The octant of a sphere as a non-degenerate triangular Bézier patch

We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all Bezier points are distinct and their associated weights are positive.

[1]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[2]  Bruce R. Piper,et al.  A trivariate Powell-Sabin interpolant , 1988, Comput. Aided Geom. Des..

[3]  Rida T. Farouki,et al.  Exact offset procedures for simple solids , 1985, Comput. Aided Geom. Des..

[4]  Les A. Piegl.  Less Data for Shapes , 1987, IEEE Computer Graphics and Applications.

[5]  Les A. Piegl.  The sphere as a rational Bézier surface , 1986, Comput. Aided Geom. Des..