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/rectangle.h >

Creation

rectangle	r(point p, point q)	introduces a variable r of type rectangle. r is initialized to the rectangle with diagonal corners p and q
rectangle	r(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 counterclockwise 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(point p)	returns the code for Cohen-Sutherland algorithm.
bool	r.inside(point p)	returns true, if p is inside of r, false otherwise.
bool	r.outside(point p)	returns true, if p is outside of r, false otherwise.
bool	r.inside_or_contains(point p)
		returns true, if p is inside of r or on the border, false otherwise.
bool	r.contains(point p)	returns true, if p is on the border of r, false otherwise.
region_kind	r.region_of(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(point p)	returns a new rectangle that includes the points of r and p.
rectangle	r.include(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(vector v)	returns a new rectangle that is the translation of r by v.
rectangle	r + vector v	returns r translated by v.
rectangle	r - 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(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(point p)	returns r reflected across p .
list<point>	r.intersection(segment s)	returns r $\cap$ s .
bool	r.clip(segment t, segment& inter)
		clips t on r and returns the result in inter.
bool	r.clip(line l, segment& inter)
		clips l on r and returns the result in inter.
bool	r.clip(ray ry, segment& inter)
		clips ry on r and returns the result in inter.
bool	r.difference(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(line l)	returns r $\cap$ l.
list<rectangle>	r.intersection(rectangle r)
		returns r $\cap$ r.
bool	r.do_intersect(rectangle b)
		returns true iff r and b intersect, false otherwise.
double	r.area()	returns the area of r.