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scripts/general/cart2sph.m

changeset 10289: 4b124317dc38
parent:eb63fbe60fab
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (50 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2009 Kai Habel

     2##

     3## This file is part of Octave.

     4##

     5## Octave is free software; you can redistribute it and/or modify it

     6## under the terms of the GNU General Public License as published by

     7## the Free Software Foundation; either version 3 of the License, or (at

     8## your option) any later version.

     9##

    10## Octave is distributed in the hope that it will be useful, but

    11## WITHOUT ANY WARRANTY; without even the implied warranty of

    12## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    13## General Public License for more details.

    14##

    15## You should have received a copy of the GNU General Public License

    16## along with Octave; see the file COPYING.  If not, see

    17## <http://www.gnu.org/licenses/>.

    18

    19## -*- texinfo -*-

    20## @deftypefn {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})

    21## Transform Cartesian to spherical coordinates.

    22## @var{x}, @var{y} and @var{z} must be the same shape, or scalar.

    23## @var{theta} describes the angle relative to the positive x-axis.

    24## @var{phi} is the angle relative to the xy-plane.

    25## @var{r} is the distance to the origin (0, 0, 0).

    26## @seealso{pol2cart, cart2pol, sph2cart}

    27## @end deftypefn

    28

    29## Author: Kai Habel <kai.habel@gmx.de>

    30## Adapted-by: jwe

    31

    32function [theta, phi, r] = cart2sph (x, y, z)

    33

    34  if (nargin != 3)

    35    print_usage ();

    36  endif

    37

    38  if ((ismatrix (x) && ismatrix (y) && ismatrix (z))

    39      && (size_equal (x, y) || isscalar (x) || isscalar (y))

    40      && (size_equal (x, z) || isscalar (x) || isscalar (z))

    41      && (size_equal (y, z) || isscalar (y) || isscalar (z)))

    42

    43    theta = atan2 (y, x);

    44    phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));

    45    r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);

    46

    47  else

    48    error ("cart2sph: arguments must be matrices of same size, or scalar");

    49  endif

    50

    51endfunction

    52

    53%!test

    54%! x = [0, 1, 2];

    55%! y = [0, 1, 2];

    56%! z = [0, 1, 2];

    57%! [t, p, r] = cart2sph (x, y, z);

    58%! assert (t, [0, pi/4, pi/4], eps);

    59%! assert (p, [0, 1, 1]*atan(sqrt(0.5)), eps);

    60%! assert (r, [0, 1, 2]*sqrt(3), eps);

    61

    62%!test

    63%! x = 0;

    64%! y = [0, 1, 2];

    65%! z = [0, 1, 2];

    66%! [t, p, r] = cart2sph (x, y, z);

    67%! assert (t, [0, 1, 1] * pi/2, eps);

    68%! assert (p, [0, 1, 1] * pi/4, eps);

    69%! assert (r, [0, 1, 2] * sqrt(2), eps);

    70

    71%!test

    72%! x = [0, 1, 2];

    73%! y = 0;

    74%! z = [0, 1, 2];

    75%! [t, p, r] = cart2sph (x, y, z);

    76%! assert (t, [0, 0, 0]);

    77%! assert (p, [0, 1, 1] * pi/4);

    78%! assert (r, [0, 1, 2] * sqrt(2));

    79

    80%!test

    81%! x = [0, 1, 2];

    82%! y = [0, 1, 2];

    83%! z = 0;

    84%! [t, p, r] = cart2sph (x, y, z);

    85%! assert (t, [0, 1, 1] * pi/4);

    86%! assert (p, [0, 0, 0]);

    87%! assert (r, [0, 1, 2] * sqrt(2));

    88