Real Segments ( real_segment )

Definition

An instance s of the data type real_segment is a directed straight line segment in the two-dimensional plane, i.e., a straight line segment [p, q] connecting two points p, q $\in$ R². p is called the source or start point and q is called the target or end point of s. The length of s is the Euclidean distance between p and q. If p = q, s is called empty. We use line(s) to denote a straight line containing s.

#include < LEDA/geo/real_segment.h >

Types

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

Creation

real_segment	s(const real_point& p, const real_point& q)
		introduces a variable s of type real_segment. s is initialized to the segment [p, q].
real_segment	s(const real_point& p, const real_vector& v)
		introduces a variable s of type real_segment. s is initialized to the segment [p, p + v]. Precondition v.dim() = 2.
real_segment	s(real x1, real y1, real x2, real y2)
		introduces a variable s of type real_segment. s is initialized to the segment [(x1, y1),(x2, y2)].
real_segment	s	introduces a variable s of type real_segment. s is initialized to the empty segment.
real_segment	s(const segment& s1, int prec = 0)
		introduces a variable s of type real_segment initialized to the segment s1. (The second argument is for compatibility with rat_segment.)
real_segment	s(const rat_segment& s1)	introduces a variable s of type real_segment initialized to the segment s1.

Operations

real_point	s.start()	returns the source point of segment s.
real_point	s.end()	returns the target point of segment s.
real	s.xcoord1()	returns the x-coordinate of s.source().
real	s.xcoord2()	returns the x-coordinate of s.target().
real	s.ycoord1()	returns the y-coordinate of s.source().
real	s.ycoord2()	returns the y-coordinate of s.target().
real	s.dx()	returns the xcoord2 - xcoord1.
real	s.dy()	returns the ycoord2 - ycoord1.
real	s.slope()	returns the slope of s. Precondition s is not vertical.
real	s.sqr_length()	returns the square of the length of s.
real	s.length()	returns the length of s.
real_vector	s.to_vector()	returns the vector s.target() - s.source().
bool	s.is_trivial()	returns true if s is trivial.
bool	s.is_vertical()	returns true iff s is vertical.
bool	s.is_horizontal()	returns true iff s is horizontal.
int	s.orientation(const real_point& p)
		computes orientation( s.source(), s.target(), p) (see below).
real	s.x_proj(real y)	returns p.xcoord(), where p $\in$ line(s) with p.ycoord() = y. Precondition s is not horizontal.
real	s.y_proj(real x)	returns p.ycoord(), where p $\in$ line(s) with p.xcoord() = x. Precondition s is not vertical.
real	s.y_abs()	returns the y-abscissa of line(s), i.e., s.y_proj(0). Precondition s is not vertical.
bool	s.contains(const real_point& p)
		decides whether s contains p.
bool	s.intersection(const real_segment& t)
		decides whether s and t intersect in one point.
bool	s.intersection(const real_segment& t, real_point& p)
		if s and t intersect in a single point this point is assigned to p and the result is true, otherwise the result is false.
bool	s.intersection_of_lines(const real_segment& t, real_point& p)
		if line(s) and line(t) intersect in a single point this point is assigned to p and the result is true, otherwise the result is false.
real_segment	s.translate(real dx, real dy)
		returns s translated by vector (dx, dy).
real_segment	s.translate(const real_vector& v)
		returns s + v, i.e., s translated by vector v. Precondition v.dim() = 2.
real_segment	s + const real_vector& v	returns s translated by vector v.
real_segment	s - const real_vector& v	returns s translated by vector - v.
real_segment	s.perpendicular(const real_point& p)
		returns the segment perpendicular to s with source p and target on line(s).
real	s.distance(const real_point& p)
		returns the Euclidean distance between p and s.
real	s.sqr_dist(const real_point& p)
		returns the squared Euclidean distance between p and s.
real	s.distance()	returns the Euclidean distance between (0, 0) and s.
real_segment	s.rotate90(const real_point& q, int i=1)
		returns s rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
real_segment	s.rotate90(int i=1)	returns s.rotate90(s.source(),i).
real_segment	s.reflect(const real_point& p, const real_point& q)
		returns s reflected across the straight line passing through p and q.
real_segment	s.reflect(const real_point& p)
		returns s reflected across point p.
real_segment	s.reverse()	returns s reversed.

Non-Member Functions

int	orientation(const real_segment& s, const real_point& p)
		computes orientation( s.source(), s.target(), p).
int	cmp_slopes(const real_segment& s1, const real_segment& s2)
		returns compare(slope(s1), slope(s2)).
int	cmp_segments_at_xcoord(const real_segment& s1, const real_segment& s2, const real_point& p)
		compares points l1 $\cap$ v and l2 $\cap$ v where li is the line underlying segment si and v is the vertical straight line passing through point p.
bool	parallel(const real_segment& s1, const real_segment& s2)
		returns true if s1 and s2 are parallel and false otherwise.