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Subject: Re: Ellipsoid
Date: Sun, 28 Nov 2010 06:06:03 +0000 (UTC)
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"Robert Phillips" <phillir1@my.erau.edu> wrote in message <icso5g$33l$1@fred.mathworks.com>...
> .......
> I have the center point S.
> I also have the vectors a_S, b_S, & c_S, which describe the semi-major and semi-minor axes a,b,c. These vectors do not necessarily lie along x, y, or z.
> How can I generate the points of an ellipsoid, along a_S, b_S, & c_S?
> .......
- - - - - - - - 
  If we assume that a_S, b_S,  and c_S are unit vectors and mutually orthongonal, then the coordinates of a point P relative to these three vectors would be XR = dot(P-S,a_S), YR = dot(P-S,b_S), and ZR = dot(P-S,c_S).  You would use these in the expression

 XR^2/a^2 + YR^2/b^2 + ZR^2/c^2 <= 1

to determine whether P is inside the ellipsoid.

Roger Stafford