Version 5.0 The LEDA User Manual

14.27 Point on Rational Circle ( r circle point )
1. 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 14.14 and
14.13). Note that c and l may intersect in two points p 1 and p 2 . 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 14.17), which
means that all operations of real point are available.
#include < LEDA/geo/r circle segment.h >
2. Types
r circle point :: tag { first, second }
3. Creation
used for selecting between the two possible intersections of a circle
and a line.
r circle point p; creates an instance p initialized to the point (0,0).
r circle point
r circle point
r circle point
p(const rat point& rat pnt);
creates an instance p initialized to the rational point rat pnt.
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).
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).
4. 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.
bool p.is rat point( ) returns true, if p can be converted to rat point. (The
value false means “do not know”.)