MinQuadrilateralTraits_2 Concept Reference

Definition

The concept MinQuadrilateralTraits_2 defines types and operations needed to compute minimum enclosing quadrilaterals of a planar point set using the functions min_rectangle_2, min_parallelogram_2 and min_strip_2.

Has Models:

CGAL::Min_quadrilateral_default_traits_2<K>

See Also

CGAL::min_rectangle_2()

CGAL::min_parallelogram_2()

CGAL::min_strip_2()

Types
typedef unspecified_type	Point_2
	type for representing points.
typedef unspecified_type	Vector_2
	type for representing vectors.
typedef unspecified_type	Direction_2
	type for representing directions.
typedef unspecified_type	Line_2
	type for representing lines.
typedef unspecified_type	Rectangle_2
	type for representing (not necessarily axis-parallel) rectangles.
typedef unspecified_type	Parallelogram_2
	type for representing parallelograms.
typedef unspecified_type	Strip_2
	type for representing strips, that is the closed region bounded by two parallel lines.

Predicates
typedef unspecified_type	Equal_2
	a model for Kernel::Equal_2.
typedef unspecified_type	Less_xy_2
	a model for Kernel::Less_xy_2.
typedef unspecified_type	Less_yx_2
	a model for Kernel::Less_yx_2.
typedef unspecified_type	Has_on_negative_side_2
	a model for Kernel::Has_on_negative_side_2.
typedef unspecified_type	Compare_angle_with_x_axis_2
	a model for Kernel::Compare_angle_with_x_axis_2.
typedef unspecified_type	Area_less_rectangle_2
	AdaptableFunctor op: Rectangle_2 \( \times\) Rectangle_2 \( \rightarrow\) bool. More...
typedef unspecified_type	Area_less_parallelogram_2
	AdaptableFunctor op: Parallelogram_2 \( \times\) Parallelogram_2 \( \rightarrow\) bool. More...
typedef unspecified_type	Width_less_strip_2
	AdaptableFunctor op: Strip_2 \( \times\) Strip_2 \( \rightarrow\) bool. More...
typedef unspecified_type	Orientation_2
	a model for Kernel::Orientation_2. More...

Constructions
typedef unspecified_type	Construct_vector_2
	a model for Kernel::Construct_vector_2.
typedef unspecified_type	Construct_vector_from_direction_2
	AdaptableFunctor. More...
typedef unspecified_type	Construct_perpendicular_vector_2
	a model for Kernel::Construct_perpendicular_vector_2.
typedef unspecified_type	Construct_direction_2
	a model for Kernel::Construct_direction_2.
typedef unspecified_type	Construct_opposite_direction_2
	a model for Kernel::Construct_opposite_direction_2.
typedef unspecified_type	Construct_line_2
	a model for Kernel::Construct_line_2.
typedef unspecified_type	Construct_rectangle_2
	Function class op: Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \times\) Point_2 \( \times\) Point_2 \( \rightarrow\) Rectangle_2. More...
typedef unspecified_type	Construct_parallelogram_2
	Function class. More...
typedef unspecified_type	Construct_strip_2
	Function class op: Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \rightarrow\) Strip_2. More...

Operations
Additionally, for each of the predicate and construction functor types listed above, there must exist a member function that requires no arguments and returns an instance of that functor type. The name of the member function is the uncapitalized name of the type returned with the suffix _object appended. For example, for the functor type Construct_vector_2 the following member function must exist:
template<class OutputIterator >
OutputIterator	copy_rectangle_vertices_2 (const Rectangle_2 &r, OutputIterator o) const
	copies the four vertices of r in counterclockwise order to o.
template<class OutputIterator >
OutputIterator	copy_parallelogram_vertices_2 (const Parallelogram_2 &p, OutputIterator o) const
	copies the four vertices of p in counterclockwise order to o.
template<class OutputIterator >
OutputIterator	copy_strip_lines_2 (const Strip_2 &s, OutputIterator o) const
	copies the two lines bounding s to o.
Construct_vector_2	construct_vector_2_object () const

Member Typedef Documentation

typedef unspecified_type MinQuadrilateralTraits_2::Area_less_parallelogram_2

AdaptableFunctor op: Parallelogram_2 \( \times\) Parallelogram_2 \( \rightarrow\) bool.

op(p1,p2) returns true, iff the area of \( p1\) is strictly less than the area of \( p2\).

typedef unspecified_type MinQuadrilateralTraits_2::Area_less_rectangle_2

AdaptableFunctor op: Rectangle_2 \( \times\) Rectangle_2 \( \rightarrow\) bool.

op(r1,r2) returns true, iff the area of \( r1\) is strictly less than the area of \( r2\).

typedef unspecified_type MinQuadrilateralTraits_2::Construct_parallelogram_2

Function class.

op: Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \times\) Point_2 \( \rightarrow\) Rectangle_2. If the points p1,p2,p3,p4 form the boundary of a convex polygon (oriented counterclockwise), op(p1,d1,p2,d2,p3,p4) returns the parallelogram with one of the points on each side and one side parallel to each of d1 and d2.

typedef unspecified_type MinQuadrilateralTraits_2::Construct_rectangle_2

Function class op: Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \times\) Point_2 \( \times\) Point_2 \( \rightarrow\) Rectangle_2.

If the points p1,p2,p3,p4 form the boundary of a convex polygon (oriented counterclockwise), op(p1,d,p2,p3,p4) returns the rectangle with one of the points on each side and one sides parallel to d.

typedef unspecified_type MinQuadrilateralTraits_2::Construct_strip_2

Function class op: Point_2 \( \times\) Direction_2 \( \times\) Point_2 \( \rightarrow\) Strip_2.

op(p1,d,p2) returns the strip bounded by the lines through p1 resp. p2 with direction d.

typedef unspecified_type MinQuadrilateralTraits_2::Construct_vector_from_direction_2

AdaptableFunctor.

op: Direction_2 \( \rightarrow\) Vector_2.

op(d) returns a vector in direction d.

typedef unspecified_type MinQuadrilateralTraits_2::Orientation_2

a model for Kernel::Orientation_2.

Remarks

The following type is used for expensive precondition checking only.

typedef unspecified_type MinQuadrilateralTraits_2::Width_less_strip_2

AdaptableFunctor op: Strip_2 \( \times\) Strip_2 \( \rightarrow\) bool.

op(s1,s2) returns true, iff the width of \( s1\) is strictly less than the width of \( s2\).