Segments in 3D-Space ( d3_segment )

Definition

An instance s of the data type d3$\_$segment is a directed straight line segment in three-dimensional space, i.e., a straight line segment [p, q] connecting two points p, q $\in$ R³. 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. A segment is called trivial if its source is equal to its target. If s is not trivial, we use line(s) to denote the straight line containing s.

#include < LEDA/d3 _segment.h >

Creation

d3_segment	s(d3_point p1, d3_point p2)
		introduces a variable s of type d3_segment. s is initialized to the segment from p1 to p2.
d3_segment	s	introduces a variable s of type d3_segment. s is initialized to the segment from (0,0,0) to (1,0,0).

Operations

bool	s.contains(d3_point p)	decides whether s contains p.
d3_point	s.source()	returns the source point of segment s.
d3_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.zcoord1()	returns the z-coordinate of s.source().
double	s.zcoord2()	returns the z-coordinate of s.target().
double	s.dx()	returns xcoord2()-xcoord1().
double	s.dy()	returns ycoord2()-ycoord1().
double	s.dz()	returns zcoord2()-zcoord1().
segment	s.project_xy()	returns the projection into the xy plane.
segment	s.project_xz()	returns the projection into the xz plane.
segment	s.project_yz()	returns the projection into the yz plane.
d3_segment	s.project(d3_point p, d3_point q, d3_point v)
		returns s projected into the plane through (p,q,v).
d3_segment	s.reflect(d3_point p, d3_point q, d3_point v)
		returns s reflected across the plane through (p,q,v).
d3_segment	s.reflect(d3_point p)	returns s reflected across point p.
d3_segment	s.reverse()	returns s reversed.
vector	s.to_vector()	returns s.target()-s.source().
bool	s.intersection(d3_segment t)
		decides, whether s and t intersect in a single point.
bool	s.intersection(d3_segment t, d3_point& p)
		decides, whether s and t intersect in a single point. If they intersect in a single point, the point is assigned to p and the result is true, otherwise the result is false
bool	s.intersection_of_lines(d3_segment t, d3_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.
bool	s.is_trivial()	returns true if s is trivial.
double	s.sqr_length()	returns the square of the length of s.
double	s.length()	returns the length of s.
d3_segment	s.translate(vector v)	returns s translated by vector v. Precond.: v.dim()=3.
d3_segment	s.translate(double dx, double dy, double dz)
		returns s translated by vector (dx,dy,dz).
d3_segment	s + vector v	returns s translated by vector v.
d3_segment	s - vector v	returns s translated by vector - v.