Calculate Bounding box coordinates from a rotated rectangle

Question

I have the coordinates of the top left point of a rectangle as well as its width, height and rotation from 0 to 180 and -0 to -180.

I am trying to get the bounding coordinates of the actual box around the rectangle.

What is a simple way of calculating the coordinates of the bounding box

• Min y, max y, min x, max x?

The A point is not always on the min y bound, it can be anywhere.

I can use matrix the transform toolkit in as3 if needed.

Answer 1

• 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.

Answer 2

I realize that you're asking for ActionScript but, just in case anyone gets here looking for the iOS or OS-X answer, it is this:

+ (CGRect) boundingRectAfterRotatingRect: (CGRect) rect toAngle: (float) radians {     CGAffineTransform xfrm = CGAffineTransformMakeRotation(radians);     CGRect result = CGRectApplyAffineTransform (rect, xfrm);      return result; } 

If your OS offers to do all the hard work for you, let it! :)

Swift:

func boundingRectAfterRotatingRect(rect: CGRect, toAngle radians: CGFloat) -> CGRect {     let xfrm = CGAffineTransformMakeRotation(radians)     return CGRectApplyAffineTransform (rect, xfrm) }