Reorient Ellipsoid Gained From Ellipsoid Function

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Sam Polk
Sam Polk 2021-6-17
I have an ellipsoid I would like to plot. I know that I can do so using the ellipsoid function (link) as follows:
[X,Y,Z] = ellipsoid(xc,yc,zc,xr,yr,zr)
surf(X,Y,Z);
This gives an ellipsoid with mean equal to [xc,yc,zc] and semiaxes with length equal to xr, yr, and zr respectively. However, the semiaxes are necessarily the canonical basis for R3: [1,0,0], [0,1,0], and [0,0,1].
Given vectors three 3-dimensional orthonormal vectors u1, u2, u3, how can I orient the ellipsoid above so that the ith semiaxis is oriented in the direction of ui?
Thank you.

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