Adolf Mathias (dolfi++at++guido.zkm.de)
Thu, 5 Jan 95 11:11:58 +0100
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 /
It offers the same advantages as the quaternions like the possibility to interpolate
rotations but doesn't have to introduce a new algebraic field and other new concepts.
The construction is based on projections and cross products.
I don't believe this is something new but haven't seen it yet elsewhere.
Maybe someone will find it useful.
Happy new year,
Dolfi
Adolf Mathias Email: <dolfi++at++zkm.de>
Zentrum fuer Kunst und Medientechnologie
Postfach 6919 76049 Karlsruhe
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