qtransv.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 1998 Auburn University.  All rights reserved.
##
## This file is part of Octave.
##
## Octave 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 2, or (at your option)
## any later version.
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## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
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## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} qtransv (@var{v}, @var{q})
## Transform the 3-D vector @var{v} by the unit quaternion @var{q}.
## Return a column vector.
##
## @example
## vi = (2*real(q)^2 - 1)*vb + 2*imag(q)*(imag(q)'*vb) 
##    + 2*real(q)*cross(imag(q),vb)
## @end example
##
## @noindent
## Where imag(q) is a column vector of length 3.
## @end deftypefn

## Author: A. S. Hodel <[e-mail]>
## Adapted-By: jwe

function vi = qtransv (vb, qib)

  if (! isvector (vb) || length (vb) != 3)
    error ("qtransv: v(%d,%d) must be a 3-D vector", rows (vb), columns (vb));
  elseif (! isvector (qib) || length (qib) != 4)
    error ("qtransv: q(%d,%d) must be a quaternion", rows (qib), columns (qib));
  elseif (max (abs (imag (vb))) + max (abs (imag (qib))) != 0)
    error ("qtransv: input values must be real");
  endif

  qr = qib(4);
  qimag = vec (qib(1:3));
  vb = vec (vb);
  vi = (2*qr^2 - 1)*vb + 2*qimag*(qimag'*vb) + 2*qr*cross (qimag, vb);

endfunction