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Hey all you math-enabled people!
I need a macro to give me the rotation vector to rotate vector A to have the
same direction as vector B. I suspect I could do it myself, but could
somebody spare me the head-ache?
Margus
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On Sun, 25 Apr 1999 04:33:36 +0300, "Margus Ramst"
<mar### [at] peak eduee> wrote:
>Hey all you math-enabled people!
>I need a macro to give me the rotation vector to rotate vector A to have the
>same direction as vector B. I suspect I could do it myself, but could
>somebody spare me the head-ache?
John VanSickle's Thoroughly Useful Macros will help with this. A copy
of the one you need can be found at http://twysted.net/macroscope
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Ronald L. Parker wrote in message <372271a9.213964711@news.povray.org>...
>
>John VanSickle's Thoroughly Useful Macros will help with this. A copy
>of the one you need can be found at http://twysted.net/macroscope
>
I don't think so. The Reorient macro is close, but it uses matrix
transformation to reorient an object. What I need is a rotation vector I
could use in vrotate().
Margus
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On Sun, 25 Apr 1999 05:01:07 +0300, "Margus Ramst"
<mar### [at] peakeduee> wrote:
>Ronald L. Parker wrote in message <372271a9.213964711@news.povray.org>...
>>
>>John VanSickle's Thoroughly Useful Macros will help with this. A copy
>>of the one you need can be found at http://twysted.net/macroscope
>>
>
>I don't think so. The Reorient macro is close, but it uses matrix
>transformation to reorient an object. What I need is a rotation vector I
>could use in vrotate().
Ah, okay, that's actually how I read it at first, but I couldn't
imagine why you would need such a thing so then I assumed that you
really wanted the Reorient macro. I can get you an angle and an axis,
which you can use with vaxis_rotate(), if you'd like. This isn't
tested, so it may be faulty. In particular, you may have to fix the
sign on the angle. (It's times like this that I don't trust a
left-handed coordinate system.) You may, of course, get rid of all
the intermediate local variables and make this a one-liner.
#macro vvec_rotate( Vec, RefA, RefB )
#local nA = vnormalize(RefA);
#local nB = vnormalize(RefB);
#local axis = vcross(nA,nB);
#local angle = degrees(atan2(vlength(axis),vdot(nA,nB)));
vaxis_rotate( Vec, axis, angle );
#end
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Margus Ramst wrote in message <3722715b.0@news.povray.org>...
>Hey all you math-enabled people!
>I need a macro to give me the rotation vector to rotate vector A to have
the
>same direction as vector B. I suspect I could do it myself, but could
>somebody spare me the head-ache?
Interrupt me if I am wrong ;-) but do I understand you correctly?
You want to rotate a vector such, that it points in the same direction as
some other vector?
If so, I don't see the need for any rotational math. I would do it like
this:
Compute the length of vector A.
lengthA = sqrt(Ax*Ax + Ay*Ay + Az*Az)
Normalize B to length 1. (B')
lengthB = sqrt(Bx*Bx + Ay*Ay + Az*Az)
B' = [ Bx/lengthB By/lengthB Bz/lengthB ]
Multiply it with the length of A (B'')
B''= [ B'x*lengthA B'y*lengthA Bz*lengthA ]
B'' is now the same direction as B and with the length of A.
All in one formula:
[ Bx / lengthB * lengthA ]
[ ]
B'' = [ By / lengthB * lengthA ]
[ ]
[ Bz / lengthB * lengthA ]
(where lengthA and lengthB as given above)
Is that what you want?
Johannes.
P.S. So, I'm showing my math in public? I *really* hope I got it right ;-)
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Thank you, this is perfect.
One of these days I'm sure I'll learn to use vdot... Maybe. I hope.
Margus
Ronald L. Parker wrote in message <372379f4.216088045@news.povray.org>...
>
>Ah, okay, that's actually how I read it at first, but I couldn't
>imagine why you would need such a thing so then I assumed that you
>really wanted the Reorient macro. I can get you an angle and an axis,
>which you can use with vaxis_rotate(), if you'd like. This isn't
>tested, so it may be faulty. In particular, you may have to fix the
>sign on the angle. (It's times like this that I don't trust a
>left-handed coordinate system.) You may, of course, get rid of all
>the intermediate local variables and make this a one-liner.
>
>#macro vvec_rotate( Vec, RefA, RefB )
> #local nA = vnormalize(RefA);
> #local nB = vnormalize(RefB);
> #local axis = vcross(nA,nB);
> #local angle = degrees(atan2(vlength(axis),vdot(nA,nB)));
> vaxis_rotate( Vec, axis, angle );
>#end
>
>
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Thanks. You understood correctly a somewhat incomplete explanation. What I
really needed was to rotate vector A by the same amount that base vector B
differs from new vector C (hope this makes sense). Ron seems to have divined
my purpose, so I have the answer.
BTW, you could've written
vlength(A)*vnormalize(B)
Trust me, I woud have understood :)
Margus
Johannes Hubert wrote in message <3722c103.0@news.povray.org>...
>
>Interrupt me if I am wrong ;-) but do I understand you correctly?
>
>You want to rotate a vector such, that it points in the same direction as
>some other vector?
>
>If so, I don't see the need for any rotational math. I would do it like
>this:
>
>Compute the length of vector A.
> lengthA = sqrt(Ax*Ax + Ay*Ay + Az*Az)
>
>Normalize B to length 1. (B')
> lengthB = sqrt(Bx*Bx + Ay*Ay + Az*Az)
> B' = [ Bx/lengthB By/lengthB Bz/lengthB ]
>
>Multiply it with the length of A (B'')
> B''= [ B'x*lengthA B'y*lengthA Bz*lengthA ]
>
>B'' is now the same direction as B and with the length of A.
>
>All in one formula:
>
> [ Bx / lengthB * lengthA ]
> [ ]
> B'' = [ By / lengthB * lengthA ]
> [ ]
> [ Bz / lengthB * lengthA ]
>
>(where lengthA and lengthB as given above)
>
>
>Is that what you want?
>
>
>Johannes.
>
>P.S. So, I'm showing my math in public? I *really* hope I got it right ;-)
>
>
>
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Margus Ramst wrote:
>
> Hey all you math-enabled people!
> I need a macro to give me the rotation vector to rotate vector A to have the
> same direction as vector B. I suspect I could do it myself, but could
> somebody spare me the head-ache?
subtract?
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