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annotate scripts/general/sph2cart.m @ 17585:36b9fa789d8e

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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{x}, @var{y}, @var{z}] =} sph2cart (@var{theta}, @var{phi}, @var{r})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} sph2cart (@var{S})
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22 ## @deftypefnx {Function File} {@var{C} =} sph2cart (@dots{})
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23 ## Transform spherical to Cartesian coordinates.
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24 ##
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25 ## @var{theta} describes the angle relative to the positive x-axis.
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26 ## @var{phi} is the angle relative to the xy-plane.
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27 ## @var{r} is the distance to the origin @w{(0, 0, 0)}.
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28 ## @var{theta}, @var{phi}, and @var{r} must be the same shape, or scalar.
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29 ## If called with a single matrix argument then each row of @var{S}
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30 ## represents the spherical coordinate (@var{theta}, @var{phi}, @var{r}).
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31 ##
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32 ## If only a single return argument is requested then return a matrix
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33 ## @var{C} where each row represents one Cartesian coordinate
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34 ## (@var{x}, @var{y}, @var{z}).
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35 ## @seealso{cart2sph, pol2cart, cart2pol}
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36 ## @end deftypefn
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37
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38 ## Author: Kai Habel <kai.habel@gmx.de>
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39 ## Adapted-by: jwe
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40
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41 function [x, y, z] = sph2cart (theta, phi, r)
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42
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43 if (nargin != 1 && nargin != 3)
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44 print_usage ();
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45 endif
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46
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47 if (nargin == 1)
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48 if (ismatrix (theta) && columns (theta) == 3)
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49 r = theta(:,3);
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50 phi = theta(:,2);
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51 theta = theta(:,1);
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52 else
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53 error ("sph2cart: matrix input must have 3 columns [THETA, PHI, R]");
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54 endif
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55 elseif (nargin == 3)
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56 if (! ((ismatrix (theta) && ismatrix (phi) && ismatrix (r))
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57 && (size_equal (theta, phi) || isscalar (theta) || isscalar (phi))
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58 && (size_equal (theta, r) || isscalar (theta) || isscalar (r))
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59 && (size_equal (phi, r) || isscalar (phi) || isscalar (r))))
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60 error ("sph2cart: THETA, PHI, and R must be matrices of the same size, or scalar");
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61 endif
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62 endif
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63
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64 x = r .* cos (phi) .* cos (theta);
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65 y = r .* cos (phi) .* sin (theta);
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66 z = r .* sin (phi);
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67
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68 if (nargout <= 1)
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69 x = [x(:), y(:), z(:)];
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70 endif
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71
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72 endfunction
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73
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74
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75 %!test
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76 %! t = [0, 0, 0];
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77 %! p = [0, 0, 0];
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78 %! r = [0, 1, 2];
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79 %! [x, y, z] = sph2cart (t, p, r);
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80 %! assert (x, r);
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81 %! assert (y, [0, 0, 0]);
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82 %! assert (z, [0, 0, 0]);
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83
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84 %!test
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85 %! t = 0;
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86 %! p = [0, 0, 0];
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87 %! r = [0, 1, 2];
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88 %! C = sph2cart (t, p, r);
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89 %! assert (C(:,1), r(:));
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90 %! assert (C(:,2), [0; 0; 0]);
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91 %! assert (C(:,3), [0; 0; 0]);
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92
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93 %!test
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94 %! t = [0, 0, 0];
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95 %! p = 0;
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96 %! r = [0, 1, 2];
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97 %! [x, y, z] = sph2cart (t, p, r);
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98 %! assert (x, r);
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99 %! assert (y, [0, 0, 0]);
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100 %! assert (z, [0, 0, 0]);
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101
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102 %!test
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103 %! t = [0, 0.5, 1]*pi;
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104 %! p = [0, 0, 0];
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105 %! r = 1;
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106 %! [x, y, z] = sph2cart (t, p, r);
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107 %! assert (x, [1, 0, -1], eps);
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108 %! assert (y, [0, 1, 0], eps);
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109 %! assert (z, [0, 0, 0], eps);
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110
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111 %!test
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112 %! S = [ 0, 0, 1; 0.5*pi, 0, 1; pi, 0, 1];
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113 %! C = [ 1, 0, 0; 0, 1, 0; -1, 0, 0];
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114 %! assert (sph2cart (S), C, eps);
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115