vectorAngle3d

VECTORANGLE3D Angle between two 3D vectors.

   THETA = vectorAngle3d(V1, V2)
   Computes the angle between the 2 3D vectors V1 and V2. The result THETA
   is given in radians, between 0 and PI.


   Example
   % angle between 2 orthogonal vectors
   vectorAngle3d([1 0 0], [0 1 0])
   ans = 
       1.5708

   % angle between 2 parallel vectors
   v0 = [3 4 5];
   vectorAngle3d(3*v0, 5*v0)
   ans = 
       0

   See also
   vectors3d, vectorNorm3d, crossProduct3d

0001 function theta = vectorAngle3d(v1, v2)
0002 %VECTORANGLE3D Angle between two 3D vectors.
0003 %
0004 %   THETA = vectorAngle3d(V1, V2)
0005 %   Computes the angle between the 2 3D vectors V1 and V2. The result THETA
0006 %   is given in radians, between 0 and PI.
0007 %
0008 %
0009 %   Example
0010 %   % angle between 2 orthogonal vectors
0011 %   vectorAngle3d([1 0 0], [0 1 0])
0012 %   ans =
0013 %       1.5708
0014 %
0015 %   % angle between 2 parallel vectors
0016 %   v0 = [3 4 5];
0017 %   vectorAngle3d(3*v0, 5*v0)
0018 %   ans =
0019 %       0
0020 %
0021 %   See also
0022 %   vectors3d, vectorNorm3d, crossProduct3d
0023 %
0024 
0025 % ------
0026 % Author: David Legland
0027 % e-mail: david.legland@inra.fr
0028 % Created: 2010-10-04,    using Matlab 7.9.0.529 (R2009b)
0029 % Copyright 2010 INRA - Cepia Software Platform.
0030 
0031 % 2011-03-10 improve computation precision
0032 
0033 % compute angle using arc-tangent to get better precision for angles near
0034 % zero, see the discussion in:
0035 % http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925#381952
0036 theta = atan2(vectorNorm3d(crossProduct3d(v1, v2)), sum(bsxfun(@times, v1, v2),2));
0037 
0038 % equivalent to:
0039 % v1 = normalizeVector3d(v1);
0040 % v2 = normalizeVector3d(v2);
0041 % theta = acos(dot(v1, v2, 2));