Fwd: Quaternion to axis/angle conversion is buggy when w(4)<0

[Vijay Pradeep]

Hello David,

I believe that you are arguing that the two sets of [ax ang] that you
computed are equivalent, and that they're simply rotations in opposite
directions.  If so, then ang1+ang2 should equal 2*PI.  However, they sum to
PI, so it's off by 180 degrees.

Vijay

On Wed, Jan 14, 2009 at 1:53 PM, David Bateman <dbateman at dbateman.org>wrote:

> Vijay Pradeep wrote:
>
>> Below is a patch (generated from [diff -cp]) for the bug listed below:
>>
>> *** quaternion.m        2008-12-10 21:16:51.000000000 -0800
>> --- quaternion_ORIGINAL.m       2008-12-10 21:15:28.000000000 -0800
>> *************** function [a, b, c, d] = quaternion (w, x
>> *** 54,63 ****
>>          if (abs (norm (w) - 1) > 1e-12)
>>            warning ("quaternion: ||w||=%e, setting=1 for vv, theta",
>> norm(w));
>>            w = w/norm(w);
>> !           endif
>> !           if (w(4)<0)
>> !               w = -w ;
>> !           end
>>          [a, b, c, d] = quaternion (w);
>>          theta = acos (d) * 2;
>>          if (abs (theta) > pi)
>> --- 54,60 ----
>>          if (abs (norm (w) - 1) > 1e-12)
>>            warning ("quaternion: ||w||=%e, setting=1 for vv, theta",
>> norm(w));
>>            w = w/norm(w);
>> !         endif
>>          [a, b, c, d] = quaternion (w);
>>          theta = acos (d) * 2;
>>          if (abs (theta) > pi)
>>
>>
>> ---------- Forwarded message ----------
>> From: Vijay Pradeep <vpradeep at willowgarage.com>
>> Date: Wed, Dec 10, 2008 at 9:13 PM
>> Subject: Quaternion to axis/angle conversion is buggy when w(4)<0
>> To: bug at octave.org
>>
>>
>> Sorry..... the auto bug-reporting tool was having issues.  I have
>> included the bug report below.
>>
>> Subject: Quaternion to axis/angle conversion is buggy when w(4)<0
>> -----------
>> Bug report for Octave 3.0.0 configured for i486-pc-linux-gnu
>>
>> Description:
>> -----------
>> A rotation represented by a quaternion w is equivalently represented
>> by -w. However, if w(4) is negative,
>> then the conversion of this quaternion to axis angle is incorrect,
>> because of the ambiguity in acos(),
>> which is used in ./octave/3.0.0/m/quaternion/quaternion.m to compute
>> the rotation angle.
>>
>> Repeat-By:
>> ---------
>> w = quaternion([1 0 0], pi/4)
>> [ax ang]   = quaternion( w)
>> [ax2 ang2] = quaternion(-w)
>>
>> The rotations represented by [ax ang] and [ax2 ang2] are not equivalent
>>
>> Fix:
>> ---
>> in /octave/3.0.0/m/quaternion/quaternion.m
>>
>> if w(4) is negative, then negate w before operating on it.
>>
>>
> I see the following
>
> octave:1> w = quaternion([1 0 0], pi/4)
> w =
>  0.38268   0.00000    0.00000    0.92388
>
> octave:2> [ax ang]   = quaternion( w)
> ax =
>  1  0  0
>
> ang = 0.78540
> octave:3> [ax2 ang2] = quaternion(-w)
> ax =
>
>  -1  -0  -0
>
> ang = 2.3562
>
>
> so I don't see what the issue is. Yes in the second case the angle is Pi
> larger, but that is normal when the first unit vector is reverse. That is
> the transformation is different but equivalent. I therefore don't consider
> this a bug as such
>
> Regards
> David
>
> --
> David Bateman                                dbateman at dbateman.org
> 35 rue Gambetta                              +33 1 46 04 02 18 (Home)
> 92100 Boulogne-Billancourt FRANCE            +33 6 72 01 06 33 (Mob)
>
>
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