Point on Rational Circle ( r_circle_point )

Definition

An instance p of type r_circle_point is a point in the two-dimensional plane that can be obtained by intersecting a rational circle c and a rational line l (cf. Sections rat_circle and rat_line). Note that c and l may intersect in two points p₁ and p₂. Assume that we order these intersections along the (directed) line l. Then p is uniquely determined by a triple (c, l, which), where which is either first or second. Observe that the coordinates of p are in general non-rational numbers (because their computation involves square roots). Therefore the class r_circle_point is derived from real_point (see Section real_point), which means that all operations of real_point are available.

#include < LEDA/geo/r_circle_point.h >

Types

r_circle_point::tag { first, second }
	used for selecting between the two possible intersections of a circle and a line.

Creation

r_circle_point	p	creates an instance p initialized to the point (0,0).
r_circle_point	p(const rat_point& rat_pnt)
		creates an instance p initialized to the rational point rat_pnt.
r_circle_point	p(const point& pnt)	creates an instance p initialized to the point pnt.
r_circle_point	p(const rat_circle& c, const rat_line& l, tag which)
		creates an instance p initialized to the point determined by (c, l, which) (see above).
r_circle_point	p(const real_point& rp, const rat_circle& c, const rat_line& l, tag which)
		creates an instance p initialized to the real point rp. Precondition rp is the point described by (c, l, which).

Operations

void	p.normalize()	simplifies the internal representation of p.
rat_circle	p.supporting_circle()	returns a rational circle passing through p.
rat_line	p.supporting_line()	returns a rational line passing through p.
tag	p.which_intersection()	returns whether p is the first or the second intersection of the supporting circle and the supporting line.
bool	p.is_rat_point()	returns true, if p can be converted to rat_point. (The value false means ``do not know''.)
const rat_point&	p.to_rat_point()	converts p to a rat_point. Precondition is_rat_point returns true.
rat_point	p.approximate_by_rat_point()
		approximates p by a rat_point.
r_circle_point	p.round(int prec = 0)	returns a rounded representation of p. (experimental)
r_circle_point	p.translate(rational dx, rational dy)
		returns p translated by vector (dx, dy).
r_circle_point	p.translate(const rat_vector& v)
		returns p translated by vector v.
r_circle_point	p + const rat_vector& v	returns p translated by vector v.
r_circle_point	p - const rat_vector& v	returns p translated by vector - v.
r_circle_point	p.rotate90(const rat_point& q, int i=1)
		returns p rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
r_circle_point	p.reflect(const rat_point& p, const rat_point& q)
		returns p reflected across the straight line passing through p and q.
r_circle_point	p.reflect(const rat_point& p)
		returns p reflected across point p.
bool	r_circle_point::intersection(const rat_circle& c, const rat_line& l, tag which, real_point& p)
		checks whether (c, l, which) is a valid triple, if so the corresponding point is assigned to the real_point p.
bool	r_circle_point::intersection(const rat_circle& c, const rat_line& l, tag which, r_circle_point& p)
		same as above, except for the fact that p is of type r_circle_point.