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.

Creation

line	l(point p, 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(segment s);	introduces a variable l of type line. l is initialized to the line supporting segment s.
line	l(ray r);	introduces a variable l of type line. l is initialized to the line supporting ray r.
line	l(point p, vector v);	introduces a variable l of type line. l is initialized to the line passing through points p and p+v.
line	l(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.direction()	returns the direction of l.
double	l.angle(line g)	returns the angle between l and g, i.e., g.direction() - l.direction().
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(point q)	returns the square of the distance between l and q.
double	l.distance(point q)	returns the distance between l and q.
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(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(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.
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(vector v)	returns l translated by vector v. Precondition: v.dim() = 2.
line	l + vector v	returns l translated by vector v.
line	l - vector v	returns l translated by vector -v.
line	l.rotate(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(point q)	returns l rotated about q by angle of 90 degrees.
line	l.reflect(point p, point q)
		returns l reflected across the straight line passing through p and q.
line	l.reverse()	returns l reversed.
segment	l.perpendicular(point p)	returns the segment perpendicular to l with source p. and target on l.

Non-Member Functions

int	orientation(line l, point p)
		computes orientation(a, b, p), where a != b and a and b appear in this order on line l.
int	cmp_slopes(line l1, line l2)
		returns compare(slope(l_1), slope(l_2)).