Segments (segment)

Definition

An instance s of the data type 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 R ^2. 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. The angle between a right oriented horizontal ray and s is called the direction of s.

Creation

segment	s(point p, point q);	introduces a variable s of type segment. s is initialized to the segment [p,q]
segment	s(point p, vector v);	introduces a variable s of type segment. s is initialized to the segment [p,p+v]. Precondition: v.dim() = 2.
segment	s(double x1, double y1, double x2, double y2);
		introduces a variable s of type segment. s is initialized to the segment [(x_1,y_1),(x_2,y_2)].
segment	s(point p, double alpha, double length);
		introduces a variable s of type segment. s is initialized to the segment with start point p, direction alpha, and length length.
segment	s;	introduces a variable s of type segment. s is initialized to the empty segment.

Operations

point	s.source()	returns the source point of segment s.
point	s.target()	returns the target point of segment s.
double	s.xcoord1()	returns the x-coordinate of s.source().
double	s.xcoord2()	returns the x-coordinate of s.target().
double	s.ycoord1()	returns the y-coordinate of s.source().
double	s.ycoord2()	returns the y-coordinate of s.target().
double	s.dx()	returns the xcoord2 - xcoord1.
double	s.dy()	returns the ycoord2 - ycoord1.
double	s.slope()	returns the slope of s. Precondition: s is not vertical.
double	s.sqr_length()	returns the square of the length of s.
double	s.length()	returns the length of s.
vector	s.to_vector()	returns the vector s.target() - s.source().
double	s.direction()	returns the direction of s as an angle in the intervall [0,2pi).
double	s.angle()	returns s.direction().
double	s.angle(segment t)	returns the angle between s and t, i.e., t.direction() - s.direction().
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.
double	s.x_proj(double y)	returns p.xcoord(), where p in line(s) with p.ycoord() = y. Precondition: s is not horizontal.
double	s.y_proj(double x)	returns p.ycoord(), where p in line(s) with p.xcoord() = x. Precondition: s is not vertical.
double	s.y_abs()	returns the y-abscissa of line(s), i.e., s.y_proj(0). Precondition: s is not vertical.
bool	s.contains(point p)	decides whether s contains p.
bool	s.intersection(segment t)	decides whether s and t intersect in one point.
bool	s.intersection(segment t, 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(segment t, 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.
segment	s.translate_by_angle(double alpha, double d)
		returns s translated in direction alpha by distance d.
segment	s.translate(double dx, double dy)
		returns s translated by vector (dx,dy).
segment	s.translate(vector v)	returns s+v, i.e., s translated by vector v. Precondition: v.dim() = 2.
segment	s + vector v	returns s translated by vector v.
segment	s - vector v	returns s translated by vector -v.
segment	s.perpendicular(point p)	returns the segment perpendicular to s with source p and target on line(s).
double	s.distance(point p)	returns the Euclidean distance between p and s.
double	s.sqr_dist(point p)	returns the squared Euclidean distance between p and s.
double	s.distance()	returns the Euclidean distance between (0,0) and s.
segment	s.rotate(point q, double a)
		returns s rotated about point q by angle a.
segment	s.rotate(double alpha)	returns s.rotate(s.source(), alpha).
segment	s.rotate90(point q)	returns s rotated about q by an angle of 90 degrees.
segment	s.rotate90()	returns s.rotate90(s.source()).
segment	s.reflect(point p, point q)
		returns s reflected across the straight line passing through p and q.
segment	s.reflect(point p)	returns s reflected across point p.
segment	s.reverse()	returns s reversed.
ostream&	ostream& O << s	writes s to output stream O.
istream&	istream& I >> segment& s	reads the coordinates of s (four double numbers) from input stream I.

Non-Member Functions

int	orientation(segment s, point p)
		computes orientation(s.source(), s.target(), p).
int	cmp_slopes(segment s1, segment s2)
		returns compare(slope(s_1), slope(s_2)).
int	cmp_segments_at_xcoord(segment s1, segment s2, point p)
		compares points l_1 <intersection> v and l_2 <intersection> v where l_i is the line underlying segment s_i and v is the vertical straight line passing through point p.
bool	parallel(segment s1, segment s2)
		returns true if s1 and s2 are parallel and false otherwise.