Color linear interpolation of ParametricPlot3D

Question

I am looking for any ideas about how to colorize an ellipsoid with a custom gradient style or by a Blend function. I would like to colorize ellipsoid as follows:

• at $(5,0,0)$ and $(-5,0,0)$ should be red color,
• at $(0,2,0)$ and $(0,-2,0)$ should be green color
• at $(0,0,2)$ and $(0,0,-2)$ should be blue color

All other points should be interpolated, respectively to their locations.

I tried to use Blend function, but something went wrong.

My code:

ParametricPlot3D[{5 Cos[u] Cos[v], 2 Cos[v] Sin[u], 2 Sin[v]},
{u, 0, 2 Pi, Pi/10}, {v, -Pi/2, Pi/2, Pi/10}, Axes -> False, 
Boxed -> False, Mesh -> None, 
ColorFunction ->Function[u, v, 
Blend[{Red, Green, Blue}, {5 Cos[u] Cos[v], 2 Cos[v] Sin[u], 2 Sin[v]}]]]

Answer 1

There are a few things wrong with your code. First of all, the ranges for the parameters are in the wrong format. They should be of the form {u, umin, umax} etc. If you want to control the step size you could use PlotPoints and MaxRecursion.

Secondly, as celtschk pointed out, the arguments in a pure function should be combined in a list. If you check the documentation of ColorFunction, you'll see that for ParametricPlot3D, the arguments provided to the ColorFunction are in this case the three spacial coordinates $x, y, z$ and the two parameters $u, v$ in that order. Therefore you could define your ColorFunction for example as

Function[{x, y, z, u, v}, Blend[{Red, Green, Blue}, {(x/5)^2, (y/2)^2, (z/2)^2}]

You would also need to set ColorFunctionScaling -> False. With these settings, the ellipsoid then becomes something like

ParametricPlot3D[{5 Cos[u] Cos[v], 2 Cos[v] Sin[u], 2 Sin[v]}, {u, 0, 
  2 Pi}, {v, -Pi/2, Pi/2}, Axes -> False, Boxed -> False, Mesh -> None,
 PlotPoints -> 40,
 ColorFunctionScaling -> False, 
 ColorFunction -> Function[{x, y, z, u, v}, Blend[{Red, Green, Blue}, 
   {(x/5)^2, (y/2)^2, (z/2)^2}]]]