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@inrae.fr
0035 % Created: 2006-04-25
0036 % Copyright 2006-2024 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
0037 
0038 % default accuracy
0039 acc = 1e-14;
0040 if ~isempty(varargin)
0041     acc = abs(varargin{1});
0042 end
0043 
0044 % normalize vectors
0045 v1 = normalizeVector(v1);
0046 v2 = normalizeVector(v2);
0047 
0048 % adapt size of inputs
0049 n1 = size(v1, 1);
0050 n2 = size(v2, 1);
0051 if n1 ~= n2
0052     if n1 == 1
0053         v1 = v1(ones(n2, 1), :);
0054     elseif n2==1
0055         v2 = v2(ones(n1, 1), :);
0056     else
0057         error('Inputs must either have same size, or one must be scalar');
0058     end
0059 end
0060 
0061 % performs test
0062 b = abs(dot(v1, v2, 2)) < acc;