A Hermite interpolatory subdivision scheme for [formula omitted]-quintics on the Powell–Sabin 12-split.

In order to construct a C 1 -quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell–Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme ( Dyn and Lyche, 1998 ). In this paper we introduce a nodal macro-element on the 12-split for the space of quintic splines that are locally C 3 and globally C 2 . For quickly evaluating any such spline, a Hermite subdivision scheme is derived, implemented, and tested in the computer algebra system Sage . Using the available first derivatives for Phong shading, visually appealing plots can be generated after just a couple of refinements. [ABSTRACT FROM AUTHOR]