Anisotropic Generalized Barycentric Coordinates and Applications

Most barycentric coordinates explicitly defined on general simple polygons do not possess the non-negative property. In addition, few works addressed the construction of generalized barycentric coordinates with the anisotropic property. This paper proposes non-negative coordinates that can be defined on general simple polygons and have the anisotropic property. Firstly, for any point in the original polygon, we first compute the corresponding visibility polygon. Secondly, we calculate the anisotropic coordinates of the point with respect to the visibility polygon based on the properties of the power diagram. Finally, the anisotropic coordinates on the visibility polygon are converted to the coordinates on the original polygon. In the application of image warping, the proposed anisotropic coordinates provide three parameters with intuitive geometric meaning for adjustment. In the experiment of function interpolation, the root mean square error obtained by using anisotropic coordinates is 44% lower than the mean value coordinates. In the experiment of image approximation, the use of anisotropic coordinates can reduce the artifacts in areas where the color changes drastically.