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.
#include < LEDA/segment.h >
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 [(x1, y1),(x2, y2)]. | ||
| 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. |
| segment | s(segment s, int prec) | introduces a variable s of type segment. s is initialized to a copy of s. |
Operations
| point | s.start() | returns the source point of segment s. |
| point | s.end() | 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(s1), slope(s2)). | ||
| int | cmp_segments_at_xcoord(segment s1, segment s2, point p) | |
| compares points l1 < intersection > v and l2 < intersection > v where li is the line underlying segment si 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. | ||