Subdivision algorithms for Bézier triangles

In an earlier paper the author studied subdivision algorithms for Bézier curves. These algorithms were generated by constructing degenerate Bézier triangles and tetrahedra and using their edges to subdivide the original curve. In this paper we take up the study of subdivision algorithms for the triangular Bézier surfaces first introduced by Sabin. It will be shown that such algorithms can be generated by constructing higher dimensional degenerate Bézier simplices and using their triangular subsimplices to subdivide the original triangular surface.