Is it possible to use custom orthonormal unit vectors to draw rotated objects in a 3D plot?

I have to draw a tensor representation (an ellipsoid). As a result of the decomposition I get three vectors describing the basis I should use to draw a rotated tensor (relative to the Carthesian coordinate system).

Is it possible to use these vectors to somehow draw a rotated ellipsoid? Theoretically I could try to solve a system of equations: v' = A*B*v (where v' is a rotated unit vector, v is a corresponding Carthesian vector and A and B are rotation matrices) to get two rotation angles (something similar to spherical coordinates) and then call rotate() twice, but it seems to be a bit cumbersome.

Here's an example of such three vectors (ellipsoid rotated about Y axis):

• v1 = [ 0.3827, 0, -0.9239]
• v2 = [ -0.9239, 0, -0.3827]
• v3 = [ 0, 1.0000, 0]

PS. I hope my question is more or less understandable ; )

[Walter Roberson]

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