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May6-11, 08:25 AM
P: 17,210
Assuming that your 3D data is in an array named dat and your common parameter for all three is in an array called param then you can write:

interp = Table[Interpolation[Transpose[{param, dat[[All, i]]}]], {i, 3}]

That will give you a table of interpolation functions for each of the three values in your dat array. Then you can write:

ParametricPlot[{interp[[1]][t], interp[[2]][t]}, {t, Min[param], Max[param]},
PlotStyle -> Thick,
ColorFunction -> Function[{x, y, t}, ColorData["Rainbow"][interp[[3]][t]]],
ColorFunctionScaling -> False]

To plot your colored curve.