Straight Rational Lines ( rat_line )

Definition

An instance l of the data type rat$\_$line is a directed straight line in the two-dimensional plane.

#include < LEDA/geo/rat_line.h >

Types

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

Creation

rat_line	l(const rat_point& p, const rat_point& q)
		introduces a variable l of type rat_line. l is initialized to the line passing through points p and q directed form p to q. Precondition p $\not=$q.
rat_line	l(const rat_segment& s)	introduces a variable l of type rat_line. l is initialized to the line supporting segment s. Precondition s is nontrivial.
rat_line	l(const rat_point& p, const rat_vector& v)
		introduces a variable l of type rat_line. l is initialized to the line passing through points p and p + v. Precondition v is a nonzero vector.
rat_line	l(const rat_ray& r)	introduces a variable l of type rat_line. l is initialized to the line supporting ray r.
rat_line	l	introduces a variable l of type rat_line.
rat_line	l(const line& l1, int prec = rat_point::default_precision)
		introduces a variable l of type rat_line. l is initialized to the line obtained by approximating the two defining points of l1.

Operations

line	l.to_float()	returns a floating point approximation of l.
void	l.normalize()	simplifies the homogenous representation by calling point1().normalize() and point2().normlize().
rat_point	l.point1()	returns a point on l.
rat_point	l.point2()	returns a second point on l.
rat_segment	l.seg()	returns a segment on l.
bool	l.is_vertical()	decides whether l is vertical.
bool	l.is_horizontal()	decides whether l is horizontal.
rational	l.slope()	returns the slope of s. Precondition l is not vertical.
rational	l.x_proj(rational y)	returns p.xcoord(), where p $\in$ line(l) with p.ycoord() = y. Precondition l is not horizontal.
rational	l.y_proj(rational x)	returns p.ycoord(), where p $\in$ line(l) with p.xcoord() = x. Precondition l is not vertical.
rational	l.y_abs()	returns the y-abscissa of line(l ), i.e., l.y_proj(0). Precondition l is not vertical.
bool	l.intersection(const rat_line& g, rat_point& inter)
		returns true if l and g intersect. In case of intersection a common point is returned in inter.
bool	l.intersection(const rat_segment& s, rat_point& inter)
		returns true if l and s intersect. In case of intersection a common point is returned in inter.
bool	l.intersection(const rat_segment& s)
		returns true, if l and s intersect, false otherwise.
rat_line	l.translate(const rational& dx, const rational& dy)
		returns l translated by vector (dx, dy).
rat_line	l.translate(integer dx, integer dy, integer dw)
		returns l translated by vector (dx/dw, dy/dw).
rat_line	l.translate(const rat_vector& v)
		returns l translated by vector v. Precondition v.dim() = 2.
rat_line	l + const rat_vector& v	returns l translated by vector v.
rat_line	l - const rat_vector& v	returns l translated by vector - v.
rat_line	l.rotate90(const rat_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.
rat_line	l.reflect(const rat_point& p, const rat_point& q)
		returns l reflected across the straight line passing through p and q.
rat_line	l.reflect(const rat_point& p)
		returns l reflected across point p.
rat_line	l.reverse()	returns l reversed.
rational	l.sqr_dist(const rat_point& q)
		returns the square of the distance between l and q.
rat_segment	l.perpendicular(const rat_point& p)
		returns the segment perpendicular to l with source p and target on l.
rat_point	l.dual()	returns the point dual to l. Precondition l is not vertical.
int	l.orientation(const rat_point& p)
		computes orientation(a, b, p), where a $\not=$b and a and b appear in this order on line l.
int	l.side_of(const rat_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 rat_point& p)
		returns true if p lies on l.
bool	l.clip(rat_point p, rat_point q, rat_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.
bool	l == const rat_line& g	returns true if the l and g are equal as oriented lines.
bool	equal_as_sets(const rat_line& l, const rat_line& g)
		returns true if the l and g are equal as unoriented lines.

Non-Member Functions

int	orientation(const rat_line& l, const rat_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 rat_line& l1, const rat_line& l2)
		returns compare(slope(l1), slope(l2)).
rat_line	p_bisector(const rat_point& p, const rat_point& q)
		returns the perpendicular bisector of p and q. The bisector has p on its left. Precondition p $\not=$q.