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))
thanx in advance