 |
PartitionIsValidTraits_2
Definition
Requirements of a traits class that is used by partition_is_valid_2, convex_partition_is_valid_2, and 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 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 is_convex_2 and the concept YMonotonePartitionTraits_2 for the additional requirements for testing for convexity and y-monotonicity, respectively.
Types
| PartitionIsValidTraits_2::Point_2 | |
|
The point type on which the partitioning algorithm operates.
| |
| PartitionIsValidTraits_2::Polygon_2 | |
|
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.
| |
| PartitionIsValidTraits_2::Is_valid | |
|
A model of the concept PolygonIsValid
| |
| PartitionIsValidTraits_2::Less_xy_2 | |
|
Predicate object type that compares Point_2s lexicographically.
Must provide bool operator()(Point_2 p, Point_2 q) where true
is returned iff p <xy q.
We have p<xyq, iff px < qx or px = qx and py < qy,
where px and py denote the x and y coordinates of point p,
respectively.
| |
| PartitionIsValidTraits_2::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.
| |
| PartitionIsValidTraits_2::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
Only a copy constructor is required.
| PartitionIsValidTraits_2 traits ( & tr); |
Operations
The following functions that create instances of the above predicate object types must exist.
| Orientation_2 | traits.is_valid_object () | |
| Less_xy_2 | traits.less_xy_2_object () | |
| Left_turn_2 | traits.left_turn_2_object () | |
| Orientation_2 | traits.orientation_2_object () | |
Has Models
CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>
See Also
CGAL::approx_convex_partition_2
CGAL::greene_approx_convex_partition_2
CGAL::optimal_convex_partition_2
CGAL::y_monotone_partition_2