\begin{definition}[Definition:Reversed Directed Smooth Curve]
Let $\R^n$ be a real cartesian space of $n$ dimensions.
Let $C$ be a directed smooth curves in $\R^n$.
Let $C$ be parameterized by the smooth path $\gamma: \left[{a \,.\,.\, b}\right] \to \R^n$.
The '''reversed directed smooth curve of $C$''' is denoted $-C$ and is defined as the directed smooth curve that is parameterized by:
:$\rho: \left[{a \,.\,.\, b}\right] \to \R^n: \rho \left({t}\right) = \gamma \left({a + b - t}\right)$
\end{definition}