halfSpin rotation in quat notation

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halfSpin rotation in quat notation

Postby thigle » Fri May 19, 2006 9:45 am

in a modelling program i use for architecture, there is this thing that has been buggin around my backhead for some time...

having an object and wanting to rotate it 2pi around z axis and pi around axis orthogonal to z, one stumbles upon a problem of Gimbal lock. that means that the software is counting it in such a way that for certain values the inerpolation collapses, because the interpolated values can cancel out at certain points. (there is quite a lot of info on GimblaLock through google so i don't explain it here)

to avoid this GimbalLock that results from expressing rotations in Euler algorithm, this software, as well many other graphic engines, allows the use of quaternions for rotations.

each quaternion is considered as an axis (of rotation) plus value of rotation. (3 imaginaries give axis, 1 scalar the value,amount of rotation)
multiplying by a quaternion rotates.

this software wants quaternions in normalized form - unit quats.

unfortunatelly, there is no good(readable) help coming with the script.
my question is this:

does anyone here use quaternions to note rotations, and if so, how would one note the above mentioned 1/2 spin ? (360around z & 180 around x, or y) ?
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Re: halfSpin rotation in quat notation

Postby wendy » Fri Jan 30, 2009 10:37 am

Looking at this, i suggest something like (1+i) A (1-i) should do the trick for you.
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Re: halfSpin rotation in quat notation

Postby pat » Wed Feb 18, 2009 5:36 am

Of course, 1 + i and 1 - i aren't unit quaternions, so you'll need to scale 'em down by sqrt(2).

That, however, looks to me like a pi/2 rotation around the the x axis with no rotation around the z-axis.

Re-reading the original post, I'm not really sure what the request is for. You want some rotation that when
done enough or interpolated enough will rotate once in the xy-plane for every time it rotates half way around
in say the yz-plane?

But, as the original post is from three years ago, I'm wondering if the answer is still of interest.
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Re: halfSpin rotation in quat notation

Postby wendy » Thu Feb 19, 2009 7:24 am

One day, i got bored, and went through the 'unanswered posts' section. Didin't look at the date.

What it does is a pair of orthogonal rotations which corresponds to a double rotation around the real plane.
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