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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 counterclockwise 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.


next up previous contents index
Next: Real Points ( real_point Up: Basic Data Types for Previous: Rational Triangles ( rat_triangle   Contents   Index
root 2008-01-09