POV-Ray : Newsgroups : povray.general : Rotation around an axis at the origin : Re: Rotation around an axis at the origin Server Time
7 Aug 2024 19:23:47 EDT (-0400)
  Re: Rotation around an axis at the origin  
From: Greg Smith
Date: 16 Jul 2001 21:17:45
Message: <3B539223.E15563D9@alumni.uwaterloo.ca>
Hey, I suggested this as a new feature a few years back.

rotate_unform <rot_vector>
   -or-
rotate_uniform angle*<normal>

rotates about the given vector, by an angle equal to the magnitude
of the vector.

The usefulness of this is that rotations interpolate much better
in this space. If you have an animation and you describe rotations
at keyframes by this means, interpolations between the keyframes
based on interpolations in the rotation vector space work much better
since the space is uniform (except for rotation close to 180 degrees).
With the standard rotation, you can get weird effects if the interpolation
path happens to come close to the 'north pole' if you see what I mean.

I see other have helped you with this already....



> I have a question that I'm currently failing to resolve,
> so any help is welcome:
>
> What is the form of the transformation matrix that would
> perform a rotation of a given angle (alpha), at the origin
> (<0,0,0>), around any possible axis (<a,b,c>).
>
> I know the form for a rotation around the X, Y or Z,
> but I just cannot figure how to do it for any vector as
> the axis of the rotation.
> If it can help, it can be assumed that the length of the vector
> is the unit (or whatever please the solver).
>
> I hope for a solution that is expressed in term of:
>  -the vector which is the normal to the plane of the rotation,
>  -the angle of the rotation, as measured in the plane of the rotation
>
> Thanks in advance.


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