coordinates Moreover our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases

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