annotate scripts/general/pol2cart.m @ 14570:d07d96e53612 stable

seconds after the minute can be 0-60, not 0-61 * system.txi (Timing Utilities): Correct possible values for number of seconds in time structures. From Rafael Arndt <rafaelarndt@gmail.com>.
author John W. Eaton <jwe@octave.org>
date Tue, 17 Apr 2012 14:42:49 -0400
parents 72c96de7a403
children f3d52523cde1
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72c96de7a403 maint: update copyright notices for 2012
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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}] =} pol2cart (@var{theta}, @var{r})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{theta}, @var{r}, @var{z})
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22 ## @deftypefnx {Function File} {[@var{x}, @var{y}] =} pol2cart (@var{p})
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23 ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} pol2cart (@var{p})
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24 ## @deftypefnx {Function File} {@var{C} =} pol2cart (@dots{})
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25 ## Transform polar or cylindrical to Cartesian coordinates.
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26 ##
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27 ## @var{theta}, @var{r}, (and @var{z}) must be the same shape, or scalar.
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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 (0, 0, z).
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30 ## If called with a single matrix argument then each row of @var{p}
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31 ## represents the polar/(cylindrical) coordinate (@var{x}, @var{y} (, @var{z})).
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32 ##
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33 ## If only a single return argument is requested then return a matrix
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34 ## @var{C} where each row represents one Cartesian coordinate
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35 ## (@var{x}, @var{y} (, @var{z})).
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36 ## @seealso{cart2pol, sph2cart, cart2sph}
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37 ## @end deftypefn
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38
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39 ## Author: Kai Habel <kai.habel@gmx.de>
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40 ## Adapted-by: jwe
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41
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42 function [x, y, z] = pol2cart (theta, r, z)
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43
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44 if (nargin < 1 || nargin > 3)
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45 print_usage ();
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46 endif
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47
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48 if (nargin == 1)
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49 if (ismatrix (theta) && (columns (theta) == 2 || columns (theta) == 3))
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50 if (columns (theta) == 3)
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51 z = theta(:,3);
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52 else
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53 z = [];
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54 endif
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55 r = theta(:,2);
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56 theta = theta(:,1);
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57 else
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58 error ("pol2car: matrix input must have 2 or 3 columns [THETA, R (, Z)]");
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59 endif
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60 elseif (nargin == 2)
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61 if (! ((ismatrix (theta) && ismatrix (r))
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62 && (size_equal (theta, r) || isscalar (theta) || isscalar (r))))
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63 error ("pol2cart: arguments must be matrices of same size, or scalar");
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64 endif
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65 elseif (nargin == 3)
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66 if (! ((ismatrix (theta) && ismatrix (r) && ismatrix (z))
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67 && (size_equal (theta, r) || isscalar (theta) || isscalar (r))
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68 && (size_equal (theta, z) || isscalar (theta) || isscalar (z))
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69 && (size_equal (r, z) || isscalar (r) || isscalar (z))))
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70 error ("pol2cart: arguments must be matrices of same size, or scalar");
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71 endif
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72 endif
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73
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74 x = r .* cos (theta);
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75 y = r .* sin (theta);
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76
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77 if (nargout <= 1)
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78 x = [x, y, z];
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79 endif
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80
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81 endfunction
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82
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83 %!test
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84 %! t = [0, 0.5, 1] * pi;
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85 %! r = 1;
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86 %! [x, y] = pol2cart (t, r);
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87 %! assert (x, [1, 0, -1], sqrt(eps));
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88 %! assert (y, [0, 1, 0], sqrt(eps));
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89
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90 %!test
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91 %! t = [0, 1, 1] * pi/4;
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92 %! r = sqrt(2) * [0, 1, 2];
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93 %! [x, y] = pol2cart (t, r);
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94 %! assert (x, [0, 1, 2], sqrt(eps));
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95 %! assert (y, [0, 1, 2], sqrt(eps));
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96
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97 %!test
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98 %! t = [0, 1, 1] * pi/4;
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99 %! r = sqrt(2) * [0, 1, 2];
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100 %! z = [0, 1, 2];
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101 %! [x, y, z2] = pol2cart (t, r, z);
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102 %! assert (x, [0, 1, 2], sqrt(eps));
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103 %! assert (y, [0, 1, 2], sqrt(eps));
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104 %! assert (z, z2);
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106 %!test
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107 %! t = 0;
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108 %! r = [0, 1, 2];
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109 %! z = [0, 1, 2];
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110 %! [x, y, z2] = pol2cart (t, r, z);
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111 %! assert (x, [0, 1, 2], sqrt(eps));
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112 %! assert (y, [0, 0, 0], sqrt(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 %! t = [1, 1, 1]*pi/4;
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117 %! r = 1;
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118 %! z = [0, 1, 2];
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119 %! [x, y, z2] = pol2cart (t, r, z);
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120 %! assert (x, [1, 1, 1] / sqrt(2), eps);
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121 %! assert (y, [1, 1, 1] / sqrt(2), 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 %! t = 0;
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126 %! r = [1, 2, 3];
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127 %! z = 1;
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128 %! [x, y, z2] = pol2cart (t, r, z);
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129 %! assert (x, [1, 2, 3], eps);
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130 %! assert (y, [0, 0, 0] / sqrt(2), eps);
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131 %! assert (z, z2);
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132
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133 %!test
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134 %! P = [0, 0; pi/4, sqrt(2); pi/4, 2*sqrt(2)];
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135 %! C = [0, 0; 1, 1; 2, 2];
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
136 %! assert (pol2cart(P), C, sqrt(eps));
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
137
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
138 %!test
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
139 %! P = [0, 0, 0; pi/4, sqrt(2), 1; pi/4, 2*sqrt(2), 2];
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
140 %! C = [0, 0, 0; 1, 1, 1; 2, 2, 2];
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
141 %! assert (pol2cart(P), C, sqrt(eps));
7357e37f34fa coordinate transforms: add option to operate on column matrix of coordinates.
Rik <octave@nomad.inbox5.com>
parents: 9168
diff changeset
142