Version 5.0 The LEDA User Manual

14.29 Polygons with circular edges ( r circle polygon
)
1. Definition
An instance P of the data type r circle polygon is a cyclic list of r circle segments,
i.e. straight line or circular segments. A polygon is called simple if all nodes of the
graph induced by its segments have degree two and it is called weakly simple, if its segments
are disjoint except for common endpoints and if the chain does not cross itself. See
the LEDA book for details.
A weakly simple polygon splits the plane into an unbounded region and one or more
bounded regions. For a simple polygon there is just one bounded region. When a weakly
simple polygon P is traversed either the bounded region is consistently to the left of P or
the unbounded region is consistently to the left of P . We say that P is positively oriented
in the former case and negatively oriented in the latter case. We use P to also denote the
region to the left of P and call this region the positive side of P .
The number of segments is called the size of P . A polygon of size zero is trivial; it either
describes the empty set or the full two-dimensional plane.
#include < LEDA/geo/r circle polygon.h >
2. Types
r circle polygon :: KIND { EMPTY, FULL, NON TRIVIAL }
describes the kind of the polygon: the empty set, the full plane or
a non-trivial polygon.
r circle polygon :: CHECK TYPE { NO CHECK, SIMPLE, WEAKLY SIMPLE, NOT
WEAKLY SIMPLE }
used to specify which checks should be applied and also describes
the outcome of a simplicity check.
r circle polygon :: RESPECT TYPE { DISREGARD ORIENTATION, RESPECT
ORIENTATION }
used in contructors to specify whether to force a positive orientation
for the constructed object (DISREGARD ORIENTATION ) or to
keep the orientation of the input (RESPECT ORIENTATION ).
3. Creation
r circle polygon P ; creates an empty polygon P .
r circle polygon P (KIND k);
creates a polygon P of kind k, where k is either EMPTY or FULL.