\begin{definition}[Definition:Crossing (Jordan Curve)/Parity]
Let $P$ be a polygon embedded in $\R^2$.
Let $q \in \R^2 \setminus \partial P$.
Let $\mathbf v \in R^2 \setminus \set {\mathbf 0}$ be a non-zero vector.
Let $\LL = \set {q + s \mathbf v: s \in \R_{\ge 0} }$ be a ray with start point $q$.
Let $\map N q$ be the number of '''crossings''' between $\LL$ and the boundary $\partial P$ of $P$.
Then the '''parity of $q$''' is defined as:
:$\map {\operatorname{par} } q := \map N q \bmod 2$.
\end{definition}