Thread View: comp.graphics.research
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Started by David Beasley
Mon, 14 Dec 1992 22:17
Multiplication of quaternion numbers
Author: David Beasley
Date: Mon, 14 Dec 1992 22:17
Date: Mon, 14 Dec 1992 22:17
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Quaternion numbers can be quite handy for representing points in 3-D space. The multiplication of one quaternion by another performs the job of 3-D rotation. But since quaternions are 4-component numbers, a trivial algorithm requires 16 real-number multiplications to be done. However, I have devised an algorithm which achieves quaternion multiplication with only 10 real-number multiplications. Does anyone know if an algorithm such as this has been published before, or have I discovered something new here? I'd be interested to hear from anyone using quaternions for 3-D manipulations. David Beasley (David.Beasley@cm.cf.ac.uk) Department of Computing Mathematics University of Wales College of Cardiff __o PO Box 916 \<, CARDIFF CF2 4YN ___________________()/ ()___ -- Moderated by SCRI Vis <> Submissions to: graphics@scri1.scri.fsu.edu Guy, John R. Murray <> Administrivia to: graphics-request@scri1.scri.fsu.edu
Re: Multiplication of quaternion numbers
Author: Timothy Wegner
Date: Wed, 16 Dec 1992 19:49
Date: Wed, 16 Dec 1992 19:49
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David.Beasley@cm.cf.ac.uk (David Beasley) writes: >However, I have devised an algorithm which achieves quaternion >multiplication with only 10 real-number multiplications. Does anyone >know if an algorithm such as this has been published before, or have >I discovered something new here? I was sent a similar "optimization" by a Fractint user for complex multiplication, and easily generalized it to quaternions. However much to my surprise the resulting code ran *slower* on my 66 Mhz 486 machine! (My code also reduced 16 multipies to 10 at the expense of more assignment statements and temporary variables. Needless to say I returned the quaternion fractal type in Fractint back to Ken Shirriff's original code. I expect however that on a 386/387 combination the result might have been different. As far as this idea being new, I think not. -- Tim Wegner Fractint co-author Internet: twegner@mwunix.mitre.org Compuserve: 71320.675@compuserve.com -- Moderated by SCRI Vis <> Submissions to: graphics@scri1.scri.fsu.edu Guy, John R. Murray <> Administrivia to: graphics-request@scri1.scri.fsu.edu
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