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Volume of partial ellipsoid cut by plane

  1. Sep 27, 2010 #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. Jul 12, 2011 #2
    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. Jul 12, 2011 #3
    No, never did. Still would like to know though!
  5. Jul 13, 2011 #4


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    Science Advisor

    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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