Iso-oriented Rectangles ( rectangle )

Definition

An instance r of the data type rectangle is an iso-oriented rectangle in the two-dimensional plane.

#include < LEDA/geo/rectangle.h >

Creation

rectangle	r(const point& p, const point& q)
		introduces a variable r of type rectangle. r is initialized to the rectangle with diagonal corners p and q
rectangle	r(const point& p, double w, double h)
		introduces a variable r of type rectangle. r is initialized to the rectangle with lower left corner p, width w and height h.
rectangle	r(double x1, double y1, double x2, double y2)
		introduces a variable r of type rectangle. r is initialized to the rectangle with diagonal corners (x1,y1) and (x2,y2).

Operations

point	r.upper_left()	returns the upper left corner.
point	r.upper_right()	returns the upper right corner.
point	r.lower_left()	returns the lower left corner.
point	r.lower_right()	returns the lower right corner.
point	r.center()	returns the center of r.
list<point>	r.vertices()	returns the vertices of r in counter-clockwise order starting from the lower left point.
double	r.xmin()	returns the minimal x-coordinate of r.
double	r.xmax()	returns the maximal x-coordinate of r.
double	r.ymin()	returns the minimal y-coordinate of r.
double	r.ymax()	returns the maximal y-coordinate of r.
double	r.width()	returns the width of r.
double	r.height()	returns the height of r.
bool	r.is_degenerate()	returns true, if r degenerates to a segment or point (the 4 corners are collinear), false otherwise.
bool	r.is_point()	returns true, if r degenerates to a point.
bool	r.is_segment()	returns true, if r degenerates to a segment.
int	r.cs_code(const point& p)	returns the code for Cohen-Sutherland algorithm.
bool	r.inside(const point& p)	returns true, if p is inside of r, false otherwise.
bool	r.outside(const point& p)	returns true, if p is outside of r, false otherwise.
bool	r.inside_or_contains(const point& p)
		returns true, if p is inside of r or on the border, false otherwise.
bool	r.contains(const point& p)
		returns true, if p is on the border of r, false otherwise.
region_kind	r.region_of(const point& p)
		returns BOUNDED_REGION if p lies in the bounded region of r, returns ON_REGION if p lies on r, and returns UNBOUNDED_REGION if p lies in the unbounded region.
rectangle	r.include(const point& p)	returns a new rectangle that includes the points of r and p.
rectangle	r.include(const rectangle& r2)
		returns a new rectangle that includes the points of r and r2.
rectangle	r.translate(double dx, double dy)
		returns a new rectangle that is the translation of r by (dx,dy).
rectangle	r.translate(const vector& v)
		returns a new rectangle that is the translation of r by v.
rectangle	r + const vector& v	returns r translated by v.
rectangle	r - const vector& v	returns r translated by -v.
point	r[int i]	returns the i-th vertex of r. Precondition: (0<i<5).
rectangle	r.rotate90(const point& p, int i=1)
		returns r rotated about p by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
rectangle	r.rotate90(int i=1)	returns r rotated by an angle of i x 90 degrees about the origin.
rectangle	r.reflect(const point& p)	returns r reflected across p .
list<point>	r.intersection(const segment& s)
		returns r $\cap$ s .
bool	r.clip(const segment& t, segment& inter)
		clips t on r and returns the result in inter.
bool	r.clip(const line& l, segment& inter)
		clips l on r and returns the result in inter.
bool	r.clip(const ray& ry, segment& inter)
		clips ry on r and returns the result in inter.
bool	r.difference(const rectangle& q, list<rectangle>& L)
		returns true iff the difference of r and q is not empty, and false otherwise. The difference L is returned as a partition into rectangles.
list<point>	r.intersection(const line& l)
		returns r $\cap$ l.
list<rectangle>	r.intersection(const rectangle& s)
		returns r $\cap$ s.
bool	r.do_intersect(const rectangle& b)
		returns true iff r and b intersect, false otherwise.
double	r.area()	returns the area of r.