annotate scripts/general/cart2pol.m @ 17585:36b9fa789d8e

Overhaul polar, spherical, cartesian conversion routiens when nargout == 1. * scripts/general/cart2pol.m: Use @var{P} (capital) in docstring. Initialize z to []. Return 3-column matrix when nargout == 1. Modify %!test to check this behavior. * scripts/general/cart2sph.m: Use @var{C} (capital) in docstring. Return 3-column matrix when nargout == 1. Modify %!test to check this behavior. scripts/general/pol2cart.m: Use @var{P} (capital) in docstring. Use 'C' in %!test to refer to single Cartesian matrix of coordinates. scripts/general/sph2cart.m: Use @var{C} (capital) in docstring. Return 3-column matrix when nargout == 1. Modify %!test to check this behavior.
author Rik <rik@octave.org>
date Sun, 06 Oct 2013 21:01:10 -0700
parents f3d52523cde1
children d63878346099
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1 ## Copyright (C) 2000-2012 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 ## @deftypefnx {Function File} {[@var{theta}, @var{r}] =} cart2pol (@var{C})
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23 ## @deftypefnx {Function File} {[@var{theta}, @var{r}, @var{z}] =} cart2pol (@var{C})
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24 ## @deftypefnx {Function File} {@var{P} =} cart2pol (@dots{})
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25 ##
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26 ## Transform Cartesian to polar or cylindrical coordinates.
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27 ##
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28 ## @var{theta} describes the angle relative to the positive x-axis.
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29 ## @var{r} is the distance to the z-axis @w{(0, 0, z)}.
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30 ## @var{x}, @var{y} (, and @var{z}) must be the same shape, or scalar.
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31 ## If called with a single matrix argument then each row of @var{C}
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32 ## represents the Cartesian coordinate (@var{x}, @var{y} (, @var{z})).
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33 ##
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34 ## If only a single return argument is requested then return a matrix
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35 ## @var{P} where each row represents one polar/(cylindrical) coordinate
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36 ## (@var{theta}, @var{phi} (, @var{z})).
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37 ## @seealso{pol2cart, cart2sph, sph2cart}
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38 ## @end deftypefn
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39
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40 ## Author: Kai Habel <kai.habel@gmx.de>
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41 ## Adapted-by: jwe
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42
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43 function [theta, r, z] = cart2pol (x, y, z = [])
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44
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45 if (nargin < 1 || nargin > 3)
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46 print_usage ();
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47 endif
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48
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49 if (nargin == 1)
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50 if (ismatrix (x) && (columns (x) == 2 || columns (x) == 3))
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51 if (columns (x) == 3)
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52 z = x(:,3);
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53 endif
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54 y = x(:,2);
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55 x = x(:,1);
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56 else
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57 error ("cart2pol: matrix input must have 2 or 3 columns [X, Y (, Z)]");
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58 endif
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59 elseif (nargin == 2)
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60 if (! ((ismatrix (x) && ismatrix (y))
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61 && (size_equal (x, y) || isscalar (x) || isscalar (y))))
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62 error ("cart2pol: arguments must be matrices of same size, or scalar");
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63 endif
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64 elseif (nargin == 3)
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65 if (! ((ismatrix (x) && ismatrix (y) && ismatrix (z))
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66 && (size_equal (x, y) || isscalar (x) || isscalar (y))
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67 && (size_equal (x, z) || isscalar (x) || isscalar (z))
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68 && (size_equal (y, z) || isscalar (y) || isscalar (z))))
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69 error ("cart2pol: arguments must be matrices of same size, or scalar");
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70 endif
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71 endif
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72
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73 theta = atan2 (y, x);
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74 r = sqrt (x .^ 2 + y .^ 2);
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75
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76 if (nargout <= 1)
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77 theta = [theta(:), r(:), z(:)];
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78 endif
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79
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80 endfunction
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81
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82
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83 %!test
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84 %! x = [0, 1, 2];
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85 %! y = 0;
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86 %! [t, r] = cart2pol (x, y);
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87 %! assert (t, [0, 0, 0]);
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88 %! assert (r, x);
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89
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90 %!test
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91 %! x = [0, 1, 2];
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92 %! y = [0, 1, 2];
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93 %! P = cart2pol (x, y);
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94 %! assert (P(:,1), [0; pi/4; pi/4], sqrt (eps));
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95 %! assert (P(:,2), sqrt (2)*[0; 1; 2], sqrt (eps));
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96
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97 %!test
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98 %! x = [0, 1, 2];
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99 %! y = [0, 1, 2];
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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, pi/4, pi/4], sqrt (eps));
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103 %! assert (r, sqrt (2)*[0, 1, 2], sqrt (eps));
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104 %! assert (z, z2);
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106 %!test
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107 %! x = [0, 1, 2];
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108 %! y = 0;
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109 %! z = 0;
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110 %! [t, r, z2] = cart2pol (x, y, z);
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111 %! assert (t, [0, 0, 0], eps);
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112 %! assert (r, x, eps);
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113 %! assert (z, z2);
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114
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115 %!test
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116 %! x = 0;
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117 %! y = [0, 1, 2];
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118 %! z = 0;
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119 %! [t, r, z2] = cart2pol (x, y, z);
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120 %! assert (t, [0, 1, 1]*pi/2, eps);
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121 %! assert (r, y, eps);
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122 %! assert (z, z2);
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123
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124 %!test
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125 %! x = 0;
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126 %! y = 0;
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127 %! z = [0, 1, 2];
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128 %! [t, r, z2] = cart2pol (x, y, z);
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129 %! assert (t, 0);
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130 %! assert (r, 0);
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131 %! assert (z, z2);
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132
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Rik <octave@nomad.inbox5.com>
parents: 10687
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133 %!test
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Rik <octave@nomad.inbox5.com>
parents: 10687
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134 %! C = [0, 0; 1, 1; 2, 2];
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Rik <octave@nomad.inbox5.com>
parents: 10687
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135 %! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)];
14363
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parents: 14138
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136 %! assert (cart2pol (C), P, sqrt (eps));
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parents: 10687
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137
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Rik <octave@nomad.inbox5.com>
parents: 10687
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138 %!test
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 10687
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139 %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2];
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Rik <octave@nomad.inbox5.com>
parents: 10687
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140 %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2];
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Rik <octave@nomad.inbox5.com>
parents: 14138
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141 %! assert (cart2pol (C), P, sqrt (eps));
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parents: 10687
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142