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

0001 function alpha = vectorAngle(v1, varargin)
0002 % Horizontal angle of a vector, or angle between 2 vectors.
0003 %
0004 %   A = vectorAngle(V);
0005 %   Returns angle between Ox axis and vector direction, in radians, in
0006 %   counter-clockwise orientation.
0007 %   The result is normalised between 0 and 2*PI.
0008 %
0009 %   A = vectorAngle(V1, V2);
0010 %   Returns the angle from vector V1 to vector V2, in counter-clockwise
0011 %   order, in radians.
0012 %
0013 %   A = vectorAngle(..., 'midAngle', MIDANGLE);
0014 %   Specifies convention for angle interval. MIDANGLE is the center of the
0015 %   2*PI interval containing the result. See <a href="matlab:doc
0016 %   ('normalizeAngle')">normalizeAngle</a> for details.
0017 %
0018 %   Example:
0019 %   rad2deg(vectorAngle([2 2]))
0020 %   ans =
0021 %       45
0022 %   rad2deg(vectorAngle([1 sqrt(3)]))
0023 %   ans =
0024 %       60
0025 %   rad2deg(vectorAngle([0 -1]))
0026 %   ans =
0027 %       270
0028 %
0029 %   See also:
0030 %     vectors2d, angles2d, normalizeAngle
0031 %
0032 
0033 % ------
0034 % Author: David Legland
0035 % e-mail: david.legland@inrae.fr
0036 % Created: 2007-10-18
0037 % Copyright 2011 INRA - Cepia Software Platform.
0038 
0039 %   HISTORY
0040 %   2010-04-16 add psb to specify center interval
0041 %   2011-04-10 add support for angle between two vectors
0042 
0043 
0044 %% Initializations
0045 
0046 % default values
0047 v2 = [];
0048 midAngle = pi; % normalize angles between 0 and 2*PI
0049 
0050 % process input arguments
0051 while ~isempty(varargin)
0052     var = varargin{1};
0053     if isnumeric(var) && isscalar(var)
0054         % argument is normalization constant
0055         midAngle = varargin{1};
0056         varargin(1) = [];
0057         
0058     elseif isnumeric(var) && size(var, 2) == 2
0059         % argument is second vector
0060         v2 = varargin{1};
0061         varargin(1) = [];
0062         
0063     elseif ischar(var) && length(varargin) >= 2
0064         % argument is option given as string + value
0065         if strcmpi(var, 'cutAngle') || strcmpi(var, 'midAngle')
0066             midAngle = varargin{2};
0067             varargin(1:2) = [];
0068             
0069         else
0070             error(['Unknown option: ' var]);
0071         end
0072         
0073     else
0074         error('Unable to parse inputs');
0075     end
0076 end
0077 
0078 
0079 %% Case of one vector
0080 
0081 % If only one vector is provided, computes its angle
0082 if isempty(v2)
0083     % compute angle and format result in a 2*pi interval
0084     alpha = atan2(v1(:,2), v1(:,1));
0085     
0086     % normalize within a 2*pi interval
0087     alpha = normalizeAngle(alpha + 2*pi, midAngle);
0088     
0089     return;
0090 end
0091 
0092 
0093 %% Case of two vectors
0094 
0095 % compute angle of each vector
0096 alpha1 = mod(atan2(v1(:,2), v1(:,1)), 2*pi);
0097 alpha2 = mod(atan2(v2(:,2), v2(:,1)), 2*pi);
0098 
0099 % difference
0100 alpha = bsxfun(@minus, alpha2, alpha1);
0101 
0102 % normalize within a 2*pi interval
0103 alpha = normalizeAngle(alpha + 2*pi, midAngle);
0104