  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. 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.
