Re: Rotating a Plane

Hi Roger,

Thank you very much for your reply. You are understanding my problem
right. I want transformation equations for rotating points on the
original circle to corresponding points on the rotated circle. I want
to "map" each point on the original circle to the rotated circle. I
don't want to spin the circle around its axis, so there will be just
one way (or two ways if we consider clockwise and anti clockwise
rotations) to rotate the circle to bring its normal from the original
z-axis to the rotated vector (a,b,c).

Again you are right, rotating the circle about a line in the xy-plane
orthogonal to the a,b,c direction seems good. I guess you mean find a
vector in x-y plane which is perpendicular to the projection of
(a,b,c) onto x-y plane and then rotate points around this vector.

I would really appreciate if you can provide some details about how
to do it. Also, how do we differentiate between clockwise and
counterclockwise rotations? This will affect mapping of my points.

Thank you very much and looking forward to hearing from you again.

Thanks,
Raman

Roger Stafford wrote:


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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