I have a function f[u,v]
from $R^2 \to R$ that I want to use like coloring function over the surface:
sigma[u_,v_]:={Cos[u]*Cos[v],Sin[u]*Cos[v],Sin[v]^3}.
For that I've used the expression:
ParametricPlot3D[sigma[u, v], {u, 0, Pi}, {v, 0, 2*Pi}, Mesh -> None,
ColorFunction -> Function[{u, v}, ColorData["Rainbow"][f[u, v]]]]
where
f[u_,v_]:=-((576 Cos[2 u])/(17 - 9 Cos[4 u])^2).
The result is:
which is not what I wanted.
I need that my coloring function evaluates colors in the coordinates position over the surfaces, depending from the sign of f[u,v]
(for instance darker blue when f in strongly negative and a lighter color when f is strongly positive).
Thank you.
ParametricPlot3D[sigma[u, v], {u, 0, Pi}, {v, 0, 2*Pi}, Mesh -> None, ColorFunction -> (ColorData["Rainbow"][#3] &)]
. $\endgroup$ – IPoiler Jan 21 '16 at 18:13