Checking whether two rectangles overlap in python using two bottom left corners and top right corners

Question

class Point:

    def __init__(self, xcoord=0, ycoord=0):
        self.x = xcoord
        self.y = ycoord

class Rectangle:
    def __init__(self, bottom_left, top_right, colour):
        self.bottom_left = bottom_left
        self.top_right = top_right
        self.colour = colour

    def intersects(self, other):

I am trying to see if two rectangles intersect based on the upper right and lower left corners however when I make the function:

def intersects(self, other):
    return self.top_right.x>=other.top_right.x>=self.bottom_left.x and self.top_right.x>=other.bottom_left.x>=self.bottom_left.x and self.top_right.y>=other.top_right.y>=self.bottom_left.y and self.top_right.x>=other.bottom_left.x>=self.bottom_left.x

The function will return false when inputting:

r1=Rectangle(Point(1,1), Point(2,2), 'blue')
r3=Rectangle(Point(1.5,0), Point(1.7,3), 'red')
r1.intersects(r3)

into the shell.

Answer 1

You can use a simple version of the Separating Axis Theorem to test for intersection. If the rectangles do not intersect, then at least one of the right sides will be to the left of the left side of the other rectangle (i.e. it will be a separating axis), or vice versa, or one of the top sides will be below the bottom side of the other rectange, or vice versa.

So change the test to check if it is not true that they don't intersect:

def intersects(self, other):
    return not (self.top_right.x < other.bottom_left.x or self.bottom_left.x > other.top_right.x or self.top_right.y < other.bottom_left.y or self.bottom_left.y > other.top_right.y)

This code assumes that the "top" has a greater y value than the "bottom" (y decreases down the screen), because that's how your example seems to work. If you were using the other convention then you'd just flip the signs of the y comparisons.