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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.

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)).


next up previous contents index
Next: Straight Rational Lines ( Up: Basic Data Types for Previous: Rational Segments ( rat_segment   Contents   Index
root 2008-01-09