Get bounds of rotated rectangle

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Known data: bounding box width W, height H, rotation angle Fi
Wanted: coordinates of rotated rectangle vertices.

Unknown source rectangle size: w x h

Bounding box size for this dimension and rotation angle:

enter image description here

 H = w * Abs(Sin(Fi)) + h * Abs(Cos(Fi))
 W = w * Abs(Cos(Fi)) + h * Abs(Sin(Fi))
 denote 
 as = Abs(Sin(Fi))
 cs = Abs(Cos(Fi))

so we can solve linear equation system and get (note singularity for Pi/4 angle)

 h = (H * cs - W * as) / (cs^2 - as^2)
 w = -(H * as - W * cs) / (cs^2 - as^2)

Vertex coordinates:

 XatTopEdge = w * cs      (AE at the picture)
 YatRightEdge = h * cs    (DH)
 XatBottomEdge = h * as   (BG)
 YatLeftEdge = w * as     (AF)

Note that with given data we cannot differ between angles Fi and 90+Fi but this fact perhaps does not influence on solution (w and h will exchange each other too)

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