Volume of partial ellipsoid cut by plane

  1. I wanted to get opinions on whether solving this problem in a non-numerical way is realistic, or if someone has the answer, all the better. I have a totally arbitrary ellipsoid (not aligned with any axes) that I can describe by matrix A, like x'Ax=1 is the ellipsoid surface. I have the points describing the primary axes of the ellipse. What I want is to cut the ellipse by a plane at Z=(some value) and get the volume above/below that plane.

    One approach that seems potentially doable is to solve for the area of the ellipse generated by a cut at Z=x and then integrate that over the range of interest. How exactly to carry that out is eluding me at the moment though. Thanks for any input.
  2. jcsd
  3. hello ! Were you able to get an answer to your question ?If yes, could you please put it here because i have the same query.
    Thank you !
  4. No, never did. Still would like to know though!
  5. Have you attempted to set up an integral? The problem I see is getting the right limits for the integral, but it should be doable.
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