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.