Question

Python: 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.
Context. Detection of the overlap of bounding boxes is used in collision detection (e.g., robotics, games). A bounding box of an object is a rectangle (2D) or box (higher dimensions) that contains the object. Since two objects can collide only if their bounding boxes overlap, collision detection of bounding boxes is used as an efficient test, with the more expensive intersection of the objects used only in the rare cases when the bounding boxes overlap. Collision detection is used during motion planning of a robot, or interactively during a game to prevent, say, running through walls. Observation. It would be more elegant to collapse the 8 parameters of this function into two rectangle parameters, but that requires more advanced Python syntax. You may revisit these functions once we have that power.

Answer 1

Code:

def rOverlap(x1,y1,w1,h1,x2,y2,w2,h2):

bottomLeft1 = (x1,y1)
bottomRight1 = (x1 + w1,y1)
topLeft1 = (x1,y1 + h1)
topRight1 = (x1 + w1,y1 + h1)

bottomLeft2 = (x2,y2)
bottomRight2 = (x2 + w2,y2)
topLeft2 = (x2,y2 + h2)
topRight2 = (x2 + w2,y2 + h2)

rect1 = [bottomLeft1,bottomRight1,topLeft1,topRight1]
rect2 = [bottomLeft2,bottomRight2,topLeft2,topRight2]

#If any two co-ordinates match, then return true
for i in rect1:
for j in rect2:
if i == j:
return True

#If one rectangle is to the side of other

if bottomRight2[0] < topLeft1[0] or topLeft2[0] > bottomRight1[0]:
return False

#If one rectangle is on the top of other

if bottomRight2[1] > topLeft1[1] or topLeft2[1] < bottomRight1[1]:
return False

#If both the conditions fail
return True

#Test
x1 = 0
y1 = 0
h1 = 10
w1 = 10

x2 = 5
y2 = 5
h2 = 3
w2 = 3

print(rOverlap(x1,y1,w1,h1,x2,y2,w2,h2))
  
The output of the above code is True for the given test case.

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