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square1 = (47,15) (51,15) (51,19) (47,19)

square2 = (19,0) (-27,46) (19,92) (65,46)

These two squares may not be parallel to X axis or Y axis.

These two squares do not intersect, but how can I find it mathematically from those points?

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  • $\begingroup$ Welcome to MSE. Please choose your tags with care. This has nothing to do with polar-coordinates. $\endgroup$ Jun 17, 2018 at 17:28
  • $\begingroup$ Assume that it is inside the square. if your professor marks it as a mistake, you know that with high probability (> 0.9?) that it is outside the square. Sorry for the joke -- couldn't resist. $\endgroup$
    – user625
    Jun 18, 2018 at 0:41

1 Answer 1

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If the squares are axis aligned like your example you can just check whether any corner of one square is within the other one. To check if $(19,0)$ is in the first square you just check if $19$ is between $47$ and $51$ and whether $0$ is between $15$ and $19$. You need both checks to pass, but here they both fail. Try the other three corners, then swap the squares and you are done.

If the sides of the squares are not parallel it is necessary to look for intersections between the sides. You can have two squares overlap without any corner being in the other-think of an eight pointed star. Compute the slope of each side as $m=\frac {y_2-y_1}{x_2-x_1}$ Taking the sides in pairs, one from each square, find the intersection point of the lines they are on. See if that point is on the side of both squares. If so, the squares intersect. You have to watch out for division by zero here.

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