File: vectorAngle.m

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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);