We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in two dimensions. Our method extends weighted GordonWixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boundary curve to define a weight function that is positive and smooth. We derive closed-form expressions for arbitrary polygons in two dimensions and compare the basis functions of our coordinates with several other types of barycentric coordinates. 2011 Elsevier Ltd. All rights reserved.
