Rational Rays ( rat_ray )

Definition

An instance r of the data type rat$\_$ray is a directed straight ray defined by two points with rational coordinates in the two-dimensional plane.

#include < LEDA/geo/rat_ray.h >

Types

rat_ray::coord_type	the coordinate type (rational).
rat_ray::point_type	the point type (rat_point).
rat_ray::float_type	the corresponding floatin-point type (ray).

Creation

rat_ray	r(const rat_point& p, const rat_point& q)
		introduces a variable r of type rat_ray. r is initialized to the ray starting at point p and passing through point q. Precondition p $\not=$q.
rat_ray	r(const rat_segment& s)	introduces a variable r of type rat_ray. r is initialized to the (rat$\_$ray(s.source(), s.target()). Precondition s is nontrivial.
rat_ray	r(const rat_point& p, const rat_vector& v)
		introduces a variable r of type rat_ray. r is initialized to ratray(p, p + v).
rat_ray	r	introduces a variable r of type rat_ray.
rat_ray	r(const ray& r1, int prec = rat_point::default_precision)
		introduces a variable r of type rat_ray. r is initialized to the ray obtained by approximating the two defining points of r1.

Operations

ray	r.to_float()	returns a floating point approximation of r.
void	r.normalize()	simplifies the homogenous representation by calling point1().normalize() and point2().normlize().
rat_point	r.source()	returns the source of r.
rat_point	r.point1()	returns the source of r.
rat_point	r.point2()	returns a point on r different from r.source().
bool	r.is_vertical()	returns true iff r is vertical.
bool	r.is_horizontal()	returns true iff r is horizontal.
bool	r.intersection(const rat_ray& s, rat_point& inter)
		returns true if r and s intersect. If so, a point of intersection is returned in inter.
bool	r.intersection(const rat_segment& s, rat_point& inter)
		returns true if r and s intersect. If so, a point of intersection is returned in inter.
bool	r.intersection(const rat_segment& s)
		test if r and s intersect.
rat_ray	r.translate(const rational& dx, const rational& dy)
		returns r translated by vector (dx, dy).
rat_ray	r.translate(integer dx, integer dy, integer dw)
		returns r translated by vector (dx/dw, dy/dw).
rat_ray	r.translate(const rat_vector& v)
		returns r + v, i.e., r translated by vector v. Precondition v.dim() = 2.
rat_ray	r + const rat_vector& v	returns r translated by vector v.
rat_ray	r - const rat_vector& v	returns r translated by vector - v.
rat_ray	r.rotate90(const rat_point& q, int i=1)
		returns r rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
rat_ray	r.reflect(const rat_point& p, const rat_point& q)
		returns r reflected across the straight line passing through p and q. Precondition p $\not=$q.
rat_ray	r.reflect(const rat_point& p)
		returns r reflected across point p.
rat_ray	r.reverse()	returns r reversed.
bool	r.contains(const rat_point& p)
		decides whether r contains p.
bool	r.contains(const rat_segment& s)
		decides whether r contains s.

Non-Member Functions

int	orientation(const rat_ray& r, const rat_point& p)
		computes orientation(a, b, p), where a $\not=$b and a and b appear in this order on ray r.
int	cmp_slopes(const rat_ray& r1, const rat_ray& r2)
		returns compare(slope(r1), slope(r2)).