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I'll explain the problem I have with a shorter example, since I'm working with a huge messy function. Suppose we have a real-function $f(t)$, and a curve $C(t) \in \mathbb R^3$. Now, I can use ParametricPlot3d to plot $C(t)$. My question is the following:

How do I color the curve $C(t)$ using the magnitude of $f(t)$ at each point, $P(x(t),y(t),z(t)) \in C(t)$.

I tried tinkering with ColorFunction for this, but was unsuccessful. Any hints would be appreciated.

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Here is an example. I am making up f[t]

f[t_] := Cos[t]

I also make C[t]

ParametricPlot3D[{Sin[t], Cos[t], t/10}, {t, 0, 20},
 ColorFunction -> Function[{x, y, z, t}, Hue[f[t]]]]

Mathematica graphics

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  • $\begingroup$ Am I correct in understanding that the Hue[f[t]] assigns the colors in this case such that the lower magnitudes are red and the higher ones are blue ? $\endgroup$ – Lelouch Jun 8 '19 at 14:00
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    $\begingroup$ @Lelouch: Just look up the documentation on Hue. $\endgroup$ – David G. Stork Jun 8 '19 at 17:15

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