CenterStage Object Class:  CurveOnSurface
Subclass of:  Curve
Requires reference to a Surface object

The CurveOnSurface class lets you create a curve that lies on a
surface that you have already defined.  You give the curve
parametrically in the domain of the surface and the resulting curve
will the the composition of the one you specified with the linked
surface.

The CurveOnSurface class supports the standard Curve directives, with
the exception that the curve function now specifies the curve
parametrically in the domain of the surface (i.e., it's two first
coordinates are used as the parameters to the surface's function).