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Graphics3D of the official "arbitrary surface"


In virtually every math book which deals with multivariable/multi-valued
functions, there are diagrams showing an "arbitrary surface".  Often there
is a vector and/or a curve drawn on that surface.  The surface itself is
the kind of thing we get from Plot3D or ParametricPlot3D.  I know I can
coble together a surface from polygons, but seems reasonable that there
should be a way of using what's already built in.  Is the way to do this
simply to use Plot3D or ParametricPlot3D, and pull the graphics data out of
the resulting object?  

I'd like to be able to simply create a surface "in place" rather than having
to transform some externally generated object into place.  If I want to
create the surface directly without using Plot3D, etc., does that mean I
have to roll my own from scratch?
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http://911research.wtc7.net
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