Volume of partial ellipsoid cut by plane


by Chuck37
Tags: ellipsoid, partial, plane, volume
Chuck37
Chuck37 is offline
#1
Sep27-10, 12:04 PM
P: 52
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.
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sakshi.mehrot
sakshi.mehrot is offline
#2
Jul12-11, 03:49 AM
P: 1
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 !
Chuck37
Chuck37 is offline
#3
Jul12-11, 09:47 AM
P: 52
No, never did. Still would like to know though!

chiro
chiro is offline
#4
Jul13-11, 09:09 AM
P: 4,570

Volume of partial ellipsoid cut by plane


Quote Quote by Chuck37 View Post
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.
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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