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annotate scripts/general/cart2sph.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{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
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21 ## @deftypefnx {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{C})
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22 ## @deftypefnx {Function File} {@var{S} =} cart2sph (@dots{})
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23 ## Transform Cartesian to spherical 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{x}, @var{y}, and @var{z} must be the same shape, or scalar.
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29 ## If called with a single matrix argument then each row of @var{C}
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30 ## represents the Cartesian coordinate (@var{x}, @var{y}, @var{z}).
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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{S} where each row represents one spherical coordinate
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34 ## (@var{theta}, @var{phi}, @var{r}).
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35 ## @seealso{sph2cart, cart2pol, pol2cart}
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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 [theta, phi, r] = cart2sph (x, y, z)
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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 (x) && columns (x) == 3)
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49 z = x(:,3);
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50 y = x(:,2);
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51 x = x(:,1);
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52 else
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53 error ("cart2sph: matrix input must have 3 columns [X, Y, Z]");
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54 endif
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55 elseif (nargin == 3)
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56 if (! ((ismatrix (x) && ismatrix (y) && ismatrix (z))
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57 && (size_equal (x, y) || isscalar (x) || isscalar (y))
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58 && (size_equal (x, z) || isscalar (x) || isscalar (z))
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59 && (size_equal (y, z) || isscalar (y) || isscalar (z))))
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60 error ("cart2sph: X, Y, Z 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 theta = atan2 (y, x);
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65 phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
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66 r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
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67
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68 if (nargout <= 1)
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69 theta = [theta(:), phi(:), r(:)];
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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 %! x = [0, 1, 2];
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77 %! y = [0, 1, 2];
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78 %! z = [0, 1, 2];
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79 %! [t, p, r] = cart2sph (x, y, z);
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80 %! assert (t, [0, pi/4, pi/4], eps);
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81 %! assert (p, [0, 1, 1]*atan (sqrt (0.5)), eps);
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82 %! assert (r, [0, 1, 2]*sqrt (3), eps);
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83
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84 %!test
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85 %! x = 0;
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86 %! y = [0, 1, 2];
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87 %! z = [0, 1, 2];
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88 %! S = cart2sph (x, y, z);
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89 %! assert (S(:,1), [0; 1; 1] * pi/2, eps);
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90 %! assert (S(:,2), [0; 1; 1] * pi/4, eps);
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91 %! assert (S(:,3), [0; 1; 2] * sqrt (2), eps);
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92
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93 %!test
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94 %! x = [0, 1, 2];
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95 %! y = 0;
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96 %! z = [0, 1, 2];
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97 %! [t, p, r] = cart2sph (x, y, z);
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98 %! assert (t, [0, 0, 0]);
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99 %! assert (p, [0, 1, 1] * pi/4);
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100 %! assert (r, [0, 1, 2] * sqrt (2));
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101
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102 %!test
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103 %! x = [0, 1, 2];
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104 %! y = [0, 1, 2];
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105 %! z = 0;
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106 %! [t, p, r] = cart2sph (x, y, z);
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107 %! assert (t, [0, 1, 1] * pi/4);
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108 %! assert (p, [0, 0, 0]);
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109 %! assert (r, [0, 1, 2] * sqrt (2));
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110
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111 %!test
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112 %! C = [0, 0, 0; 1, 0, 1; 2, 0, 2];
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113 %! S = [0, 0, 0; 0, pi/4, sqrt(2); 0, pi/4, 2*sqrt(2)];
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114 %! assert (cart2sph (C), S, eps);
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115