Version 5.0 The LEDA User Manual

ool collinear(const point& a, const point& b, const 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 point& a, const point& b, const 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 point& a, const point& b, const point& c)
returns true if points a, b, c form a left turn, i.e.,
orientation(a, b, c) > 0, and false otherwise.
int side of halfspace(const point& a, const point& b, const point& c)
returns the sign of the scalar product (b − a) · (c − a).
If b ≠ a this amounts to: Let h be the open halfspace
orthogonal to the vector b − a, containing b, and having
a in its boundary. Returns +1 if c is contained in h,
returns 0 is c lies on the the boundary of h, and returns
−1 is c is contained in the interior of the complement of
h.
int side of circle(const point& a, const point& b, const point& c, const point& d)
returns +1 if point d lies left of the directed circle
through points a, b, and c, 0 if a,b,c,and d are cocircular,
and −1 otherwise.
bool inside circle(const point& a, const point& b, const point& c, const point& d)
returns true if point d lies in the interior of the circle
through points a, b, and c, and false otherwise.
bool outside circle(const point& a, const point& b, const point& c, const point& d)
returns true if point d lies outside of the circle through
points a, b, and c, and false otherwise.
bool on circle(const point& a, const point& b, const point& c, const point& d)
returns true if points a, b, c, and d are cocircular.
bool cocircular(const point& a, const point& b, const point& c, const point& d)
returns true if points a, b, c, and d are cocircular.
int compare by angle(const point& a, const point& b, const point& c,
const point& d)
compares vectors b−a and d−c by angle (more efficient
than calling compare by angle(b − a, d − x) on vectors).
bool affinely independent(const array& A)
decides whether the points in A are affinely independent.