Subject:
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Re: Mathematical assistance please
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Newsgroups:
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lugnet.cad.dev
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Date:
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Fri, 7 Jan 2005 00:09:37 GMT
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Viewed:
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1883 times
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In lugnet.cad.dev, Ross Crawford wrote:
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Or maybe another way to look at it (got this from old lecture notes):
Goal: rotate about arbitrary vector A by alpha
Idea: we know how to rotate about X,Y,Z
So, rotate about Y by beta until A lies in the YZ plane
Then rotate about X by gamma until A coincides with +Z
Then rotate about Z by alpha
Then reverse the rotation about X (by -gamma)
Then reverse the rotation about Y (by -beta)
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OK, here’s my VERY LAST word on the subject:
Transforming both 4-4cyls S0-S1 and vector S1-S2:
- Rotate about Y by beta until S0-S1 lies in the YZ plane
- Rotate about X by gamma until S0-S1 coincides with +Z
- Rotate about Z by delta until S1-S2 lies in XZ plane
Now rotate 4-4cyls S0-S1 only about Z until the shortest side is on the XZ
plane, on the same side of the Y axis as the vector S1-S2
Then:
- Reverse the rotation about Z (by -delta)
- Reverse the rotation about X (by -gamma)
- Reverse the rotation about Y (by -beta)
That should get you the result you need.
Of course it can probably be optimised somewhat :)
ROSCO
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Message is in Reply To:
 | | Re: Mathematical assistance please
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| (...) Or maybe another way to look at it (got this from old lecture notes): Goal: rotate about arbitrary vector A by alpha Idea: we know how to rotate about X,Y,Z So, rotate about Y by beta until A lies in the YZ plane Then rotate about X by gamma (...) (20 years ago, 6-Jan-05, to lugnet.cad.dev)
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