Ellipsoid volume cut by a plane

I have an ellipsoid at a random orientation and position in space. This ellipsoid is to be cut by a plane parallel to the xy plane. How can I determine the volume of ellipsoid below the intersection ?

Answer 1

[Michael]

I think you'll need to give a bit more information about your situation in order to get a useful answer. What have you done so far?

[Sakshi]

I have defined the ellipsoid using function, 'ellipsoid'. Then I carried out the rotation and translation. This is a processs done for 100 ellipsoids.AFter placing all the ellipsoids in a cube of 100 length, I am cutting the cube by planes parallel to xy planes and getting the total volume of ellipsoids below each plane.So for ellipsoids, fully inside the plane, the volume is full. However, My query is for those ellipsoids that are cut by the plane and I only need the volume of the ellipsoid below the plane.