Rational Planes ( d3_rat_plane )

Definition

An instance P of the data type d3_rat_plane is an oriented rational plane in the three-dimensional space R³. It can be defined by a tripel (a,b,c) of non-collinear rational points or a single rational point a and a normal vector v.

#include < LEDA/d3 _rat _plane.h >

Creation

d3_rat_plane	p	introduces a variable p of type d3_rat_plane initialized to the trivial plane.
d3_rat_plane	p(d3_rat_point a, d3_rat_point b, d3_rat_point c)
		introduces a variable p of type d3_rat_plane initialized to the plane through (a, b, c). Precondition a, b, and c are not collinear.
d3_rat_plane	p(d3_rat_point a, rat_vector v)
		introduces a variable p of type d3_rat_plane initialized to the plane that contains a with normal vector v. Precondition v.dim() = 3 and v.length() > 0.
d3_rat_plane	p(d3_rat_point a, d3_rat_point b)
		introduces a variable p of type d3_rat_plane initialized to the plane that contains a with normal vector b - a.

Operations

d3_rat_point	p.point1()	returns the first point of p.
d3_rat_point	p.point2()	returns the second point of p.
d3_rat_point	p.point3()	returns the third point of p.
rat_vector	p.normal()	returns a normal vector of p.
d3_plane	p.to_float()	returns a floating point approximation of p.
rational	p.sqr_dist(d3_rat_point q)
		returns the square of the Euclidean distance between p and q.
rat_vector	p.normal_project(d3_rat_point q)
		returns the vector pointing from q to its projection on p along the normal direction.
int	p.intersection(const d3_rat_point p1, const d3_rat_point p2, d3_rat_point& q)
		if the line l through p1 and p2 intersects p in a single point this point is assigned to q and the result is 1, if l and p do not intersect the result is 0, and if l is contained in p the result is 2.
int	p.intersection(d3_rat_plane Q, d3_rat_point& i1, d3_rat_point& i2)
		if p and plane Q intersect in a line L then (i1, i2) are assigned two different points on L and the result is 1, if p and Q do not intersect the result is 0, and if p = Q the result is 2.
d3_rat_plane	p.translate(rational dx, rational dy, rational dz)
		returns p translated by vector (dx, dy, dz).
d3_rat_plane	p.translate(integer dx, integer dy, integer dz, integer dw)
		returns p translated by vector (dx/dw, dy/dw, dz/dw).
d3_rat_plane	p.translate(rat_vector v)	returns p+ v, i.e., p translated by vector v. Precondition v.dim() = 3.
d3_rat_plane	p + rat_vector v	returns p translated by vector v.
d3_rat_plane	p.reflect(d3_rat_plane Q)	returns p reflected across plane Q.
d3_rat_plane	p.reflect(d3_rat_point q)	returns p reflected across point q.
d3_rat_point	p.reflect_point(d3_rat_point q)
		returns q reflected across plane p.
int	p.side_of(d3_rat_point q)	computes the side of p on which q lies.
bool	p.contains(d3_rat_point q)
		returns true if point q lies on plane p, i.e., (p.side_of(q) == 0), and false otherwise .
bool	p.parallel(d3_rat_plane Q)
		returns true if planes p and Q are parallel, and false otherwise.
ostream&	ostream& O << p	writes p to output stream O.
istream&	istream& I >> d3_rat_plane& p
		reads p from input stream I.

Non-Member Functions

int	orientation(d3_rat_plane p, d3_rat_point q)
		computes the orientation of p.sideof(q).