Straight Lines ( line )

Definition

An instance l of the data type line is a directed straight line in the two-dimensional plane. The angle between a right oriented horizontal line and l is called the direction of l.

#include < LEDA/geo/line.h >

Types

line::coord_type	the coordinate type (double).
line::point_type	the point type (point).

Creation

line	l(const point& p, const point& q)
		introduces a variable l of type line. l is initialized to the line passing through points p and q directed form p to q.
line	l(const segment& s)	introduces a variable l of type line. l is initialized to the line supporting segment s.
line	l(const ray& r)	introduces a variable l of type line. l is initialized to the line supporting ray r.
line	l(const point& p, const vector& v)
		introduces a variable l of type line. l is initialized to the line passing through points p and p + v.
line	l(const point& p, double alpha)
		introduces a variable l of type line. l is initialized to the line passing through point p with direction alpha.
line	l	introduces a variable l of type line. l is initialized to the line passing through the origin with direction 0.

Operations

point	l.point1()	returns a point on l.
point	l.point2()	returns a second point on l.
segment	l.seg()	returns a segment on l.
double	l.angle(const line& g)	returns the angle between l and g, i.e., g.direction() - l.direction().
double	l.direction()	returns the direction of l.
double	l.angle()	returns l.direction().
bool	l.is_vertical()	returns true iff l is vertical.
bool	l.is_horizontal()	returns true iff l is horizontal.
double	l.sqr_dist(const point& q)
		returns the square of the distance between l and q.
double	l.distance(const point& q)
		returns the distance between l and q.
int	l.orientation(const point& p)
		returns orientation(l.point1(), l.point2(), p).
double	l.slope()	returns the slope of l. Precondition l is not vertical.
double	l.y_proj(double x)	returns p.ycoord(), where p $\in$ l with p.xcoord() = x. Precondition l is not vertical.
double	l.x_proj(double y)	returns p.xcoord(), where p $\in$ l with p.ycoord() = y. Precondition l is not horizontal.
double	l.y_abs()	returns the y-abscissa of l (l.y_proj(0)). Precondition l is not vertical.
bool	l.intersection(const line& g, 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 segment& s, 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 segment& s)
		returns true, if l and s intersect, false otherwise.
line	l.translate_by_angle(double a, double d)
		returns l translated in direction a by distance d.
line	l.translate(double dx, double dy)
		returns l translated by vector (dx, dy).
line	l.translate(const vector& v)
		returns l translated by vector v. Precondition v.dim() = 2.
line	l + const vector& v	returns l translated by vector v.
line	l - const vector& v	returns l translated by vector - v.
line	l.rotate(const point& q, double a)
		returns l rotated about point q by angle a.
line	l.rotate(double a)	returns l.rotate( point(0, 0), a).
line	l.rotate90(const 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.
line	l.reflect(const point& p, const point& q)
		returns l reflected across the straight line passing through p and q.
line	l.reverse()	returns l reversed.
segment	l.perpendicular(const point& p)
		returns the segment perpendicular to l with source p. and target on l.
point	l.dual()	returns the point dual to l. Precondition l is not vertical.
int	l.side_of(const 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 point& p)
		returns true if p lies on l.
bool	l.clip(point p, point q, 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 line& l, const point& p)
		computes orientation(a, b, p), where a $\not=$b and a and b appear in this order on line l.
int	cmp_slopes(const line& l1, const line& l2)
		returns compare(slope(l1), slope(l2)).