ABSTRACT
In 1980, Robin Sibson [2] defined natural neighbor coordinate systems asso ciated with scattered points in lRm. These coordinates have proved to be useful in a variety of interpolation and surface building schemes (see [2] and [1]). Given a set of points { p i , P 2, · · · , P n } scattered in lRm, Sibson defined coordinate functions 6*(p) for points p in the convex hull of the data sites {pijwhich satisfy the following identities:
The coordinate functions 6t are C 1, except at the data sites, where they are C°, and they have local support
We will define, in an analogous manner, coordinate systems associated with points scattered on the sphere and prove that the coordinate functions are C l except at the data sites, where they are C°, We will also introduce a natural way to smooth these coordinate functions, making them globally C 1.
