When is a point considered inside/outside a polygon?

Question

Are the vertices of the polygon considered to be inside of the said polygon? Also, how about points intersected by the edges of the polygon?

Answer 1

Within discrete and computational geometry, a polygon $P$ is usually defined to include its boundary $\partial P$. So then the vertices and points on edges are "in" $P$. Often the phrase "strictly interior" to $P$ is used to indicate a point in $P$ but not on $\partial P$; a boundary point is "on" (not "in") the boundary $\partial P$.

Sometimes a polygon is defined to be just the vertices and edges, and other times to be the closed region of $\mathbb{R}^2$ bounded by $\partial P$. Generally authors try to make clear their assumptions to avoid ambiguity.