Re: Rotating a Plane

In article <ef5bd06.-1@xxxxxxxxxxxxxxxxxxxxxxx>, Raman
<raman@xxxxxxxxxxxxxxx> wrote:

I have a circle with center at origin (0,0,0) and its axis pointing
in z-direction (0,0,1). I have to rotate the circle about the origin
(in 3D) so that it's normal points in a given direction (a,b,c). Can
you please suggest a method to do this?
I know the problem is not very hard but I am getting confused. Any
help is deeply appreciated.

Thanks,
Raman
----------------
You don't make it clear just what you want here, Raman. Is it merely
some equations defining a new circle with axis orthogonal to a,b,c that
you want, or do you want the transformation equations for rotating points
on the original circle over to corresponding points on the "rotated"
circle? If it is the latter case, in what way would this differ from your
asking for the complete transformation equations of such a rotation, quite
independent of any particular circle? In other words, what would the
circle have to do with finding the transformation equations for the
rotation you describe? These would apply to any points in your 3D space.

I should also point out that your description does not completely
characterize a rotation. You can arrive at a rotated version of your
circle in infinitely many ways, as you can see by spinning it arbitrarily
about its new axis after it has arrived in its new plane. Of course, the
most obvious rotation is that about a line in the xy-plane orthogonal to
the a,b,c direction. Is that the rotation you have in mind?

Roger Stafford
.

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