Question

In Python rOverlap (x1, y1, w1, h1, x2, y2, w2, h2) A rectangle is axis-aligned if its sides are parallel to the coordinate axes. An axis-aligned rectangle will be defined by its bottom left corner (x,y), its (nonnegative) width w, and its (nonnegative) height h. The Cartesian coordinates (x,y) behave in the normal mathematical way: increasing x moves right, increasing y moves up. (In future, we will see situations where different conventions are used.) Write the function rOverlap that tests whether 2 axis-aligned rectangles overlap. rOverlap takes 8 floats (x1,y1,w1,y1 represent the first rectangle and x2,y2,w2,y2 represent the second rectangle) and returns True if the two rectangles overlap/touch, even if only at a single point, and False otherwise.

Answer 1

If we know the top-right and the bottom-left coordinates of both the triangle then we can tell if they overlap or not:

The two triangles cannot overlap in the following four cases:

1. when rectangle 1 is entire on left of rectangle 2
2. when rectangle 1 is entire on right of rectangle 2
3. when rectangle 1 is entire on top of rectangle 2
4. when rectangle 1 is entire on bottom of rectangle 2

Condition for left: The rectangle1 will be on left of rectangle 2 if the top right x-coordinate of the rectangle 1 will be less than bottom left x-coordinate of rectangle 2

Condition for right: The rectangle1 will be on right of rectangle 2 if the top right x-coordinate of the rectangle 2 will be less than bottom left x-coordinate of rectangle 1

Condition for top: The rectangle 1 will be on top of rectangle 2 if the top right y-coordinate of the rectangle 2 will be less than bottom left y-coordinate of rectangle 1

Condition for bottom: The rectangle1 will be on bottom of rectangle 2 if the top right y-coordinate of the rectangle 1 will be less than bottom left y-coordinate of rectangle 2

Here is the code to do so:

Here is the sample output:

and here is another sample output:

The codes are well commented and easy to understand, if the answer helped you please upvote and if you have any doubts please comment i will surely help. please take care of the indentation while copying the code. Check from the screenshots provided.

Here is the code:

def rOverlap(x1rec1, y1rec1, w1, h1, x1rec2, y1rec2, w2, h2):
# get the top right corner cordinates for the two rectangles
x2rec1 = x1rec1 + w1
y2rec1 = y1rec1 + h1
x2rec2 = x1rec2 + w2
y2rec2 = y1rec2 + h2
  
if (x2rec1 <= x1rec2 or # left
y2rec1 <= y1rec2 or # bottom
x1rec1 >= x2rec2 or # right
y1rec1 >= y2rec2): # top
return True
else:
return False
# Take the input and run a sample test to check whether they overlap or not
x1rec1 = float(input("Enter the left-most x-coordinate of first rectangle: "))
y1rec1 = float(input("Enter the left-most x-coordinate of first rectangle: "))
w1= float(input("Enter the width of first rectangle: "))
h1= float(input("Enter the height of first rectangle: "))

x1rec2 = float(input("Enter the left-most x-coordinate of second rectangle: "))
y1rec2 = float(input("Enter the left-most y-coordinate of second rectangle: "))
w2= float(input("Enter the width of second rectangle: "))
h2= float(input("Enter the height of second rectangle: "))

if rOverlap(x1rec1, y1rec1, w1, h1, x1rec2, y1rec2, w2, h2):
print("The two triangles dont overlap")
else:
print("the two triangles overlap")