Version 5.0 The LEDA User Manual

int cmp signed dist(const rat point& a, const rat point& b, const rat point& c,
const rat point& d)
compares (signed) distances of c and d to the straight line
passing through a and b (directed from a to b). Returns
+1 (−1) if c has larger (smaller) distance than d and 0 if
distances are equal.
int orientation(const rat point& a, const rat point& b, const rat point& c)
computes the orientation of points a, b, c as the sign of
the determinant
∣
∣
a x a y a ∣∣∣∣∣∣ w
b x b y b w
c x c y c w
i.e., it returns +1 if point c lies left of the directed line
through a and b, 0 if a,b, and c are collinear, and −1 otherwise.
int cmp distances(const rat point& p1 , const rat point& p2 ,
const rat point& p3 , const rat point& p4 )
compares the distances (p1 , p2 ) and (p3 , p4 ). Returns +1
(−1) if distance (p1 , p2 ) is larger (smaller) than distance
(p3 , p4 ), otherwise 0.
rat point midpoint(const rat point& a, const rat point& b)
returns the midpoint of a and b.
rational area(const rat point& a, const rat point& b, const rat point& c)
computes the signed area of the triangle determined by
a,b,c, positive if orientation(a, b, c) > 0 and negative otherwise.
bool collinear(const rat point& a, const rat point& b, const rat point& c)
returns true if points a, b, c are collinear, i.e.,
orientation(a, b, c) = 0, and false otherwise.
bool right turn(const rat point& a, const rat point& b, const rat point& c)
returns true if points a, b, c form a righ turn, i.e.,
orientation(a, b, c) < 0, and false otherwise.
bool left turn(const rat point& a, const rat point& b, const rat point& c)
returns true if points a, b, c form a left turn, i.e.,
orientation(a, b, c) > 0, and false otherwise.