A General Construction of Hyperbolic Barycentric Coordinates

We provide a general method for defining and efficiently computing barycentric coordinates with respect to polygons on the hyperbolic plane. More precisely, we develop a novel explicit construction which allows us to compute the hyperbolic barycentric coordinates from their 2D-Euclidean counterparts. In particular, we give two interesting families of hyperbolic coordinates, one is defined for convex and non-convex hyperbolic polygons. An important consequence is the possibility to construct new barycentric coordinates on Poincaré disk model. Furthermore, we show that our hyperbolic coordinates are widely applicable to many domains, and give several examples related to hyperbolic blending and space deformations.