MPI-I-2006-4-010

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 $\mathbb{R}^{3}$. We show that these spherical and 3D mean value coordinates are well-defined on the whole sphere and the whole space $\mathbb{R}^{3}$, respectively.