Re: Alternative Orientation

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Adolf Mathias (dolfi++at++guido.zkm.de)
Thu, 5 Jan 95 11:55:18 +0100

>Hello all,
>
>I recently computed a matrix construction for the rotation about an axis
>v=(v0,v1,v2) with angle phi which seems much handier to me than the quaternion
>representation:
>
> / 1 0 0 \ / v0*v0 v0*v1 v0*v2 \ / 0 v2 -v1 \
>M=cos(phi)*| 0 1 0 | + (1-cos(phi))*| v1*v0 v1*v1 v1*v2 | + sin(phi)*|-v2 0 v0 |
> \ 0 0 1 / \ v2*v0 v2*v1 v2*v2 / \ v1 -v0 0 /

I forgot to mention: Of course, v has to be length 1. I didn't think about the
implications of this not being so, but perhaps, with some modifications, regular
scaling in all three axes on the one hand or separate scaling along the rotation
axis or in the rotation plane on the other hand could be affected.

Dolfi

Adolf Mathias Email: <dolfi++at++zkm.de>
Zentrum fuer Kunst und Medientechnologie
Postfach 6919 76049 Karlsruhe
Tel. +49 (0)721 9340 404 Fax. ...9340 49

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