/usr/share/octave/packages/geometry-1.7.0/geom2d/vectorAngle.m is in octave-geometry 1.7.0-1build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 | ## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{alpha} =} vectorAngle (@var{v1})
## Angle of a vector, or between 2 vectors
##
## A = vectorAngle(V);
## Returns angle between Ox axis and vector direction, in Counter
## clockwise orientation.
## The result is normalised between 0 and 2*PI.
##
## A = vectorAngle(V1, V2);
## Returns the angle from vector V1 to vector V2, in counter-clockwise
## order, and in radians.
##
## A = vectorAngle(..., 'cutAngle', CUTANGLE);
## A = vectorAngle(..., CUTANGLE); # (deprecated syntax)
## Specifies convention for angle interval. CUTANGLE is the center of the
## 2*PI interval containing the result. See <a href="matlab:doc
## ('normalizeAngle')">normalizeAngle</a> for details.
##
## Example:
## rad2deg(vectorAngle([2 2]))
## ans =
## 45
## rad2deg(vectorAngle([1 sqrt(3)]))
## ans =
## 60
## rad2deg(vectorAngle([0 -1]))
## ans =
## 270
##
## @seealso{vectors2d, angles2d, normalizeAngle}
## @end deftypefn
function alpha = vectorAngle(v1, varargin)
## Initializations
# default values
v2 = [];
cutAngle = pi;
# process input arguments
while ~isempty(varargin)
var = varargin{1};
if isnumeric(var) && isscalar(var)
# argument is normalization constant
cutAngle = varargin{1};
varargin(1) = [];
elseif isnumeric(var) && size(var, 2) == 2
# argument is second vector
v2 = varargin{1};
varargin(1) = [];
elseif ischar(var) && length(varargin) >= 2
# argument is option given as string + value
if strcmpi(var, 'cutAngle')
cutAngle = varargin{2};
varargin(1:2) = [];
else
error(['Unknown option: ' var]);
end
else
error('Unable to parse inputs');
end
end
## Case of one vector
# If only one vector is provided, computes its angle
if isempty(v2)
# compute angle and format result in a 2*pi interval
alpha = atan2(v1(:,2), v1(:,1));
# normalize within a 2*pi interval
alpha = normalizeAngle(alpha + 2*pi, cutAngle);
return;
end
## Case of two vectors
# compute angle of each vector
alpha1 = atan2(v1(:,2), v1(:,1));
alpha2 = atan2(v2(:,2), v2(:,1));
# difference
alpha = bsxfun(@minus, alpha2, alpha1);
# normalize within a 2*pi interval
alpha = normalizeAngle(alpha + 2*pi, cutAngle);
endfunction
%!test
%! ang = vectorAngle([1 0]);
%! assert(0, ang, 1e-6);
%!test
%! ang = vectorAngle([0 1]);
%! assert(pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([-1 0]);
%! assert(pi, ang, 1e-6);
%!test
%! ang = vectorAngle([0 -1]);
%! assert(3*pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([-1 1]);
%! assert(3*pi/4, ang, 1e-6);
%!test
%! ang = vectorAngle([1 0], pi);
%! assert(0, ang, 1e-6);
%!test
%! ang = vectorAngle([0 1], pi);
%! assert(pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([-1 0], pi);
%! assert(pi, ang, 1e-6);
%!test
%! ang = vectorAngle([0 -1], pi);
%! assert(3*pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([-1 1], pi);
%! assert(3*pi/4, ang, 1e-6);
%!test
%! vecs = [1 0;0 1;-1 0;0 -1;1 1];
%! angs = [0;pi/2;pi;3*pi/2;pi/4];
%! assert(angs, vectorAngle(vecs));
%! assert(angs, vectorAngle(vecs, pi));
%!test
%! ang = vectorAngle([1 0], 0);
%! assert(0, ang, 1e-6);
%!test
%! ang = vectorAngle([0 1], 0);
%! assert(pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([0 -1], 0);
%! assert(-pi/2, ang, 1e-6);
%!test
%! ang = vectorAngle([-1 1], 0);
%! assert(3*pi/4, ang, 1e-6);
%!test
%! vecs = [1 0;0 1;0 -1;1 1;1 -1];
%! angs = [0;pi/2;-pi/2;pi/4;-pi/4];
%! assert(angs, vectorAngle(vecs, 0), 1e-6);
%!test
%! v1 = [1 0];
%! v2 = [0 1];
%! ang = pi /2 ;
%! assert(ang, vectorAngle(v1, v2), 1e-6);
%!test
%! v1 = [1 0];
%! v2 = [0 1; 0 1; 1 1; -1 1];
%! ang = [pi / 2 ;pi / 2 ;pi / 4 ; 3 * pi / 4];
%! assert(ang, vectorAngle(v1, v2), 1e-6);
%!test
%! v1 = [0 1; 0 1; 1 1; -1 1];
%! v2 = [-1 0];
%! ang = [pi / 2 ;pi / 2 ; 3 * pi / 4 ; pi / 4];
%! assert(ang, vectorAngle(v1, v2), 1e-6);
%!test
%! v1 = [1 0; 0 1; 1 1; -1 1];
%! v2 = [0 1; 1 0; -1 1; -1 0];
%! ang = [pi / 2 ;3 * pi / 2 ;pi / 2 ; pi / 4];
%! assert(ang, vectorAngle(v1, v2), 1e-6);
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