# Calculate Bounding box coordinates from a rotated rectangle

actionscript-3bounding-boxgeometrymathrotation

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.

#### Best Solution

• 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.