Version 5.0 The LEDA User Manual

int side of halfspace(const rat point& a, const rat point& b, const rat 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 rat point& a, const rat point& b, const rat point& c,
const rat 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 incircle(const rat point& a, const rat point& b, const rat point& c,
const rat point& d)
returns true if point d lies in the interior of the circle
through points a, b, and c, and false otherwise.
bool outcircle(const rat point& a, const rat point& b, const rat point& c,
const rat 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 rat point& a, const rat point& b, const rat point& c,
const rat point& d)
returns true if points a, b, c, and d are cocircular.
bool cocircular(const rat point& a, const rat point& b, const rat point& c,
const rat point& d)
returns true if points a, b, c, and d are cocircular.
int compare by angle(const rat point& a, const rat point& b, const rat point& c,
const rat point& d)
compares vectors b − a and d − c by angle (more efficient
than calling vector :: compare by angle(b − a, d − x)
on rat vectors).
bool affinely independent(const array& A)
decides whether the points in A are affinely independent.
bool contained in simplex(const array& A, const rat point& p)
determines whether p is contained in the simplex spanned
by the points in A. A may consist of up to 3 points.
Precondition: The points in A are affinely independent.
bool contained in affine hull(const array& A, const rat point& p)
determines whether p is contained in the affine hull of the
points in A.