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. Author manuscript; available in PMC: 2012 Oct 1.

Published in final edited form as: Comput Aided Des. 2011 Oct 1;43(10):1213–1221. doi: 10.1016/j.cad.2011.06.017

Geometric calculation of a Sibson coordinate. C_i is the area of the Voronoi region associated to vertex v_i inside . D(x) is the area of the Voronoi region associated to x if it is added to the vertex list. The quantity D(x) ∩ C_i is exactly D(x) if x = v_i and decays to zero as x moves away from v_i, with value identically zero at all vertices besides v_i. The bottom right figure shows how the level sets of the Sibson coordinate associated to v_i sit inside a single polygon. More figures can be found in Milbradt and Pick [21]

Inline graphic — Geometric calculation of a Sibson coordinate. C_i is the area of the Voronoi region associated to vertex v_i inside . D(x) is the area of the Voronoi region associated to x if it is added to the vertex list. The quantity D(x) ∩ C_i is exactly D(x) if x = v_i and decays to zero as x moves away from v_i, with value identically zero at all vertices besides v_i. The bottom right figure shows how the level sets of the Sibson coordinate associated to v_i sit inside a single polygon. More figures can be found in Milbradt and Pick [21]