Binary predicate object type comparing Point_2s lexicographically.

It must provide bool operator()(Point_2 p, Point_2 q) that returns true iff $p <_{xy} q$. We have $p<_{xy}q$, iff $p_x < q_x$ or $p_x = q_x$ and $p_y < q_y$, where $p_x$ and $p_y$ denote the $x$ and $y$ coordinates of point $p$, resp.

Predicate object type that determines the orientation of three points.

It must provide Orientation operator()(Point_2 p, Point_2 q, Point_2 r) that returns LEFT_TURN, if $r$ lies to the left of the oriented line $l$ defined by $p$ and $q$, returns RIGHT_TURN if $r$ lies to the right of $l$, and returns COLLINEAR if $r$ lies on $l$.