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# Calculating the center of an ellipse given the foci

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If one has an ellipse that lies in the arbitrary plane
Ax + By + Cz - D = 0

with the foci
fa = <fax, fay, faz>

and
fb = <fbx, fby, fbz>

where fa and fb lie in the plane and are specified relative to the origin, then can the center point of the ellipse be calculated with
c = fa + ((fb - fa) / 2)

where c is a vector pointing from the origin to the center point? If not, can someone please point me in the right direction. Thanks for your help. [edited by - SpiffGQ on October 5, 2003 8:55:01 PM]

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I think yes, but writing your equation as c = (fa+fb)/2 would be
a) shorter
b) more intuitive to me: The center of an ellipse (or ellipsoid) is in the middle of the two foci.

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quote:
Original post by Atheist
I think yes, but writing your equation as c = (fa+fb)/2 would be
a) shorter
b) more intuitive to me: The center of an ellipse (or ellipsoid) is in the middle of the two foci.

Thanks.

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