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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$ 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. The angle between a right oriented horizontal ray and s is called the direction of s.

#include < LEDA/geo/segment.h >

Types

segment::coord_type the coordinate type (double).

segment::point_type the point type (point).

Creation

segment s(const point& p, const point& q)
    introduces a variable s of type segment. s is initialized to the segment [p, q].

segment s(const point& p, const 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(const 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(const segment& s1, int) introduces a variable s of type segment. s is initialized to a copy of s1.

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, 2$ \pi$).

double s.angle() returns s.direction().

double s.angle(const 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.

int s.orientation(const point& p)
    computes orientation( s.source(), s.target(), p) (see below).

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(const point& p)
    decides whether s contains p.

bool s.intersection(const segment& t)
    decides whether s and t intersect in one point.

bool s.intersection(const 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(const 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(const vector& v)
    returns s + v, i.e., s translated by vector v.
Precondition v.dim() = 2.

segment s + const vector& v returns s translated by vector v.

segment s - const vector& v returns s translated by vector - v.

segment s.perpendicular(const point& p)
    returns the segment perpendicular to s with source p and target on line(s).

double s.distance(const point& p)
    returns the Euclidean distance between p and s.

double s.sqr_dist(const 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(const 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(const 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.

segment s.rotate90(int i=1) returns s.rotate90(s.source(),i).

segment s.reflect(const point& p, const point& q)
    returns s reflected across the straight line passing through p and q.

segment s.reflect(const point& p) returns s reflected across point p.

segment s.reverse() returns s reversed.

Non-Member Functions

int orientation(const segment& s, const point& p)
    computes orientation( s.source(), s.target(), p).

int cmp_slopes(const segment& s1, const segment& s2)
    returns compare(slope(s1), slope(s2)).

int cmp_segments_at_xcoord(const segment& s1, const segment& s2, const 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 segment& s1, const segment& s2)
    returns true if s1 and s2 are parallel and false otherwise.


next up previous contents index
Next: Straight Rays ( ray Up: Basic Data Types for Previous: Points ( point )   Contents   Index
root 2008-01-09