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Determing if a point is inside an ellipsoid

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Omair
Omair 2013-11-25
评论： Ilja Westra 2022-10-7
How can you determine if a given set of points is inside an off center rotated ellipsoid?

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David Sanchez
David Sanchez 2013-11-25
the point (x,y,z) will be inside the ellipsoid when
(x-xo)^2/a + (y-yo)^2/b +(z-zo)^2/c < 1
it will be outside the ellipsoid when
(x-xo)^2/a + (y-yo)^2/b +(z-zo)^2/c > 1
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Omair
Omair 2013-11-26
I know that my data is distributed along the x=y=z line in the [0,300] for all three variables. The rotation matrix i derived using this information.
Ilja Westra
Ilja Westra 2022-10-7
If anybody else stumbles upon this and has trouble with the equation not working:
((x-xo)/a)^2 + ((y-yo)/b)^2 +((z-zo)/c)^2 < 1
Taking the whole fractions squared instead of just the distance from the point to the ellipsoid center worked for me.

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