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

[David Bateman]

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

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David Bateman                                dbateman at dbateman.org
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