\begin{definition}[Definition:Perpendicular Projection]
Let $\PP$ denote the plane.
Let $L$ denote a straight line in $\PP$.
For all $p \in \PP$, let $K_p$ denote the straight line through $P$ perpendicular to $L$.
Let $p_L$ denote the point on $L$ where $K_p$ intersects $L$.
Let $\pi_L: \PP \to L$ denote the mapping defined as:
:$\forall p \in \PP: \map {\pi_L} p = p_L$
That is, $\pi_L$ sends every point $p$ in $\PP$ to the foot of the perpendicular from $p$ to $L$.
$\pi_L$ is called the '''perpendicular projection of the plane onto $L$'''.
\end{definition}