rectangle - rectangular portion of the plane

include "draw.m";
draw:= load Draw Draw->PATH;
Rect: adt
{
 min:      Point;
 max:      Point;
 canon:    fn(r: self Rect)          : Rect;
 dx:       fn(r: self Rect)          : int;
 dy:       fn(r: self Rect)          : int;
 eq:       fn(r: self Rect, s: Rect) : int;
 Xrect:    fn(r: self Rect, s: Rect) : int;
 inrect:   fn(r: self Rect, s: Rect) : int;
 clip:     fn(r: self Rect, s: Rect) : (Rect, int);
 contains: fn(r: self Rect, p: Point): int;
 addpt:    fn(r: self Rect, p: Point): Rect;
 subpt:    fn(r: self Rect, p: Point): Rect;
 inset:    fn(r: self Rect; n: int)  : Rect;
};

Description

The type Rect defines a rectangular portion of the integer grid.


min, max	These members define the upper left (min) and lower right (max) points for the rectangle. The rectangle contains the pixels min.x <= x < max.x and min.y <= y <max.y. In general, Rect coordinates should be in canonical form: min.x <= max.x and min.y <= max.y Some functions give undefined results if the input rectangles are not canonical.
r.canon ( )	Returns a canonical rectangle by sorting the coordinates of r.
r.dx ( )	Returns the horizontal dimension of r.
r.dy ( )	Returns the vertical dimension of r.
r.eq (s)	Returns non-zero if the rectangles r and s have the same coordinates and zero otherwise.
r.Xrect (s)	Returns non-zero if the rectangles r and s intersect and zero otherwise. Intersection means the rectangles share at least one pixel; zero-sized rectangles do not intersect.
r.inrect (s)	Returns non-zero if r is completely inside s and zero otherwise. Rectangles with equal coordinates are considered to be inside each other. Zero-sized rectangles contain no rectangles.
r.clip (s)	Computes the intersection between r and s. If the input rectangles intersect, clip returns the resulting rectangle and a non-zero integer value. If the rectangles do not intersect, _clip returns r and a zero value.
r.contains (p)	Returns non-zero if the rectangle r contains the pixel with the coordinates of p and zero otherwise. Zero-sized rectangles contain no points.
r.addpt (p)	Returns the rectangle `(`r.min.add`(`p`),` r.max.add`(`p`))`.
r.subpt (p)	Returns the rectangle `(`r.min.sub`(`p`),` r.max.sub`(`p`))`.
r.inset (n)	Returns the rectangle `(`r.min.add`((`n,n`)),` r.max.sub`((`n,n`))`. The result will not be in canonical form if the inset amount is too large for the rectangle.

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