Re: Rotations in R^3
- From: beeworks@xxxxxxxxxxx
- Date: Mon, 5 May 2008 09:20:35 -0700 (PDT)
On May 5, 9:39 am, Maury Barbato <mauriziobarb...@xxxxxxxx> wrote:
Hello,
let R, S be two rotations with axes r, s. If r, s are in
the same plane, then R°S is a rotation or a translation.
But what happens when r and s are not in the same plane?
Thank you very very much for your attention.
My Best Regards,
Maury
I believe you meant to write:
"If r and s in R3 are parallel then R*S is a rotation or a
translation."
To answer your question, if r and s are not parallel then the R*S is a
rotation about some third axis t.
For others responding to the OP, note that the rotation axis need not
be through the origin. The OP is not asking about orthogonal
transformation, but rather is asking about the more general rotation
in R3. If the rotation axis is not through the origin, then the
rotation can be decomposed into a translation that makes the rotation
axis pass through the origin, followed by a rotation about this
translated axis, followed by the inverse translation that takes the
axis back to its original position:
R = (T)^(-1)(R')(T)
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