How to color Contours in ContourPlot with custom ColorFunction

Question

I am plotting a contour as

ContourPlot[f[x,y]==f0,{x,0,1},{y,0,1}]

and I want to use my custom ColorFunction->Function[{x,y}, ... ] to color the contour (so that the contour varies its color). So far, I have not succeeded and not found an answer on forums.
Any ideas? Thanks, Sergey

Answer 1

You can post-process the output of ContourPlot to extract the lines and create a BSplineFunction for each line, and plot the functions using ParametricPlot with the desired ColorFunction:

cp = ContourPlot[Cos[x] Cos[y] == .1, {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
   ContourStyle -> Thick, ImageSize -> 300];
bsps = Cases[Normal[cp], Line[x_] :> BSplineFunction[x],  All];
pp = ParametricPlot[Evaluate@Through[bsps @ t], {t, 0, 1}, 
   PlotStyle -> Thick, Frame -> True, 
   ColorFunction -> (ColorData["Rainbow"][# + #2] &), 
   ImageSize -> 300];

Row[{Labeled[cp, ContourPlot, Top], Labeled[pp, ParametricPlot, Top]},  Spacer[5]]

Additional examples:

Row[Table[With[{f = f}, 
   ParametricPlot[Evaluate @ bsps @ t], {t, 0, 1}, 
    PlotStyle -> Thick, Frame -> True, ImageSize -> 300,
    PlotLabel -> HoldForm[f], ColorFunction -> f]], 
  {f, {ColorData["Rainbow"][# #2] &, 
    ColorData["SolarColors"][#3] &, 
    ColorData["TemperatureMap"][# #3] &}}], Spacer[5]]