Requirements for Rectangular $$p-center Traits Classes

Definition

Types

Rpc_traits::FT
	class used for doing computations on point coordinates (has to fulfill field-type requirements).
Rpc_traits::Point_2
	class used for representing the input points.
Rpc_traits::Iso_rectangle_2
	class used for representing axis-parallel rectangles.
Rpc_traits::Less_x_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ bool returns true, iff the first point has smaller x-coordinate than the second.
Rpc_traits::Less_y_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ bool returns true, iff the first point has smaller y-coordinate than the second.
Rpc_traits::Greater_x_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ bool returns true, iff the first point has greater x-coordinate than the second.
Rpc_traits::Greater_y_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ bool returns true, iff the first point has greater y-coordinate than the second.
Rpc_traits::Signed_x_distance_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ FT returns the signed distance of two points' $$x-coordinates.
Rpc_traits::Signed_y_distance_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ FT returns the signed distance of two points' $$y-coordinates.
Rpc_traits::Infinity_distance_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ FT returns the $$|| · || distance of two points.
Rpc_traits::Signed_infinity_distance_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ FT returns the signed $$|| · || distance of two points.
Rpc_traits::Construct_min_point_2
	adaptable unary function class: Iso_rectangle_2 $$ Point_2 returns the lower-left corner of a rectangle.
Rpc_traits::Construct_max_point_2
	adaptable unary function class: Iso_rectangle_2 $$ Point_2 returns the upper-right corner of a rectangle.
Rpc_traits::Construct_corner_2
	adaptable binary function class: Iso_rectangle_2 $$ × unsigned int $$ Point_2 returns the i-th (starting from lower-left and then counterclockwise) corner of a rectangle.
Rpc_traits::Construct_projection_onto_horizontal_implicit_line_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ Point_2 returns the (orthogonal) projection of the first point onto the horizontal line through the second point.
Rpc_traits::Construct_iso_rectangle_2
	4-argument function class: Point_2 $$ × Point_2 $$ × Point_2 $$ × Point_2 $$ Iso_rectangle_2 returns the rectangle with point $$i on the left, bottom, right, top resp. side.
Rpc_traits::Construct_point_2_below_left_implicit_point_2
	3-argument function class: Point_2 $$ × Point_2 $$ × FT $$ Point_2. For arguments $$(p,q,r) it returns the lower-left corner of the iso-oriented square with sidelength $$r and upper-right corner at the intersection of the vertical line through $$p and the horizontal line through $$q.
Rpc_traits::Construct_point_2_below_right_implicit_point_2
	3-argument function class: Point_2 $$ × Point_2 $$ × FT $$ Point_2. For arguments $$(p,q,r) it returns the lower-right corner of the iso-oriented square with sidelength $$r and upper-left corner at the intersection of the vertical line through $$p and the horizontal line through $$q.
Rpc_traits::Construct_point_2_above_right_implicit_point_2
	3-argument function class: Point_2 $$ × Point_2 $$ × FT $$ Point_2. For arguments $$(p,q,r) it returns the upper-right corner of the iso-oriented square with sidelength $$r and lower-left corner at the intersection of the vertical line through $$p and the horizontal line through $$q.
Rpc_traits::Construct_point_2_above_left_implicit_point_2
	3-argument function class: Point_2 $$ × Point_2 $$ × FT $$ Point_2. For arguments $$(p,q,r) it returns the upper-left corner of the iso-oriented square with sidelength $$r and lower-right corner at the intersection of the vertical line through $$p and the horizontal line through $$q.

These can be derived from Less and Greater:

Rpc_traits::Min_x_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ Point_2 returns the point with smaller x-coordinate.
Rpc_traits::Max_x_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ Point_2 returns the point with greater x-coordinate.
Rpc_traits::Min_y_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ Point_2 returns the point with smaller y-coordinate.
Rpc_traits::Max_y_2
	adaptable binary function class: Point_2 $$ × Point_2 $$ Point_2 returns the point with greater y-coordinate.

Operations

For every function class listed above there is a member function to fetch the corresponding function object.

Inf_distance_2	t.inf_distance_2_object () const
Signed_inf_distance_2
	t.signed_inf_distance_2_object () const
Construct_min_point_2
	t.construct_min_point_2_object () const
Construct_max_point_2
	t.construct_max_point_2_object () const
Construct_corner_2	t.construct_corner_2_object () const
Construct_iso_rectangle_2
	t.construct_iso_rectangle_2_object () const
Construct_projection_onto_horizontal_implicit_line_2
	t.construct_projection_onto_horizontal_implicit_line_2_object () const
Construct_iso_rectangle_2_below_left_point_2
	t.construct_iso_rectangle_2_below_left_point_2_object () const
Construct_iso_rectangle_2_above_left_point_2
	t.construct_iso_rectangle_2_above_left_point_2_object () const
Construct_iso_rectangle_2_below_right_point_2
	t.construct_iso_rectangle_2_below_right_point_2_object () const
Construct_iso_rectangle_2_above_right_point_2
	t.construct_iso_rectangle_2_above_right_point_2_object () const
Min_x_2	t.min_x_2_object () const
Max_x_2	t.max_x_2_object () const
Min_y_2	t.min_y_2_object () const
Max_y_2	t.max_y_2_object () const