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Math Help - defining ellipsoid based on 3 given ellipses which are parallel to Cartesian planes

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    defining ellipsoid based on 3 given ellipses which are parallel to Cartesian planes

    hello all

    for a 3d imaging software i am coding:

    I need to define an ellipsoid E, which can have any radii, centers and rotations in space



    the user interface allows the user to control 3 ellipses, which are "slices" of the ellipsoid (red,green,blue in the image) ,and are parallel (by definition) to the main Cartesian planes (x-y, y-z. x-z)
    these 3 ellipses are part of, and define, the whole ellipsoid




    each slice can be dragged, resized or rotated in space and each slice is fully defined: it's center's 3d position in space, it's 2 radiuses, it's distance from the axis planes.

    each change should, obviously, affect the parameters of the ellipsoid E, and the other 2 derived ellipses.

    i need the equation to re-calculate ellipsoid E based on the changes made to a slice

    (The preferred type of equation for the ellipsoid should make it easy to derive the X-Y ellipse cuts (variable z))

    any ideas?
    thanx in advance
    Saar
    Attached Thumbnails Attached Thumbnails defining ellipsoid based on 3 given ellipses which are parallel to  Cartesian planes-elipsiod.png   defining ellipsoid based on 3 given ellipses which are parallel to  Cartesian planes-slices.png  
    Last edited by saar62097; November 25th 2010 at 05:10 AM.
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