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We can instead check whether any outermost point of one interval is inside of another interval:
def check_intervals_intersection(a,b,c,d):
if (a <= d and a >= c) or (b <= d and b >= c) or (c <= b and c >= a) or (d <= b and d >= a):
return True
else:
return False
If a bbox degenerates into an interval (x_min=x_max or y_min=y_max), then corresponding width=0 and intersection is not counted
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