## Curves

A smooth, oriented curve (trajectory) {$\ct$} is a map from an interval {$ [a,b]$} into {$\RR^n$} such that {$\ct'(t)$} exists and {$|\ct'(t)| \ne 0$}. The image {$\ct([a,b])$} (i.e. the collection of corresponding points in {$\RR^n$} is called a Curve {$C$}.

**Parametrization independent quantities:** Those that depend only on {$C$} and
possibly the orientation, but not on the specific trajectory {$\ct$}.

**unit tangent:**{$\TT = \frac{\ct'(t)}{|\ct'(t)|}$}**unit normal (2D):**{$\NN = \TT^\perp$}**total displacement**,**total arc length**