Iso_rectangle_2<Kernel>

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CGAL::Iso_rectangle_2<Kernel>

Definition

An object s of the data type Iso_rectangle_2<Kernel> is a rectangle in the Euclidean plane

² with sides parallel to the x and y axis of the coordinate system.

Although they are represented in a canonical form by only two vertices, namely the lower left and the upper right vertex, we provide functions for ``accessing'' the other vertices as well. The vertices are returned in counterclockwise order.

Iso-oriented rectangles and bounding boxes are quite similar. The difference however is that bounding boxes have always double coordinates, whereas the coordinate type of an iso-oriented rectangle is chosen by the user.

Creation

Iso_rectangle_2<Kernel> r ( Point_2<Kernel> p, Point_2<Kernel> q);

introduces an iso-oriented rectangle r with diagonal opposite vertices p and q. Note that the object is brought in the canonical form.

Iso_rectangle_2<Kernel> r ( Point_2<Kernel> p, Point_2<Kernel> q, int);

introduces an iso-oriented rectangle r with diagonal opposite vertices p and q. The int argument value is only used to distinguish the two overloaded functions.

Precondition:

p.x()<=q.x() and p.y()<=q.y().

Iso_rectangle_2<Kernel> r ( Point_2<Kernel> left, Point_2<Kernel> right, Point_2<Kernel> bottom, Point_2<Kernel> top);

introduces an iso-oriented rectangle r whose minimal x coordinate is the one of left, the maximal x coordinate is the one of right, the minimal y coordinate is the one of bottom, the maximal y coordinate is the one of top.

Iso_rectangle_2<Kernel> r ( Kernel::RT min_hx, Kernel::RT min_hy, Kernel::RT max_hx, Kernel::RT max_hy, Kernel::RT hw = RT(1));

introduces an iso-oriented rectangle r with diagonal opposite vertices (min_hx/hw, min_hy/hw) and (max_hx/hw, max_hy/hw).

Precondition:

hw ≠ 0.

Operations

bool

r.operator== ( r2)

Test for equality: two iso-oriented rectangles are equal, iff their lower left and their upper right vertices are equal.

bool

r.operator!= ( r2)

Test for inequality.

Point_2<Kernel>

r.vertex ( int i)

returns the i'th vertex modulo 4 of r in counterclockwise order, starting with the lower left vertex.

Point_2<Kernel>

r.operator[] ( int i)

returns vertex(i).

Point_2<Kernel>

r.min ()

returns the lower left vertex of r (= vertex(0)).

Point_2<Kernel>

r.max ()

returns the upper right vertex of r (= vertex(2)).

Kernel::FT

r.xmin ()

returns the x coordinate of lower left vertex of r.

Kernel::FT

r.ymin ()

returns the y coordinate of lower left vertex of r.

Kernel::FT

r.xmax ()

returns the x coordinate of upper right vertex of r.

Kernel::FT

r.ymax ()

returns the y coordinate of upper right vertex of r.

Kernel::FT

r.min_coord ( int i)

returns the i'th Cartesian coordinate of the lower left vertex of r.

Precondition:

0 ≤ i ≤ 1.

Kernel::FT

r.max_coord ( int i)

returns the i'th Cartesian coordinate of the upper right vertex of r.

Precondition:

0 ≤ i ≤ 1.

Predicates

bool	r.is_degenerate ()	r is degenerate, if all vertices are collinear.

Bounded_side	r.bounded_side ( Point_2<Kernel> p)
		returns either ON_UNBOUNDED_SIDE, ON_BOUNDED_SIDE, or the constant ON_BOUNDARY, depending on where point p is.

bool	r.has_on_boundary ( Point_2<Kernel> p)
bool	r.has_on_bounded_side ( Point_2<Kernel> p)
bool	r.has_on_unbounded_side ( Point_2<Kernel> p)

Miscellaneous

Kernel::FT

r.area ()

returns the area of r.

Bbox

r.bbox ()

returns a bounding box containing r.

Iso_rectangle_2<Kernel>

r.transform ( Aff_transformation_2<Kernel> t)

returns the iso-oriented rectangle obtained by applying t on the lower left and the upper right corner of r.

Precondition:

The angle at a rotation must be a multiple of π/2, otherwise the resulting rectangle does not have the same side length. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented rectangle.

CGAL::Iso_rectangle_2<Kernel>

Definition

Creation

Operations

Predicates

Miscellaneous

See Also