Chapter 5.5, Problem 7SA

Write a program that traverses the path $P$ according to an arbitrary progress curve $C\left(s\right)$, $0\le s\le 1$, with $C\left(0\right)=0$ and $C\left(1\right)=1$ . The object is to move along the curve $C$ in such a way that the proportion $C\left(s\right)$ of the path’s total arc length is traversed between 0 and $s$ . For example, constant speed along the path would be represented by $C\left(s\right)=s$ . Try progress curves $C\left(s\right)=s^{1/3}$, $C\left(s\right)=s^2$, $C\left(s\right)=\sin s\pi /2$ or $C\left(s\right)=1/2+\left(1/2\right)\sin \left(2s-1\right)\pi /2$, for example.