CGAL::Iso_rectangle_2<Kernel>

Definition

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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> 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 $$t on the lower left and the upper right corner of r. Precondition: The angle at a rotation must be a multiple of $$/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.

See Also