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Math Help - Calculating ellipse dimensions from bounding box

  1. #1
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    Calculating ellipse dimensions from bounding box

    Imagine a rotating ellipse. A bounding box is placed around the ellipse oriented always parallel to the axes. How can I calculate the width, height and angle of rotation of this ellipse? The information I do have is the bounding box dimensions and the area of the ellipse.
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  2. #2
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    Re: Calculating ellipse dimensions from bounding box

    Hello, Ferguzz!

    Imagine a rotating ellipse.
    A bounding box is placed around the ellipse oriented always parallel to the axes.
    How can I calculate the width, height and angle of rotation of this ellipse?
    The information I do have is the bounding box dimensions and the area of the ellipse.

    I don't understand the difficulty.

    We have an ellipsoid of revolution.
    The box has length L and height H.
    The width of the box equals the height: W = H.

    Code:
          : - - - - - L - - - - - :
        = *---------*-*-*---------* =
        : |    *      :      *    | :
        : | *         :         * | :
        : |*          :          *| b
        : |           :           | :
        : *           :           * :
        H * - - - - - * - - - - - * =
        : *           :           * :
        : |           :           | :
        : |*          :          *| b
        : | *         :         * | :
        : |    *      :        *  | :
        = *---------*-*-*---------* =
          : - - a - - | - - a - - :

    The "width" of the ellipsoid is L.
    The "height" of the ellipsoid is H.

    An equation of the ellipse is: . \frac{x^2}{a^2} + \frac{y^2}{b^2} \:=\:1
    . . where: . a = \tfrac{L}{2},\;b = \tfrac{H}{2}

    "The angle of rotation" has no meaning.

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