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Straight Lines in 3D-Space ( d3_line )

Definition

An instance l of the data type d3_line is a directed straight line in three-dimensional space.

#include < LEDA/geo/d3_line.h >

Creation

d3_line l(const d3_point& p1, const d3_point& p2)

introduces a variable l of type d3_line. l is initialized to the line through points p1,p2.
Precondition: p1 != p2.

d3_line l(const d3_segment& s) introduces a variable l of type d3_line. l is initialized to the line supporting segment s.
Precondition: s is not trivial.

d3_line l introduces a variable l of type d3_line. l is initialized to the line through points (0,0,0) and (1,0,0).

Operations

bool l.contains(const d3_point& p)

returns true if p lies on l.

d3_point l.point1() returns a point on l.

d3_point l.point2() returns a second point on l.

d3_segment l.seg() returns a non-trivial segment on l with the same direction.

bool l.project_xy(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(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(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(const d3_point& p, const d3_point& q, const d3_point& v, d3_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_line l.translate(double dx, double dy, double dz)

returns l translated by vector (dx,dy,dz).

d3_line l.translate(const vector& v)

returns l translated by v.
Precond.: v.dim()=3.

d3_line l + const vector& v returns l translated by vector v.

d3_line l - const vector& v returns l translated by vector - v.

d3_line l.reflect(const d3_point& p, const d3_point& q, const d3_point& v)

returns l reflected across the plane through (p,q,v).

d3_line l.reflect(const d3_point& p)

returns l reflected across point p.

d3_line l.reverse() returns l reversed.

vector l.to_vector() returns point2()-point1().

bool l.intersection(const d3_segment& s)

decides, whether l and s intersect in a single point.

bool l.intersection(const d3_segment& s, d3_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(const d3_line& m)

decides, whether l and m intersect.

bool l.intersection(const d3_line& m, d3_point& p)

decides, whether l and m intersect in a single point. If so, the point of intersection is assigned to p.

double l.sqr_dist(const d3_point& p)

returns the square of the distance between l and p.

double l.distance(const d3_point& p)

returns the distance between l and p.

Next: Planes ( d3_plane ) Up: Basic Data Types for Previous: Segments in 3D-Space ( Contents Index

d3_line	l(const d3_point& p1, const d3_point& p2)
		introduces a variable l of type d3_line. l is initialized to the line through points p1,p2. Precondition: p1 != p2.
d3_line	l(const d3_segment& s)	introduces a variable l of type d3_line. l is initialized to the line supporting segment s. Precondition: s is not trivial.
d3_line	l	introduces a variable l of type d3_line. l is initialized to the line through points (0,0,0) and (1,0,0).

bool	l.contains(const d3_point& p)
		returns true if p lies on l.
d3_point	l.point1()	returns a point on l.
d3_point	l.point2()	returns a second point on l.
d3_segment	l.seg()	returns a non-trivial segment on l with the same direction.
bool	l.project_xy(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(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(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(const d3_point& p, const d3_point& q, const d3_point& v, d3_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_line	l.translate(double dx, double dy, double dz)
		returns l translated by vector (dx,dy,dz).
d3_line	l.translate(const vector& v)
		returns l translated by v. Precond.: v.dim()=3.
d3_line	l + const vector& v	returns l translated by vector v.
d3_line	l - const vector& v	returns l translated by vector - v.
d3_line	l.reflect(const d3_point& p, const d3_point& q, const d3_point& v)
		returns l reflected across the plane through (p,q,v).
d3_line	l.reflect(const d3_point& p)
		returns l reflected across point p.
d3_line	l.reverse()	returns l reversed.
vector	l.to_vector()	returns point2()-point1().
bool	l.intersection(const d3_segment& s)
		decides, whether l and s intersect in a single point.
bool	l.intersection(const d3_segment& s, d3_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(const d3_line& m)
		decides, whether l and m intersect.
bool	l.intersection(const d3_line& m, d3_point& p)
		decides, whether l and m intersect in a single point. If so, the point of intersection is assigned to p.
double	l.sqr_dist(const d3_point& p)
		returns the square of the distance between l and p.
double	l.distance(const d3_point& p)
		returns the distance between l and p.