Mean value coordinates for arbitrary spherical polygons and polyhedra in $\mathbb{R}^{3}$

Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to ’3. We show that these spherical and 3D mean value coordinates are well-defined on the whole sphere and the whole space ’3, respectively.