isPerpendicular3d

ISPERPENDICULAR3D Check orthogonality of two 3D vectors.

   B = isPerpendicular3d(V1, V2)
   where V1 and V2 are 2 [1x3] arrays, returns 1 if the vectors are
   orthogonal, and 0 otherwise.

   Also works when V1 and V2 are two [Nx3] arrays with same number of
   rows. In this case, return a [Nx1] array containing 1 at the positions
   of parallel vectors.

   Also works when one of V1 or V2 is scalar and the other one is [Nx3]
   array, in this case return [Nx1] results.

   B = isPerpendicular3d(V1, V2, TOL)
   Specifies the absolute tolerance (default is 1e-14).


   Example
   isPerpendicular3d([1 0 0], [0 1 0])
   ans =
       1

   isPerpendicular3d([1 0 1], [1 0 0])
   ans =
       0

   See also
   vectors3d, isParallel3d

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2006-04-25
 Copyright 2006 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).

0001 function b = isPerpendicular3d(v1, v2, varargin)
0002 %ISPERPENDICULAR3D Check orthogonality of two 3D vectors.
0003 %
0004 %   B = isPerpendicular3d(V1, V2)
0005 %   where V1 and V2 are 2 [1x3] arrays, returns 1 if the vectors are
0006 %   orthogonal, and 0 otherwise.
0007 %
0008 %   Also works when V1 and V2 are two [Nx3] arrays with same number of
0009 %   rows. In this case, return a [Nx1] array containing 1 at the positions
0010 %   of parallel vectors.
0011 %
0012 %   Also works when one of V1 or V2 is scalar and the other one is [Nx3]
0013 %   array, in this case return [Nx1] results.
0014 %
0015 %   B = isPerpendicular3d(V1, V2, TOL)
0016 %   Specifies the absolute tolerance (default is 1e-14).
0017 %
0018 %
0019 %   Example
0020 %   isPerpendicular3d([1 0 0], [0 1 0])
0021 %   ans =
0022 %       1
0023 %
0024 %   isPerpendicular3d([1 0 1], [1 0 0])
0025 %   ans =
0026 %       0
0027 %
0028 %   See also
0029 %   vectors3d, isParallel3d
0030 %
0031 % ------
0032 % Author: David Legland
0033 % e-mail: david.legland@grignon.inra.fr
0034 % Created: 2006-04-25
0035 % Copyright 2006 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).
0036 
0037 % 2011.03.20 add support for tolerance, fix computation
0038 
0039 % check if tolerance is specified
0040 tol = 1e-14;
0041 if ~isempty(varargin)
0042     tol = varargin{1};
0043 end
0044 
0045 % compute perpendicularity test
0046 b = abs(sum(bsxfun(@times, v1, v2), 2)) < tol;