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annotate scripts/geometry/rotx.m @ 27801:1d04f049a859

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doc: spellcheck documentation ahead of 6.1 release. * aspell-octave.en.pws: Add new Octave-specific words to dictionary. * rotx.m, roty.m, rotz.m, print.m: Fix typos. * legend.m, colorbar.m: Add @nospell macro around "loc".
author Rik <rik@octave.org>
date Tue, 10 Dec 2019 17:55:29 -0800
parents 45ad2127582b
children b442ec6dda5c
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27274
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1 ## Copyright (C) 2019 Nicholas R. Jankowski
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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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {@var{T} =} rotx (@var{angle})
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21 ##
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22 ## @code{rotx} returns the 3x3 transformation matrix corresponding to an active
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23 ## rotation of the vector about the x-axis by the specified @var{angle}, given
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24 ## in degrees, where a positive angle corresponds to a counterclockwise
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25 ## rotation when viewing the y-z plane from the positive x side.
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26 ##
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27 ## The form of the transformation matrix is:
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28 ## @tex
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29 ## $$
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30 ## T = \left[\matrix{ 1 & 0 & 0 \cr
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31 ## 0 & \cos(angle) & -\sin(angle)\cr
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32 ## 0 & \sin(angle) & \cos(angle)}\right].
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33 ## $$
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34 ## @end tex
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35 ## @ifnottex
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36 ##
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37 ## @example
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38 ## @group
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39 ## | 1 0 0 |
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40 ## T = | 0 cos(@var{angle}) -sin(@var{angle}) |
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41 ## | 0 sin(@var{angle}) cos(@var{angle}) |
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42 ## @end group
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43 ## @end example
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44 ## @end ifnottex
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45 ##
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46 ## This rotation matrix is intended to be used as a left-multiplying matrix
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47 ## when acting on a column vector, using the notation @var{v} = @var{T}@var{u}.
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48 ## For example, a vector, @var{u}, pointing along the positive y-axis, rotated
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49 ## 90-degrees about the x-axis, will result in a vector pointing along the
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50 ## positive z-axis:
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51 ##
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52 ## @example
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53 ## @group
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54 ## >> u = [0 1 0]'
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55 ## u =
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56 ## 0
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57 ## 1
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58 ## 0
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59 ##
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60 ## >> T = rotx (90)
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61 ## T =
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62 ## 1.00000 0.00000 0.00000
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63 ## 0.00000 0.00000 -1.00000
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64 ## 0.00000 1.00000 0.00000
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65 ##
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66 ## >> v = T*u
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67 ## v =
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68 ## 0.00000
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69 ## 0.00000
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70 ## 1.00000
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71 ## @end group
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72 ## @end example
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73 ##
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74 ## @seealso{roty, rotz}
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75 ## @end deftypefn
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76
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77 ## Author: Nicholas Jankowski <jankowskin@asme.org>
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78 ## Created: 2017-04-09
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79
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80 function retmat = rotx (angle_in_deg)
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81
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82 if ((nargin != 1) || ! isscalar (angle_in_deg))
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83 print_usage ();
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84 endif
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85
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86 angle_in_rad = angle_in_deg * pi / 180;
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87
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88 s = sin (angle_in_rad);
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89 c = cos (angle_in_rad);
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90
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91 retmat = [1 0 0; 0 c -s; 0 s c];
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92
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93 endfunction
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94
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95 ## Function output tests
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96 %!assert (rotx (0), [1 0 0; 0 1 0; 0 0 1]);
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97 %!assert (rotx (45), [1, 0, 0; [0; 0],[(sqrt(2)/2).*[1 -1; 1 1]]], 1e-12);
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98 %!assert (rotx (90), [1 0 0; 0 0 -1; 0 1 0], 1e-12);
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99 %!assert (rotx (180), [1 0 0; 0 -1 0; 0 0 -1], 1e-12);
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100
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101 ## Test input validation
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102 %!error rotx ()
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103 %!error rotx (1, 2)
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104 %!error rotx ([1 2 3])