On Spherical Barycentric Coordinates

This paper describes a novel construction of generalized barycentric coordinates of<br>points on a sphere with respect to the vertices of a given spherical polygon that is contained in a common hemisphere. While in the standard approach such coordinates are<br>derived from their classical planar counterparts (e.g. Wachspress, or mean value), we<br>instead derive them from 3D barycentric coordinates of the origin and show that they<br>are endowed with some useful properties such as edge linearity and Lagrange property.<br>In addition, we show that spherical mean value coordinates of both approaches coincide<br>while their corresponding spherical wachspress coordinates are in general different