Rational Segments in 3D-Space ( d3_rat_segment )

Definition

An instance s of the data type d3$\_$rat$\_$segment is a directed straight line segment in three-dimensional space, i.e., a line segment connecting two rational points p, q $\in$ R³. p is called the source or start point and q is called the target or end point of s. 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 _rat _segment.h >

Creation

d3_rat_segment	s(d3_rat_point p1, d3_rat_point p2)
		introduces a variable S of type d3_rat_segment. S is initialized to the segment through points p1,p2.
d3_rat_segment	s	introduces a variable S of type d3_rat_segment. S is initialized to the segment through points (0,0,0,1) and (1,0,0,1).

Operations

d3_segment	s.to_float()	returns a floating point approximation of s.
bool	s.contains(d3_rat_point p)
		decides whether s contains p.
d3_rat_point	s.source()	returns the source point of segment s.
d3_rat_point	s.target()	returns the target point of segment s.
rational	s.xcoord1()	returns the x-coordinate of s.source().
rational	s.xcoord2()	returns the x-coordinate of s.target().
rational	s.ycoord1()	returns the y-coordinate of s.source().
rational	s.ycoord2()	returns the y-coordinate of s.target().
rational	s.zcoord1()	returns the z-coordinate of s.source().
rational	s.zcoord2()	returns the z-coordinate of s.target().
rational	s.dx()	returns xcoord2()-xcoord1().
rational	s.dy()	returns ycoord2()-ycoord1().
rational	s.dz()	returns zcoord2()-zcoord1().
rat_segment	s.project_xy()	returns the projection into the xy plane.
rat_segment	s.project_xz()	returns the projection into the xz plane.
rat_segment	s.project_yz()	returns the projection into the yz plane.
d3_rat_segment	s.project(d3_rat_point p, d3_rat_point q, d3_rat_point v)
		returns s projected into the plane through (p,q,v).
d3_rat_segment	s.reflect(d3_rat_point p, d3_rat_point q, d3_rat_point v)
		returns s reflected across the plane through (p,q,v).
d3_rat_segment	s.reflect(d3_rat_point p)	returns s reflected across point p.
d3_rat_segment	s.reverse()	returns s reversed.
rat_vector	s.to_vector()	returns S.target()-S.source().
bool	s.intersection(d3_rat_segment t)
		decides, whether s and t intersect in a single point.
bool	s.intersection(d3_rat_segment t, d3_rat_point& p)
		decides, whether s and t intersect. If they intersect in a single point, the point is assigned to p
bool	s.intersection_of_lines(d3_rat_segment t, d3_rat_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.
rational	s.sqr_length()	returns the square of the length of s.
d3_rat_segment	s.translate(rat_vector v)	returns s translated by vector v. Precond.: v.dim()=3.
d3_rat_segment	s.translate(rational dx, rational dy, rational dz)
		returns s translated by vector (dx,dy,dz).
d3_rat_segment	s.translate(integer dx, integer dy, integer dz, integer dw)
		returns s translated by vector (dx/dw,dy/dw,dz/w).
d3_rat_segment	s + rat_vector v	returns s translated by vector v.
d3_rat_segment	s - rat_vector v	returns s translated by vector - v.