Barycentric coordinates for arbitrary polygons in the plane

Barycentric coordinates for triangles are commonly used in computer graphics, geometric modelling, and other computational sciences for various purposes. In this paper, we extend this well-known concept and propose a generalization to sets of arbitrary polygons in the plane. Besides many other important properties, our coordinate functions are local and smooth and allow an efficient and robust implementation. These coordinates are particularly useful for interpolating data that is given at the vertices of the polygons and we present several examples of their application to common problems in computer graphics and geometric modelling.