Straight Real Lines ( real_line )

Definition

An instance l of the data type real_line is a directed straight line in the two-dimensional plane.

#include < LEDA/geo/real_line.h >

Types

real_line::coord_type	the coordinate type (real).
real_line::point_type	the point type (real_point).

Creation

real_line	l(const real_point& p, const real_point& q)
		introduces a variable l of type real_line. l is initialized to the line passing through points p and q directed form p to q.
real_line	l(const real_segment& s)	introduces a variable l of type real_line. l is initialized to the line supporting segment s.
real_line	l(const real_ray& r)	introduces a variable l of type real_line. l is initialized to the line supporting ray r.
real_line	l(const real_point& p, const real_vector& v)
		introduces a variable l of type real_line. l is initialized to the line passing through points p and p + v.
real_line	l	introduces a variable l of type real_line. l is initialized to the line passing through the origin with direction 0.
real_line	l(const line& l1, int prec = 0)
		introduces a variable l of type real_line initialized to the line l1. (The second argument is for compatibility with rat_line.)
real_line	l(const rat_line& l1)	introduces a variable l of type real_line initialized to the line l1.

Operations

real_point	l.point1()	returns a point on l.
real_point	l.point2()	returns a second point on l.
real_segment	l.seg()	returns a segment on l.
bool	l.is_vertical()	returns true iff l is vertical.
bool	l.is_horizontal()	returns true iff l is horizontal.
real	l.sqr_dist(const real_point& q)
		returns the square of the distance between l and q.
real	l.distance(const real_point& q)
		returns the distance between l and q.
int	l.orientation(const real_point& p)
		returns orientation(l.point1(), l.point2(), p).
real	l.slope()	returns the slope of l. Precondition l is not vertical.
real	l.y_proj(real x)	returns p.ycoord(), where p $\in$ l with p.xcoord() = x. Precondition l is not vertical.
real	l.x_proj(real y)	returns p.xcoord(), where p $\in$ l with p.ycoord() = y. Precondition l is not horizontal.
real	l.y_abs()	returns the y-abscissa of l (l.y_proj(0)). Precondition l is not vertical.
bool	l.intersection(const real_line& g, real_point& p)
		if l and g intersect in a single point this point is assigned to p and the result is true, otherwise the result is false.
bool	l.intersection(const real_segment& s, real_point& inter)
		if l and s intersect in a single point this point is assigned to p and the result is true, otherwise the result is false.
bool	l.intersection(const real_segment& s)
		returns true, if l and s intersect, false otherwise.
real_line	l.translate(real dx, real dy)
		returns l translated by vector (dx, dy).
real_line	l.translate(const real_vector& v)
		returns l translated by vector v. Precondition v.dim() = 2.
real_line	l + const real_vector& v	returns l translated by vector v.
real_line	l - const real_vector& v	returns l translated by vector - v.
real_line	l.rotate90(const real_point& q, int i=1)
		returns l rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
real_line	l.reflect(const real_point& p, const real_point& q)
		returns l reflected across the straight line passing through p and q.
real_line	l.reverse()	returns l reversed.
real_segment	l.perpendicular(const real_point& p)
		returns the segment perpendicular to l with source p. and target on l.
real_point	l.dual()	returns the point dual to l. Precondition l is not vertical.
int	l.side_of(const real_point& p)
		computes orientation(a, b, p), where a $\not=$b and a and b appear in this order on line l.
bool	l.contains(const real_point& p)
		returns true if p lies on l.
bool	l.clip(real_point p, real_point q, real_segment& s)
		clips l at the rectangle R defined by p and q. Returns true if the intersection of R and l is non-empty and returns false otherwise. If the intersection is non-empty the intersection is assigned to s; it is guaranteed that the source node of s is no larger than its target node.

Non-Member Functions

int	orientation(const real_line& l, const real_point& p)
		computes orientation(a, b, p) (see the manual page of real_point), where a $\not=$b and a and b appear in this order on line l.
int	cmp_slopes(const real_line& l1, const real_line& l2)
		returns compare(slope(l1), slope(l2)).