Iso-oriented Rational Rectangles ( rat_rectangle )

Definition

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

#include < LEDA/geo/rat_rectangle.h >

Creation

rat_rectangle	r(const rat_point& p, const rat_point& q)
		introduces a variable r of type rat_rectangle. r is initialized to the rat_rectangle with diagonal corners p and q
rat_rectangle	r(const rat_point& p, rational w, rational h)
		introduces a variable r of type rat_rectangle. r is initialized to the rat_rectangle with lower left corner p, width w and height h.
rat_rectangle	r(rational x1, rational y1, rational x2, rational y2)
		introduces a variable r of type rat_rectangle. r is initialized to the rat_rectangle with diagonal corners (x1,y1) and (x2,y2).
rat_rectangle	r(const rectangle& r, int prec = rat_point::default_precision)
		introduces a variable r of type rat_rectangle. r is initialized to the rectangle obtained by approximating the defining points of r.

Operations

rectangle	r.to_float()	returns a floating point approximation of R.
void	r.normalize()	simplifies the homogenous representation by calling p.normalize() for every vertex of r.
rat_point	r.upper_left()	returns the upper left corner.
rat_point	r.upper_right()	returns the upper right corner.
rat_point	r.lower_left()	returns the lower left corner.
rat_point	r.lower_right()	returns the lower right corner.
rat_point	r.center()	returns the center of r.
list<rat_point>	r.vertices()	returns the vertices of r in counter-clockwise order starting from the lower left point.
rational	r.xmin()	returns the minimal x-coordinate of r.
rational	r.xmax()	returns the maximal x-coordinate of r.
rational	r.ymin()	returns the minimal y-coordinate of r.
rational	r.ymax()	returns the maximal y-coordinate of r.
rational	r.width()	returns the width of r.
rational	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 rat_point& p)
		returns the code for Cohen-Sutherland algorithm.
bool	r.inside(const rat_point& p)
		returns true, if p is inside of r, false otherwise.
bool	r.inside_or_contains(const rat_point& p)
		returns true, if p is inside of r or on the border, false otherwise.
bool	r.outside(const rat_point& p)
		returns true, if p is outside of r, false otherwise.
bool	r.contains(const rat_point& p)
		returns true, if p is on the border of r, false otherwise.
region_kind	r.region_of(const rat_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.
rat_rectangle	r.include(const rat_point& p)
		returns a new rat_rectangle that includes the points of r and p.
rat_rectangle	r.include(const rat_rectangle& r2)
		returns a new rat_rectangle that includes the points of r and r2.
rat_rectangle	r.translate(rational dx, rational dy)
		returns r translated by (dx,dy).
rat_rectangle	r.translate(const rat_vector& v)
		returns r translated by v.
rat_rectangle	r + const rat_vector& v	returns r translated by v.
rat_rectangle	r - const rat_vector& v	returns r translated by vector -v.
rat_point	r[int i]	returns the i-th vertex of r. Precondition: (0<i<5).
rat_rectangle	r.rotate90(const rat_point& p, int i=1)
		returns r rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
rat_rectangle	r.rotate90(int i=1)	returns r rotated by an angle of i x 90 degrees about the origin.
rat_rectangle	r.reflect(const rat_point& p)
		returns r reflected across p.
bool	r.clip(const rat_segment& t, rat_segment& inter)
		clips t on r and returns the result in inter.
bool	r.clip(const rat_line& l, rat_segment& inter)
		clips l on r and returns the result in inter.
bool	r.clip(const rat_ray& ry, rat_segment& inter)
		clips ry on r and returns the result in inter.
bool	r.difference(const rat_rectangle& q, list<rat_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<rat_point>	r.intersection(const rat_segment& s)
		returns r $\cap$ s.
list<rat_point>	r.intersection(const rat_line& l)
		returns r $\cap$ l.
list<rat_rectangle>	r.intersection(const rat_rectangle& s)
		returns r $\cap$ s.
bool	r.do_intersect(const rat_rectangle& b)
		returns true iff r and b intersect, false otherwise.
rational	r.area()	returns the area of r.