# Thread: Calculating ellipse dimensions from bounding box

1. ## 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.

2. ## 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.