\begin{definition}[Definition:Contour/Endpoints]
Let $\R^n$ be a real cartesian space of $n$ dimensions.
Let $C_1, \ldots, C_n$ be directed smooth curves in $\R^n$.
Let $C_i$ be parameterized by the smooth path $\rho_i: \left[{a_i \,.\,.\, b_i}\right] \to \R^n$ for all $i \in \left\{ {1, \ldots, n}\right\}$.
Let $C$ be the contour defined by the finite sequence $C_1, \ldots, C_n$.
The '''start point''' of $C$ is $\rho_1 \left({a_1}\right)$.
The '''end point''' of $C$ is $\rho_n \left({b_n}\right)$.
Collectively, $\rho_1 \left({a_1}\right)$ and $\rho_n \left({b_n}\right)$ are referred to as the '''endpoints''' of $C$.
\end{definition}