  Each point of a simplex is expressed as a unique convex combination of the
vertices. The coefficients in the combination are the barycentric coordinates
of the point. For each point in a general convex polytope, there may be
multiple representations, so its barycentric coordinates are not necessarily
unique. There are various schemes to fix particular barycentric coordinates:
Gibbs, Wachspress, cartographic, etc. In this paper, a method for producing
sparse barycentric coordinates in polytopes will be discussed. It uses a purely
algebraic treatment of affine spaces and convex sets, with barycentric
algebras. The method is based on a certain decomposition of each
finite-dimensional convex polytope into a union of simplices of the same
dimension.
