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Update section 17.7 (Coordinate Transformations) of arith.txi
author Rik <rdrider0-list@yahoo.com>
date Sat, 02 May 2009 07:20:35 -0700
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children a8ce6bdecce5
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eb63fbe60fab update copyright notices
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{r}] =} cart2pol (@var{x}, @var{y})
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21 ## @deftypefnx {Function File} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{x}, @var{y}, @var{z})
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22 ## Transform Cartesian to polar or cylindrical coordinates.
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23 ## @var{x}, @var{y} (and @var{z}) must be the same shape, or scalar.
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24 ## @var{theta} describes the angle relative to the positive x-axis.
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25 ## @var{r} is the distance to the z-axis (0, 0, z).
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26 ## @seealso{pol2cart, cart2sph, 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, r, z] = cart2pol (x, y, z)
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33
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34 if (nargin < 2 || nargin > 3)
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35 error ("cart2pol: number of arguments must be 2 or 3");
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36 endif
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37
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38 if (nargin == 2 && nargout > 2)
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39 error ("cart2pol: number of output arguments must not be greater than number of input arguments");
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40 endif
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41
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42 if ((ismatrix (x) && ismatrix (y) && (nargin == 2 || ismatrix (z)))
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43 && (size_equal (x, y) || isscalar (x) || isscalar (y))
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44 && (nargin == 2 || size_equal (x, z) || isscalar (x) || isscalar (z))
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45 && (nargin == 2 || size_equal (y, z) || isscalar (y) || isscalar (z)))
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46
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47 theta = atan2 (y, x);
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48 r = sqrt (x .^ 2 + y .^ 2);
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49
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50 else
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51 error ("cart2pol: arguments must be matrices of same size, or scalar");
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52 endif
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53
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54 endfunction
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55
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56 %!test
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57 %! x = [0, 1, 2];
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58 %! y = 0;
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59 %! [t, r] = cart2pol (x, y);
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60 %! assert (t, [0, 0, 0]);
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61 %! assert (r, x);
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62
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63 %!test
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64 %! x = [0, 1, 2];
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65 %! y = [0, 1, 2];
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66 %! [t, r] = cart2pol (x, y);
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67 %! assert (t, [0, pi/4, pi/4], sqrt(eps));
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68 %! assert (r, sqrt(2)*[0, 1, 2], sqrt(eps));
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70 %!test
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71 %! x = [0, 1, 2];
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72 %! y = [0, 1, 2];
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73 %! z = [0, 1, 2];
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74 %! [t, r, z2] = cart2pol (x, y, z);
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75 %! assert (t, [0, pi/4, pi/4], sqrt(eps));
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76 %! assert (r, sqrt(2)*[0, 1, 2], sqrt(eps));
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77 %! assert (z, z2);
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78
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79 %!test
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80 %! x = [0, 1, 2];
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81 %! y = 0;
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82 %! z = 0;
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83 %! [t, r, z2] = cart2pol (x, y, z);
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84 %! assert (t, [0, 0, 0], eps);
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85 %! assert (r, x, eps);
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86 %! assert (z, z2);
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87
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88 %!test
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89 %! x = 0;
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90 %! y = [0, 1, 2];
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91 %! z = 0;
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92 %! [t, r, z2] = cart2pol (x, y, z);
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93 %! assert (t, [0, 1, 1]*pi/2, eps);
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94 %! assert (r, y, eps);
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95 %! assert (z, z2);
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96
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97 %!test
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98 %! x = 0;
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99 %! y = 0;
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100 %! z = [0, 1, 2];
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101 %! [t, r, z2] = cart2pol (x, y, z);
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102 %! assert (t, 0);
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103 %! assert (r, 0);
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104 %! assert (z, z2);
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105