CGAL 5.1.2 - 2D Polygon Partitioning
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Requirements of a traits class that is used by CGAL::partition_is_valid_2()
, CGAL::convex_partition_is_valid_2()
, and CGAL::y_monotone_partition_is_valid_2()
for testing if a given set of polygons are nonoverlapping and if their union is a polygon that is the same as a polygon represented by a given sequence of points. Note that the traits class for CGAL::partition_is_valid_2()
may have to satisfy additional requirements if each partition polygon is to be tested for having a particular property; see, for example, the descriptions of the function CGAL::is_convex_2()
and the concept YMonotonePartitionTraits_2
for the additional requirements for testing for convexity and \( y\)-monotonicity, respectively.
Types | |
typedef unspecified_type | Point_2 |
The point type on which the partitioning algorithm operates. | |
typedef unspecified_type | Polygon_2 |
The polygon type created by the partitioning function. More... | |
typedef unspecified_type | Is_valid |
A model of the concept PolygonIsValid | |
typedef unspecified_type | Less_xy_2 |
Predicate object type that compares Point_2 s lexicographically. More... | |
typedef unspecified_type | Left_turn_2 |
Predicate object type that provides bool operator()(Point_2 p,Point_2 q,Point_2 r) , which returns true iff r lies to the left of the oriented line through p and q . | |
typedef unspecified_type | Orientation_2 |
Predicate object type that provides CGAL::Orientation operator()(Point_2 p, Point_2 q, Point_2 r) that returns CGAL::LEFT_TURN , if \( r\) lies to the left of the oriented line \( l\) defined by \( p\) and \( q\), returns CGAL::RIGHT_TURN if \( r\) lies to the right of \( l\), and returns CGAL::COLLINEAR if \( r\) lies on \( l\). | |
Creation | |
PartitionIsValidTraits_2 (PartitionIsValidTraits_2 tr) | |
Operations | |
The following functions that create instances of the above predicate object types must exist. | |
Orientation_2 | is_valid_object () |
Less_xy_2 | less_xy_2_object () |
Left_turn_2 | left_turn_2_object () |
Orientation_2 | orientation_2_object () |
Predicate object type that compares Point_2
s lexicographically.
Must provide bool operator()(Point_2 p, Point_2 q)
where true
is returned iff \( p <_{xy} q\). We have \( p<_{xy}q\), iff \( p_x < q_x\) or \( p_x = q_x\) and \( p_y < q_y\), where \( p_x\) and \( p_y\) denote the \( x\) and \( y\) coordinates of point \( p\), respectively.
The polygon type created by the partitioning function.
This type should provide a nested type Vertex_const_iterator
that is the type of the non-mutable iterator over the polygon vertices.