In Response To 'Re: 2-parameter surface colouring'
it looks good. Please remember though that I want to display two different datasets/functions on the surface simultaneously. That's my prime goal.
Currently my best way of doing so is to use the checkered version, or to switch back and forth between two one-parameter versions using the Refresh technique that you suggested.
If it were possible I would like to colour the mesh lines according to the evaluation of the surface function. I can't find a way to make the mesh vary by location, so I may stretch the "checkered" technique to overlay the (one-parameter coloured) surface with periodic thin bands in the x-, y-, and z- directions, with transparent surface between them.
Alternatively it would be good to display contours on the surface. I.e. determine the surface by ContourPlot3D (of Function1) then colour it (according to Function2), and plot contour lines (of Function3) onto the surface in a manner similar to ContourPlot.
However I haven't worked out how to do this yet, if it possible. Calculation time is not an important issue, as I have access to a supercomputer, but my programming skills/mathematica's limitations are stopping me.
Thanks again for your help.