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 R ^3. 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.

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 a point of p.
rat_vector	p.normal()	returns a normal vector of p.
d3_plane	p.to_d3_plane()	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.
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).