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Math Help - Get corner points from bounding box and rotation.

  1. #1
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    Get corner points from bounding box and rotation.

    Knowing the Bounding box corner points (circled in red) and the rotation angle, is it possible to find the other point coordinates circled in blue?

    Attached Thumbnails Attached Thumbnails Get corner points from bounding box and rotation.-transition.jpg  
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  2. #2
    MHF Contributor undefined's Avatar
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    I assume there is a tilted rectangle in the figure. If so, then the answer is to your question is yes, it is possible.

    I assume you want to know how?

    (You should write more specifically.)

    Here is one way. Refer to my attachment.

    L and H are known, from the coordinates circled in red.

    We have similar triangles.

    \frac{w}{z} = \frac{y}{x}

    Also,

    x+w=L

    y+z=H

    Substitute

    \frac{L-x}{H-y} = \frac{y}{x}

    x^2-y^2-Lx+Hy=0

    We know that

    \tan 25^\circ=\frac{y}{x}

    We can now solve for x (discard the value x=0). From this we can obtain the values of all variables.

    When L = 7.5 and H = 8.5, I get x \approx 4.51901.
    Attached Thumbnails Attached Thumbnails Get corner points from bounding box and rotation.-transition2.png  
    Last edited by undefined; June 1st 2010 at 02:25 PM.
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