isPerpendicular

ISPERPENDICULAR Check orthogonality of two vectors.

   B = isPerpendicular(V1, V2)
   where V1 and V2 are two 1-by-2 row arrays, returns 1 if the vectors are
   perpendicular, and 0 otherwise.

   Also works when V1 and V2 are two N-by-2 arrays with same number of
   rows. In this case, return a N-by-1 array containing 1 at the positions
   of perpendicular vectors.

   Also works when one of V1 or V2 is 1-by-2 and the other one is a N-by-2
   array. In this case the result has size N-by-1.

   B = isPerpendicular(V1, V2, ACCURACY)
   specifies accuracy of numerical tests, default is 1e-14.


   Example
   isPerpendicular([1 2 1], [2 4 2])
   ans =
       1

   isPerpendicular([1 2 1], [1 3 2])
   ans =
       0

   See also
   vectors2d, isParallel, lines2d

0001 function b = isPerpendicular(v1, v2, varargin)
0002 %ISPERPENDICULAR Check orthogonality of two vectors.
0003 %
0004 %   B = isPerpendicular(V1, V2)
0005 %   where V1 and V2 are two 1-by-2 row arrays, returns 1 if the vectors are
0006 %   perpendicular, and 0 otherwise.
0007 %
0008 %   Also works when V1 and V2 are two N-by-2 arrays with same number of
0009 %   rows. In this case, return a N-by-1 array containing 1 at the positions
0010 %   of perpendicular vectors.
0011 %
0012 %   Also works when one of V1 or V2 is 1-by-2 and the other one is a N-by-2
0013 %   array. In this case the result has size N-by-1.
0014 %
0015 %   B = isPerpendicular(V1, V2, ACCURACY)
0016 %   specifies accuracy of numerical tests, default is 1e-14.
0017 %
0018 %
0019 %   Example
0020 %   isPerpendicular([1 2 1], [2 4 2])
0021 %   ans =
0022 %       1
0023 %
0024 %   isPerpendicular([1 2 1], [1 3 2])
0025 %   ans =
0026 %       0
0027 %
0028 %   See also
0029 %   vectors2d, isParallel, lines2d
0030 %
0031 
0032 % ------
0033 % Author: David Legland
0034 % e-mail: david.legland@inra.fr
0035 % Created: 2006-04-25
0036 % Copyright 2006 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).
0037 
0038 %   HISTORY
0039 %   2007-09-18 copy from isPerpendicular, adapt to any dimension, and add
0040 %       psb to specify precision
0041 %   2009-09-21 fix bug for array of 3 vectors
0042 %   2011-01-20 replace repmat by ones-indexing (faster)
0043 %   2017-08-31 use normalized vectors
0044 
0045 % default accuracy
0046 acc = 1e-14;
0047 if ~isempty(varargin)
0048     acc = abs(varargin{1});
0049 end
0050 
0051 % normalize vectors
0052 v1 = normalizeVector(v1);
0053 v2 = normalizeVector(v2);
0054 
0055 % adapt size of inputs
0056 n1 = size(v1, 1);
0057 n2 = size(v2, 1);
0058 if n1 ~= n2
0059     if n1 == 1
0060         v1 = v1(ones(n2, 1), :);
0061     elseif n2==1
0062         v2 = v2(ones(n1, 1), :);
0063     else
0064         error('Inputs must either have same size, or one must be scalar');
0065     end
0066 end
0067 
0068 % performs test
0069 b = abs(dot(v1, v2, 2)) < acc;