Rational Lines in 3D-Space ( d3_rat_line )

Definition

An instance l of the data type d3_rat_line is a directed straight line in three-dimensional space.

#include < LEDA/d3 _rat _line.h >

Creation

d3_rat_line	l(d3_rat_point p1, d3_rat_point p2)
		introduces a variable l of type d3_rat_line. l is initialized to the line through points p1,p2.
d3_rat_line	l(d3_rat_segment s)	introduces a variable l of type d3_rat_line. l is initialized to the line supporting segment s.
d3_rat_line	l	introduces a variable l of type d3_rat_line. l is initialized to the line through points (0,0,0,1) and (1,0,0,1).

Operations

d3_line	l.to_float()	returns a floating point approximation of l.
bool	l.contains(d3_rat_point p)
		returns true if p lies on l.
d3_rat_point	l.point1()	returns a point on l.
d3_rat_point	l.point2()	returns a second point on l.
d3_rat_segment	l.seg()	returns a segment on l.
bool	l.project_xy(rat_line& m)	if the projection of l into the xy plane is not a point, the function returns true and assignes the projection to m. Otherwise false is returned.
bool	l.project_xz(rat_line& m)	if the projection of l into the xz plane is not a point, the function returns true and assignes the projection to m. Otherwise false is returned.
bool	l.project_yz(rat_line& m)	if the projection of l into the yz plane is not a point, the function returns true and assignes the projection to m. Otherwise false is returned.
bool	l.project(d3_rat_point p, d3_rat_point q, d3_rat_point v, d3_rat_line& m)
		if the projection of l into the plane through (p,q,v) is not a point, the function returns true and assignes the projection to m. Otherwise false is returned.
d3_rat_line	l.translate(integer dx, integer dy, integer dz, integer dw)
		returns l translated by vector (dx/dw,dy/dw,dz/dw).
d3_rat_line	l.translate(rat_vector v)	returns l translated by v. Precond.: v.dim()=3.
d3_rat_line	l + rat_vector v	returns l translated by vector v.
d3_rat_line	l - rat_vector v	returns l translated by vector - v.
d3_rat_line	l.reflect(d3_rat_point p, d3_rat_point q, d3_rat_point v)
		returns l reflected across the plane through (p,q,v).
d3_rat_line	l.reflect(d3_rat_point p)	returns l reflected across point p.
d3_rat_line	l.reverse()	returns l reversed.
rat_vector	l.to_vector()	returns point2()-point1().
bool	l.intersection(d3_rat_segment s)
		decides, whether l and s intersect in a single point.
bool	l.intersection(d3_rat_segment s, d3_rat_point& p)
		decides, whether l and s intersect in a single point. If so, the point of intersection is assigned to p.
bool	l.intersection(d3_rat_line m)
		decides, whether l and m intersect in a single point.
bool	l.intersection(d3_rat_line m, d3_rat_point& p)
		decides, whether l and m intersect in a single point. If so, the point of intersection is assigned to p.
rational	l.sqr_dist(d3_rat_point p)
		returns the square of the distance between l and p.