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update copyright notices
author John W. Eaton <jwe@octave.org>
date Sat, 07 Mar 2009 10:41:27 -0500
parents fb1b87ea4af9
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2009 Kai Habel
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
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21 ## Transform cartesian to spherical coordinates.
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22 ## @var{x}, @var{y} and @var{z} must be of same shape, or scalar.
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23 ## @var{theta} describes the angle relative to the x-axis.
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24 ## @var{phi} is the angle relative to the xy-plane.
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25 ## @var{r} is the distance to the origin (0, 0, 0).
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26 ## @seealso{pol2cart, cart2pol, sph2cart}
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27 ## @end deftypefn
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28
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29 ## Author: Kai Habel <kai.habel@gmx.de>
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30 ## Adapted-by: jwe
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31
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32 function [theta, phi, r] = cart2sph (x, y, z)
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33
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34 if (nargin != 3)
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35 print_usage ();
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36 endif
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37
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38 if ((ismatrix (x) && ismatrix (y) && ismatrix (z))
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39 && (size_equal (x, y) || isscalar (x) || isscalar (y))
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40 && (size_equal (x, z) || isscalar (x) || isscalar (z))
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41 && (size_equal (y, z) || isscalar (y) || isscalar (z)))
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42
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43 theta = atan2 (y, x);
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44 phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
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45 r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
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46
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47 else
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48 error ("cart2sph: arguments must be matrices of same size, or scalar");
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49 endif
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50
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51 endfunction
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52
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53 %!test
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54 %! x = [0, 1, 2];
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55 %! y = [0, 1, 2];
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56 %! z = [0, 1, 2];
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57 %! [t, p, r] = cart2sph (x, y, z);
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58 %! assert (t, [0, pi/4, pi/4], eps);
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59 %! assert (p, [0, 1, 1]*atan(sqrt(0.5)), eps);
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60 %! assert (r, [0, 1, 2]*sqrt(3), eps);
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61
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62 %!test
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63 %! x = 0;
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64 %! y = [0, 1, 2];
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65 %! z = [0, 1, 2];
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66 %! [t, p, r] = cart2sph (x, y, z);
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67 %! assert (t, [0, 1, 1] * pi/2, eps);
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68 %! assert (p, [0, 1, 1] * pi/4, eps);
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69 %! assert (r, [0, 1, 2] * sqrt(2), eps);
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71 %!test
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72 %! x = [0, 1, 2];
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73 %! y = 0;
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74 %! z = [0, 1, 2];
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75 %! [t, p, r] = cart2sph (x, y, z);
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76 %! assert (t, [0, 0, 0]);
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77 %! assert (p, [0, 1, 1] * pi/4);
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78 %! assert (r, [0, 1, 2] * sqrt(2));
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79
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80 %!test
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81 %! x = [0, 1, 2];
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82 %! y = [0, 1, 2];
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83 %! z = 0;
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84 %! [t, p, r] = cart2sph (x, y, z);
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85 %! assert (t, [0, 1, 1] * pi/4);
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86 %! assert (p, [0, 0, 0]);
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87 %! assert (r, [0, 1, 2] * sqrt(2));
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88