PlanarMapTraits_2

Definition

Types

The geometric types defined below must have a default constructor, copy constructor, assignment operator and operator==.

PlanarMapTraits_2::X_monotone_curve_2
	A type that holds an $$x-monotone curve in the plane.
PlanarMapTraits_2::Point_2
	A type that holds the position of a vertex in the plane. The type of the end points of X_monotone_curve_2 curves.

Categories

The following categories declare the implementation of the method curves_compare_y_at_x_left(). If the category Has_left_category is Tag_true the method is required specifically. Otherwise, if the category Has_reflect_category is Tag_true the method curves_compare_y_at_x_left() is implemented using the required methods point_reflect_in_x_and_y() and curve_reflect_in_x_and_y(). If none of the categories is Tag_true, a default implementation is used, that does not require any of the above methods.

PlanarMapTraits_2::Has_left_category
	A boolean category that indicates whether the method curves_compare_y_at_x_left() is required. It must be either Tag_true or Tag_false.
PlanarMapTraits_2::Has_reflect_category
	A boolean category that indicates whether the methods point_reflect_in_x_and_y() and curve_reflect_in_x_and_y() are required. It must be either Tag_true or Tag_false.

Enumerations

Creation

PlanarMapTraits_2 pm_traits;
	A default constructor.

Operations

Comparison_result	pm_traits.compare_x ( Point_2 p0, Point_2 p1)
		compares the x-coordinates of $$p0 and $$p1. Returns LARGER if $$x(p0) > x(p1); SMALLER if $$x(p0) < x(p1); EQUAL otherwise.
Comparison_result	pm_traits.compare_xy ( Point_2 p0, Point_2 p1)
		compares the two points $$p0 and $$p1 lexigoraphically. First the $$x-coordinates are compared. In case of a tie, the $$y-coordinates are compared. Returns LARGER if $$x(p1) > x(p2), or if $$x(p1) = x(p2) and $$y(p1) > y(p2); SMALLER if $$x(p1) < x(p2), or if $$x(p1) = x(p2) and $$y(p1) < y(p2); EQUAL otherwise.
bool	pm_traits.curve_is_vertical ( X_monotone_curve_2 cv)
		returns true if cv is a vertical segment, false otherwise.
bool	pm_traits.point_in_x_range ( X_monotone_curve_2 cv, Point_2 pnt)
		returns true if pnt is in the $$x range of cv, false otherwise.
Comparison_result	pm_traits.curves_compare_y_at_x ( X_monotone_curve_2 cv1, X_monotone_curve_2 cv2, Point_2 pnt)
		compares the $$y-coordinate of $$cv1 and $$cv2 at the $$x-coordinate of $$pnt. Returns LARGER if $$cv1(x(q)) > cv2(x(q)); SMALLER if $$cv1(x(q)) < cv2(x(q)); EQUAL otherwise. Precondition: $$cv1 and $$cv2 are defined at $$pnt's $$x-coordinate.
Comparison_result	pm_traits.curves_compare_y_at_x_right ( X_monotone_curve_2 cv1, X_monotone_curve_2 cv2, Point_2 pnt)
		compares the $$y-coordinate of $$cv1 and $$cv2 immediately to the right of the $$x-coordinate of $$pnt. Precondition: $$cv1 and $$cv2 meet at $$pnt $$x-coordinate. Precondition: $$cv1 and $$cv2 are defined lexigoraphically to the right of $$pnt's $$x-coordinate.
Comparison_result	pm_traits.curves_compare_y_at_x_left ( X_monotone_curve_2 cv1, X_monotone_curve_2 cv2, Point_2 pnt)
		compares the $$y-coordinate of $$cv1 and $$cv2 immediately to the left of the $$x-coordinate of $$pnt. This predicate is not required for the aggregate insertion of curves into the planar map. Recall, that the aggregate insertion is based on a sweep-line algorithm. Precondition: $$cv1 and $$cv2 meet at $$pnt $$x-coordinate. Precondition: $$cv1 and $$cv2 are defined lexigoraphically to the left of $$pnt's $$x-coordinate.
Point_2	pm_traits.point_reflect_in_x_and_y ( Point_2 pt)
		returns the reflection of the point pt about the origin For example, the reflection of the point $$(2,2) is the point as $$(-2,-2). This predicate is not required for the aggregate insertion of curves into the planar map, or if the method curves_compare_y_at_x_left() is provided and the Has_left_category category is Tag_true.
X_monotone_curve_2	pm_traits.curve_reflect_in_x_and_y ( X_monotone_curve_2 cv)
		returns the reflection of the curve cv about the origin. For example, the reflection of the line segment $$((2,2),(3,3)) is $$((-2,-2),(-3,-3)). This predicate is not required for the aggregate insertion of curves into the planar map, or if the method curves_compare_y_at_x_left() is provided and the Has_left_category category is Tag_true.
Comparison_result	pm_traits.curve_compare_y_at_x ( Point_2 pnt, X_monotone_curve_2 cv)
		compares the $$y-coordinates of $$pnt and the vertical projection of $$pnt on $$cv. Returns SMALLER if $$y(pnt) < cv(x(pnt)); LARGER if $$y(pnt) > cv(x(pnt)); EQUAL otherwise ($$pnt is on the curve). Precondition: $$cv is defined at $$pnt's $$x-coordinate.
bool	pm_traits.curve_equal ( X_monotone_curve_2 cv1, X_monotone_curve_2 cv2)
		returns true if cv1 and cv2 have the same graph, false otherwise.
bool	pm_traits.point_equal ( Point_2 p1, Point_2 p2)
		returns true if p1 is the same as p2, false otherwise.
Point_2	pm_traits.curve_source ( X_monotone_curve_2 cv)
		returns the source of cv.
Point_2	pm_traits.curve_target ( X_monotone_curve_2 cv)
		returns the target of cv.

Has Models

The PlanarMapWithIntersectionsTraits_2 and ArrangementTraits_2 concepts are refinements of the PlanarMapTraits_2 concept, in other words, a model of the formers is a model of the latter. Thus, all supplied (or user written ) arrangement traits classes can be passed as the Traits template parameter when instantiating an object of type Planar_map_2<Dcel,Traits>. See the list of the arrangement traits classes in chapter  , Arrangement.