  This paper describes a novel construction of generalized barycentric
coordinates of 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 derived from their classical planar
counterparts (e.g. Wachspress, or mean value), we instead derive them from 3D
barycentric coordinates of the origin and show that they are endowed with some
useful properties such as edge linearity and Lagrange property. In addition, we
show that spherical mean value coordinates of both approaches coincide while
their corresponding spherical wachspress coordinates are in general different.
