rectangle.py

#thanks to kind stranger: https://stackoverflow.com/questions/25068538/intersection-and-difference-of-two-rectangles

import itertools

class Rectangle:
    def intersection(self, other):
        a, b = self, other
        x1 = max(min(a.x1, a.x2), min(b.x1, b.x2))
        y1 = max(min(a.y1, a.y2), min(b.y1, b.y2))
        x2 = min(max(a.x1, a.x2), max(b.x1, b.x2))
        y2 = min(max(a.y1, a.y2), max(b.y1, b.y2))
        if x1<x2 and y1<y2:
            return type(self)(x1, y1, x2, y2)
    __and__ = intersection

    def difference(self, other):
        inter = self&other
        if not inter:
            yield self
            return
        xs = {self.x1, self.x2}
        ys = {self.y1, self.y2}
        if self.x1<other.x1<self.x2: xs.add(other.x1)
        if self.x1<other.x2<self.x2: xs.add(other.x2)
        if self.y1<other.y1<self.y2: ys.add(other.y1)
        if self.y1<other.y2<self.y2: ys.add(other.y2)
        for (x1, x2), (y1, y2) in itertools.product(
            pairwise(sorted(xs)), pairwise(sorted(ys))
        ):
            rect = type(self)(x1, y1, x2, y2)
            if rect!=inter:
                yield rect
    __sub__ = difference

    def __init__(self, x1, y1, x2, y2):
        if x1>x2 or y1>y2:
            raise ValueError("Coordinates are invalid")
        self.x1, self.y1, self.x2, self.y2 = x1, y1, x2, y2

    def __iter__(self):
        yield self.x1
        yield self.y1
        yield self.x2
        yield self.y2

    def __eq__(self, other):
        return isinstance(other, Rectangle) and tuple(self)==tuple(other)
    def __ne__(self, other):
        return not (self==other)

    def __repr__(self):
        return type(self).__name__+repr(tuple(self))
    
    def __hash__(self):
        return hash((self.x1, self.y1, self.x2, self.y2))


def pairwise(iterable):
    # https://docs.python.org/dev/library/itertools.html#recipes
    a, b = itertools.tee(iterable)
    next(b, None)
    return zip(a, b)

# 1.
a = Rectangle(0, 0, 1, 1)
b = Rectangle(0.5, 0.5, 1.5, 1.5)
print(a&b)
# Rectangle(0.5, 0.5, 1, 1)
print(list(a-b))
# [Rectangle(0, 0, 0.5, 0.5), Rectangle(0, 0.5, 0.5, 1), Rectangle(0.5, 0, 1, 0.5)]

# 2.
b = Rectangle(0.25, 0.25, 1.25, 0.75)
print(a&b)
# Rectangle(0.25, 0.25, 1, 0.75)
print(list(a-b))
# [Rectangle(0, 0, 0.25, 0.25), Rectangle(0, 0.25, 0.25, 0.75), Rectangle(0, 0.75, 0.25, 1), Rectangle(0.25, 0, 1, 0.25), Rectangle(0.25, 0.75, 1, 1)]

# 3.
b = Rectangle(0.25, 0.25, 0.75, 0.75)
print(a&b)
# Rectangle(0.25, 0.25, 0.75, 0.75)
print(list(a-b))
# [Rectangle(0, 0, 0.25, 0.25), Rectangle(0, 0.25, 0.25, 0.75), Rectangle(0, 0.75, 0.25, 1), Rectangle(0.25, 0, 0.75, 0.25), Rectangle(0.25, 0.75, 0.75, 1), Rectangle(0.75, 0, 1, 0.25), Rectangle(0.75, 0.25, 1, 0.75), Rectangle(0.75, 0.75, 1, 1)]

# 4.
b = Rectangle(5, 5, 10, 10)
print(a&b)
# None
print(list(a-b))
# [Rectangle(0, 0, 1, 1)]

# 5.
b = Rectangle(-5, -5, 10, 10)
print(a&b)
# Rectangle(0, 0, 1, 1)
print(list(a-b))
# []