Calculate Bounding box coordinates from a rotated rectangle

by
  • Transform the coordinates of all four corners
  • Find the smallest of all four x’s as min_x
  • Find the largest of all four x’s and call it max_x
  • Ditto with the y’s
  • Your bounding box is (min_x,min_y), (min_x,max_y), (max_x,max_y), (max_x,min_y)

AFAIK, there isn’t any royal road that will get you there much faster.

If you are wondering how to transform the coordinates, try:

x2 = x0+(x-x0)*cos(theta)+(y-y0)*sin(theta)
y2 = y0-(x-x0)*sin(theta)+(y-y0)*cos(theta)

where (x0,y0) is the center around which you are rotating. You may need to tinker with this depending on your trig functions (do they expect degrees or radians) the sense / sign of your coordinate system vs. how you are specifying angles, etc.

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