Version 5.0 The LEDA User Manual

14.6 Polygons ( POLYGON )
1. Definition
There are three instantiations of POLYGON : polygon (floating point kernel), rat polygon
(rational kernel) and real polygon (real kernel). The respective header file name corresponds
to the type name (with “.h” appended).
An instance P of the data type POLYGON is a cyclic list of points (equivalently segments)
in the plane. 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 more
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 vertices is called the size of P . A polygon with empty vertex sequence is
called empty.
Only the types rat polygon and real polygon guarantee correct results. Almost all operations
listed below are available for all the three instantiations of POLYGON . There is
a small number of operations that are only available for polygon, they are indicated as
such.
#include < LEDA/geo/generic/POLYGON.h >
2. Types
POLYGON :: coord type
POLYGON :: point type
POLYGON :: float type
the coordinate type (e.g. rational).
the point type (e.g. rat point).
the corresponding floating-point type (polygon).
3. Creation
POLYGON P ; introduces a variable P of type POLYGON . P is initialized
to the empty polygon.