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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
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27919
1891570abac8 update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2000-2020 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{theta}, @var{phi}, @var{r})
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25 ## @deftypefnx {} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{S})
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26 ## @deftypefnx {} {@var{C} =} sph2cart (@dots{})
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27 ## Transform spherical coordinates to Cartesian coordinates.
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28 ##
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29 ## The inputs @var{theta}, @var{phi}, and @var{r} must be the same shape, or
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30 ## scalar. If called with a single matrix argument then each row of @var{S}
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31 ## represents the spherical coordinate (@var{theta}, @var{phi}, @var{r}).
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32 ##
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33 ## @var{theta} describes the angle relative to the positive x-axis.
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34 ##
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35 ## @var{phi} is the angle relative to the xy-plane.
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36 ##
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37 ## @var{r} is the distance to the origin @w{(0, 0, 0)}.
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38 ##
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39 ## If only a single return argument is requested then return a matrix @var{C}
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40 ## where each row represents one Cartesian coordinate
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41 ## (@var{x}, @var{y}, @var{z}).
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42 ## @seealso{cart2sph, pol2cart, cart2pol}
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43 ## @end deftypefn
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44
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45 ## Author: Kai Habel <kai.habel@gmx.de>
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46
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47 function [x, y, z] = sph2cart (theta, phi, r)
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48
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49 if (nargin != 1 && nargin != 3)
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50 print_usage ();
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51 endif
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52
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53 if (nargin == 1)
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54 if (! (isnumeric (theta) && ismatrix (theta) && columns (theta) == 3))
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55 error ("sph2cart: matrix input must have 3 columns [THETA, PHI, R]");
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56 endif
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57 r = theta(:,3);
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58 phi = theta(:,2);
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59 theta = theta(:,1);
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60 else
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61 if (! isnumeric (theta) || ! isnumeric (phi) || ! isnumeric (r))
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62 error ("sph2cart: THETA, PHI, R must be numeric arrays of the same size, or scalar");
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63 endif
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64 [err, theta, phi, r] = common_size (theta, phi, r);
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65 if (err)
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66 error ("sph2cart: THETA, PHI, R must be numeric arrays of the same size, or scalar");
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67 endif
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68 endif
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69
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70 x = r .* cos (phi) .* cos (theta);
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71 y = r .* cos (phi) .* sin (theta);
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72 z = r .* sin (phi);
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73
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74 if (nargout <= 1)
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75 x = [x(:), y(:), z(:)];
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76 endif
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77
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78 endfunction
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79
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80
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81 %!test
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82 %! t = [0, 0, 0];
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83 %! p = [0, 0, 0];
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84 %! r = [0, 1, 2];
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85 %! [x, y, z] = sph2cart (t, p, r);
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86 %! assert (x, r);
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87 %! assert (y, [0, 0, 0]);
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88 %! assert (z, [0, 0, 0]);
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89
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90 %!test
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91 %! t = 0;
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92 %! p = [0, 0, 0];
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93 %! r = [0, 1, 2];
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94 %! C = sph2cart (t, p, r);
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95 %! assert (C(:,1), r(:));
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96 %! assert (C(:,2), [0; 0; 0]);
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97 %! assert (C(:,3), [0; 0; 0]);
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98
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99 %!test
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100 %! t = [0, 0, 0];
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101 %! p = 0;
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102 %! r = [0, 1, 2];
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103 %! [x, y, z] = sph2cart (t, p, r);
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104 %! assert (x, r);
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105 %! assert (y, [0, 0, 0]);
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106 %! assert (z, [0, 0, 0]);
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107
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108 %!test
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109 %! t = [0, 0.5, 1]*pi;
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110 %! p = [0, 0, 0];
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111 %! r = 1;
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112 %! [x, y, z] = sph2cart (t, p, r);
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113 %! assert (x, [1, 0, -1], eps);
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114 %! assert (y, [0, 1, 0], eps);
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115 %! assert (z, [0, 0, 0], eps);
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116
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117 %!test
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118 %! [x, y, z] = sph2cart ([0 0 0], 0, 1);
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119 %! assert (x, [1, 1, 1], eps);
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120 %! assert (y, [0, 0, 0], eps);
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121 %! assert (z, [0, 0, 0], eps);
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122
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123 %!test
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124 %! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1];
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125 %! C = [ 1, 0, 0; 0, 1, 0; -1, 0, 0];
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126 %! assert (sph2cart (S), C, eps);
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127
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128 %!test
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129 %! [t, p, r] = meshgrid ([0, pi/2], [0, pi/2], [0, 1]);
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130 %! [x, y, z] = sph2cart (t, p, r);
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131 %! X = zeros(2, 2, 2);
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132 %! X(1, 1, 2) = 1;
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133 %! Y = zeros(2, 2, 2);
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134 %! Y(1, 2, 2) = 1;
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135 %! Z = zeros(2, 2, 2);
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136 %! Z(2, :, 2) = [1 1];
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137 %! assert (x, X, eps);
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138 %! assert (y, Y, eps);
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139 %! assert (z, Z);
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140
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141 ## Test input validation
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142 %!error sph2cart ()
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143 %!error sph2cart (1,2)
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144 %!error sph2cart (1,2,3,4)
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145 %!error <matrix input must have 3 columns> sph2cart ({1,2,3})
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146 %!error <matrix input must have 3 columns> sph2cart (ones (3,3,2))
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147 %!error <matrix input must have 3 columns> sph2cart ([1,2,3,4])
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148 %!error <numeric arrays of the same size> sph2cart ({1,2,3}, [1,2,3], [1,2,3])
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149 %!error <numeric arrays of the same size> sph2cart ([1,2,3], {1,2,3}, [1,2,3])
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150 %!error <numeric arrays of the same size> sph2cart ([1,2,3], [1,2,3], {1,2,3})
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151 %!error <numeric arrays of the same size> sph2cart (ones (3,3,3), 1, ones (3,2,3))
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152 %!error <numeric arrays of the same size> sph2cart (ones (3,3,3), ones (3,2,3), 1)