/usr/share/octave/packages/quaternion-2.2.2/q2rot.m is in octave-quaternion 2.2.2-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | ## Copyright (C) 1998, 1999, 2000, 2002, 2005, 2006, 2007 Auburn University
## Copyright (C) 2010-2014 Lukas F. Reichlin
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q})
## Extract vector/angle form of a unit quaternion @var{q}.
##
## @strong{Inputs}
## @table @var
## @item q
## Unit quaternion describing the rotation.
## @end table
##
## @strong{Outputs}
## @table @var
## @item axis
## Eigenaxis as a 3-d unit vector @code{[x, y, z]}.
## @item angle
## Rotation angle in radians. The positive direction is
## determined by the right-hand rule applied to @var{axis}.
## The angle lies in the interval [0, 2*pi].
## @end table
##
## @strong{Example}
## @example
## @group
## octave:1> axis = [0, 0, 1]
## axis =
## 0 0 1
## octave:2> angle = pi/4
## angle = 0.78540
## octave:3> q = rot2q (axis, angle)
## q = 0.9239 + 0i + 0j + 0.3827k
## octave:4> [vv, th] = q2rot (q)
## vv =
## 0 0 1
## th = 0.78540
## octave:5> theta = th*180/pi
## theta = 45.000
## octave:6>
## @end group
## @end example
##
## @end deftypefn
## Adapted from: quaternion by A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: May 2010
## Version: 0.3
function [vv, theta] = q2rot (q)
if (nargin != 1 || nargout != 2)
print_usage ();
endif
if (! isa (q, "quaternion") || ! isscalar (q.w))
error ("q2rot: require scalar quaternion as input");
endif
if (abs (norm (q) - 1) > 1e-12)
warning ("q2rot: ||q||=%e, setting=1 for vv, theta", norm (q));
q = unit (q); # do we still need this with the atan2 formula?
endif
s = q.w;
vv = [q.x, q.y, q.z];
norm_vv = norm (vv);
## According to Wikipedia,
## http://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation#Unit_Quaternions
## the formula using atan2 should be numerically more stable than
## theta = acos (s) * 2;
## Possibly it helps if the quaternion has not exactly unit length.
theta = 2 * atan2 (norm_vv, s);
## if (abs (theta) > pi)
## theta = theta - sign (theta) * 2 * pi;
## endif
## NOTE: sin (theta/2) = norm (vv)
if (norm_vv != 0)
vv ./= norm_vv;
endif
endfunction
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