With $x,y \in {\mathbb{R}}^n$, a curve $\gamma : [a,b] \rightarrow {\mathbb{R}}^n$ with $\gamma (a)=x$, $\gamma (b)=y$ and $\gamma '(t) \neq 0$ $\forall t \in [a,b]$ and the length of $\gamma$ is ${||y-x||}_2$. And let ${||\cdot ||}_2$ be the euclidean norm.
Assuming $\gamma$ is parameterized, how do I have to reparameterize $\gamma$ such that $\gamma \circ \varphi(t)=x+t(y-x)$?
Greetings