isTransform3d

ISTRANSFORM3D Check if input is a affine transformation matrix.

   A = isTransform3d(TRANS) where TRANS should be a transformation matrix.
   The function accepts transformations given using the following formats:
   [a b c]   ,   [a b c j] , or  [a b c j]
   [d e f]       [d e f k]       [d e f k]
   [g h i]       [g h i l]       [g h i l]
                                 [0 0 0 1]
   
   If the transformation matrix should only contain rotation and
   translation without reflection, scaling, shearing, ... set 'rotation'
   to true. Default is false.

   Example
     rot = ...
         createRotationOx(rand*2*pi)*...
         createRotationOy(rand*2*pi)*...
         createRotationOx(rand*2*pi);
     trans = rot*createTranslation3d(rand(1,3));
     isTransform3d(trans, 'rot', true)

   See also
   composeTransforms3d, createBasisTransform3d, recenterTransform3d,
   transformPoint3d

 ------
 Author: oqilipo
 Created: 2018-07-08
 Copyright 2018

0001 function a = isTransform3d(trans, varargin)
0002 %ISTRANSFORM3D Check if input is a affine transformation matrix.
0003 %
0004 %   A = isTransform3d(TRANS) where TRANS should be a transformation matrix.
0005 %   The function accepts transformations given using the following formats:
0006 %   [a b c]   ,   [a b c j] , or  [a b c j]
0007 %   [d e f]       [d e f k]       [d e f k]
0008 %   [g h i]       [g h i l]       [g h i l]
0009 %                                 [0 0 0 1]
0010 %
0011 %   If the transformation matrix should only contain rotation and
0012 %   translation without reflection, scaling, shearing, ... set 'rotation'
0013 %   to true. Default is false.
0014 %
0015 %   Example
0016 %     rot = ...
0017 %         createRotationOx(rand*2*pi)*...
0018 %         createRotationOy(rand*2*pi)*...
0019 %         createRotationOx(rand*2*pi);
0020 %     trans = rot*createTranslation3d(rand(1,3));
0021 %     isTransform3d(trans, 'rot', true)
0022 %
0023 %   See also
0024 %   composeTransforms3d, createBasisTransform3d, recenterTransform3d,
0025 %   transformPoint3d
0026 %
0027 % ------
0028 % Author: oqilipo
0029 % Created: 2018-07-08
0030 % Copyright 2018
0031 
0032 narginchk(1,5)
0033 
0034 p = inputParser;
0035 logParValidFunc = @(x) (islogical(x) || isequal(x,1) || isequal(x,0));
0036 addParameter(p,'rotation', 0, logParValidFunc);
0037 valTol = @(x) validateattributes(x,{'numeric'},{'scalar', '>=',eps(class(trans)), '<=',1});
0038 addParameter(p,'tolerance', 1e-8, valTol);
0039 parse(p,varargin{:});
0040 rotation = p.Results.rotation;
0041 tolerance = p.Results.tolerance;
0042 
0043 % eventually add null translation
0044 if size(trans, 2) == 3
0045     trans = [trans zeros(size(trans, 1), 1)];
0046 elseif size(trans, 2) < 3 || size(trans, 2) > 4
0047     a=false;
0048     return
0049 end
0050 
0051 % eventually add normalization
0052 if size(trans, 1) == 3
0053     trans = [trans;0 0 0 1];
0054 elseif size(trans, 1) < 3 || size(trans, 1) > 4
0055     a=false;
0056     return
0057 end
0058 
0059 a=true;
0060 
0061 % NaN is invalid
0062 if any(isnan(trans(:)))
0063     a=false;
0064     return
0065 end
0066 
0067 % Infinity is invalid
0068 if any(isinf(trans(:)))
0069     a=false;
0070     return
0071 end
0072 
0073 % trans(4,4) has to be a one
0074 if ~isequal(1, trans(4,4))
0075     a = false;
0076     return
0077 end
0078 
0079 % trans(4,1:3) have to be zeros
0080 if ~isequal(zeros(1,3), trans(4,1:3))
0081     a = false;
0082     return
0083 end
0084 
0085 if rotation
0086     % transpose(trans(1:3,1:3)) * trans(1:3,1:3) has to be eye(3)
0087     if any(abs(eye(3) - (trans(1:3,1:3)'*trans(1:3,1:3))) > tolerance)
0088         a = false;
0089         return;
0090     end
0091     
0092     % determinant of trans(1:3) has to be one
0093     if abs(1-det(trans)) > tolerance
0094         a = false;
0095         return
0096     end
0097 end
0098 
0099 end
0100