[Math] Rectangle in rotated bounding rectangle

rotations

I'm looking to find the width and height of a rectangle without rotation within a rotated bounding rectangle. I have rotation in degrees and the width and height of the bounding rectangle. Basically I'm looking to find the largest ( largest area ) un-rotated rectangle that will fit inside a rotated rectangle of any given size.

Best Answer

If you don't have the coordinates of the rotated corners, just rotate each point.

Once you have that, find the smallest and largest $x,y$ coordinates of the 4 points.

The smallest and largest $x,y$ pairs correspond to the bottom-left and top-right corners of your rectangle.

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