Parametric Curve

Definition: Parametric Curve

A parametric curve is a continuous function $\gamma :I\subseteq \mathbb{R}\to {\mathbb{R}}^n$ whose domain $I$ is either

• an interval of the form $[a;b]$, $(a;b)$, $[a;b)$, $(a;b]$;
• a ray of the form $(-\infty ;a)$, $(-\infty ;a]$, $[b;\infty )$, $(b;\infty )$,

where $a,b\in \mathbb{R}$.

Definition: Endpoints

If $a\in I$ (or $b\in I$), then $\gamma (a)$ (or $\gamma (b)$) is known as an endpoint of $\gamma$.

NOTATION

Curve parameterisations are sometimes denoted in bold such as $\mathbf{r}(t)$.