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In this paper, we study and compare different types of generalized barycentric coordinates in detail, including Wachspress, discrete harmonic and mean value coordinates for convex, n-sided polygons. Contour lines are computed in each barycentric coordinate method, and curvature plots of these contour line curves are visualized. Moreover, different distortions of uniform patterns are also shown, providing exact visual method to compare these methods. To overcome the shortcomings of different generalized barycentric computations, affine combination of methods is provided. [ABSTRACT FROM AUTHOR]