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How does one find the coordinates of the 4 corners of a bounding box of a square of width w and height h that is rotated theta degrees and is offset from the origin x in the x direction and y in the y direction?

Here is a visual example of what I mean:

image of 4 corners of bounding box

Here is some python3 code that I came up with, but it only works in the right quadrants except when theta = 0 or 360 or etc.:

import math def bounds(x,y,w,h,theta): theta = theta * math.pi / 180 A = ( x, y+round((math.sin(theta)*w), 2) ) B = ( x+round((w/math.sin(theta)), 2), y+round((math.sin(theta)*w), 2) ) C = ( x+round((w/math.sin(theta)), 2), y+round((math.cos(theta)*h), 2) ) D = ( x, y+round((math.cos(theta)*h), 2) ) print(A) print(B) print(C) print(D)

I was reading this but I could not figure it out for my specific problem.

Any help is much appreciated. Next time I will use matrices to store all the transformation data because this would be so much easier that way.

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    \$\begingroup\$ i recommend you the book Christer Ericson Real-Time Collision Detection thank me latter. Bye bye \$\endgroup\$ Commented May 21, 2017 at 17:33
  • \$\begingroup\$ @Haruko Thanks for this. This should be especially helpful when building a 3D environment that involves any sort of collision. \$\endgroup\$ Commented May 21, 2017 at 18:38

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Figured it out. The main part is finding out how to get the corners of the square. I suggest brute forcing through the trigonometry on paper to figure out how to get the 4 corners of the square. After that, it's just a matter of finding the width between the furthest corners in the x direction and finding the height between the furthest corners in the y direction, and finally adding them up with the top-left x,y coordinates of the bounding box, appropriately for each corner of the bounding box.

Here is a pseudo code:

// corner functions (tricky part) get_top_left_corner = function() { return [my_x, my_y] } get_top_right_corner = function() { angle = to_radians(my_angle) return [my_x + cos(angle) * my_w, my_y - sin(angle) * my_w] } get_bottom_left_corner = function() { angle = to_radians(my_angle) return [my_x + sin(angle) * my_h, my_y + cos(angle) * my_h] } get_bottom_right_corner = function() { angle = to_radians(my_angle) return [(my_x + cos(angle) * my_w) + (sin(angle) * my_h), (my_y - sin(angle) * my_w) + (cos(angle) * my_h)] } // [x,y] coordinates of corners of rotated square tl = get_top_left_corner() tr = get_top_right_corner() bl = get_bottom_left_corner() br = get_bottom_right_corner() // coordinates of bounding box's top left corner ax = min( tl.x, tr.x, bl.x, br.x ) ay = min( tl.y, tr.y, bl.y, br.y ) // width & height of bounding box w = max( tl.x, tr.x, bl.x, br.x ) - ax h = max( tl.y, tr.y, bl.y, br.y ) - ay // [x,y] coordinates of bounding box's corners A = [ax, ay] B = [ax + w, ay] C = [ax + w, ay + h] D = [ax, ay + h]
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