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how to calculate collision between point and rectangular shape in 2D?

I have a rectangular shape, which can slide over the game screen and I want to know how to calculate whether the rectangle collides with the screen? and a point, how to calculate whether point collides with a rectangular shape?

A:

This is a general math problem, not related to any specific language or library. I mean two point-space vectors (x, y) to form a rectangle and two point-space vectors (x, y) to form a unit square.
Using the Pythagorean theorem, if (x1, y1) is the top left corner of a rectangle (m, n), (x2, y2) its bottom right corner, (x3, y3) its corner on the opposite side and (x4, y4) the top left corner of a square (i, j), the following equations are valid:
m^2 + n^2 = i^2 + j^2 + 2*i*j*cos(45)
m^2 + n^2 = i^2 + j^2 + 2*i*j*sin(45)

You can easily see that if x1 = x2 then y1 = y2 (so, if one of the corners is on the bottom left corner, the other corner must be on the top left corner as well) and if x2 = x3 (or y2 = y3) then x1 = x3 (or y1 = y3) as well. This means that you can have 4 possible combinations of valid math, depending on the order you have the values (so, if one of them is on top left corner, the other can only be on top left corner, but never on a corner). I won’t write that here, but if you calculate the cos and sin function for each possibility, you can easily write the equations for the collisions.

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