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## Copyright (C) 2024 David Legland
## 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.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function alpha = vectorAngle(v1, varargin)
%VECTORANGLE Horizontal angle of a vector, or angle between 2 vectors.
%
% A = vectorAngle(V);
% Returns angle between Ox axis and vector direction, in radians, 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, in radians.
%
% A = vectorAngle(..., 'midAngle', MIDANGLE);
% Specifies convention for angle interval. MIDANGLE 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
%
% See also
% vectors2d, angles2d, normalizeAngle
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-10-18
% Copyright 2007-2023 INRA - Cepia Software Platform
%% Initializations
% default values
v2 = [];
midAngle = pi; % normalize angles between 0 and 2*PI
% process input arguments
while ~isempty(varargin)
var = varargin{1};
if isnumeric(var) && isscalar(var)
% argument is normalization constant
midAngle = 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') || strcmpi(var, 'midAngle')
midAngle = 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, midAngle);
return;
end
%% Case of two vectors
% compute angle of each vector
alpha1 = mod(atan2(v1(:,2), v1(:,1)), 2*pi);
alpha2 = mod(atan2(v2(:,2), v2(:,1)), 2*pi);
% difference
alpha = bsxfun(@minus, alpha2, alpha1);
% normalize within a 2*pi interval
alpha = normalizeAngle(alpha + 2*pi, midAngle);
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