Version 5.0 The LEDA User Manual

14.28 Segment of Rational Circle ( r circle segment
)
1. Definition
An instance cs of type r circle segment is a segment of a rational circle (see Section 14.14),
i.e. a circular arc. A segment is called trivial if it consists of a single point. A non-trivial
instance cs is defined by two points s and t (of type r circle point) and an oriented circle
c (of type rat circle) such that c contains both s and t. We call s and t the source and
the target of cs, and c is called its supporting circle. We want to point out that the circle
may be a line, which means that cs is a straight line segment. An instance cs is called
degenerate, if it is trivial or a straight line segment.
#include < LEDA/geo/r circle segment.h >
2. Creation
r circle segment cs;
creates a trivial instance cs with source and target equal to the
point (0, 0).
r circle segment cs(const r circle point& src, const r circle point& tgt,
const rat circle& c);
creates an instance cs with source src, target tgt and supporting
circle c.
Precondition: src ≠ tgt, c is not trivial and contains src and tgt.
r circle segment cs(const r circle point& src, const r circle point& tgt,
const rat line& l);
creates an instance cs with source src, target tgt and supporting
line l.
Precondition: src ≠ tgt, l contains src and tgt.
r circle segment cs(const rat point& src, const rat point& middle, const rat point& tgt);
creates an instance cs with source src and target tgt which passes
through middle.
Precondition: the three points are distinct.
r circle segment cs(const r circle point& p);
creates a trivial instance cs with source and target equal to p.
r circle segment cs(const rat point& rat pnt);
creates a trivial instance cs with source and target equal to rat pnt.