[Octave-patch-tracker] [patch #8824] added affine2d class

[Avinoam Kalma]

Follow-up Comment #8, patch #8824 (project octave):

Consider the following script:


isTranslation(affine2d ([1 0 0; 0 -1 0; 0 0 1]))
isRigid(affine2d ([1 0 0; 0 -1 0; 0 0 1]))
isSimilarity(affine2d ([1 2 0; 3 4 0; 0 0 1]))
a = invert(affine2d ([1 2 0; 3 4 0; 10 20 1]))
b = affine2d(a.T)


The first 3 command give 1, which is wrong.
The last command fails with an error.

The reasons are:
isTranslation: the check is

check = all ((abs (abs (submatrix) - eye (this.Dimensionality)) < e^-10)(:));

which is wrong - the 2nd abs should be removed. It should be
check = all ((abs(submatrix - eye (this.Dimensionality)) < e^-10)(:));

Since I do not like those e^-10, I would prefer
check = all (abs (submatrix - eye (this.Dimensionality)) < eps)(:));
or even
check = !any (abs (submatrix - eye (this.Dimensionality)) > 0)(:));

Explanation: submatrix should be the Identity matrix (in the accuracy limits),
so maybe the check should be different for
the diagonal entries (which should be 1), and the non-diagonal  
(which should be 0)

isRigid: The submatrix should be a rotation matrix, without 
scale or shear, so its determinant should be 1:
check = abs ((det (submatrix)) -1) < eps;

isSimilarity: The submatrix should be a rotation matrix multiplied by
constant, so the condition is something like

      s2 = submatrix*submatrix';
      ans = all((abs(s2 - s2(1,1)*eye(2)) < ones(2)*eps)(:));

s2 should be the Identity Matrix multiplied by a constant.

When I do 
a = invert(affine2d ([1 2 0; 3 4 0; 10 20 1]))
a.T(3,3)-1 = -1.1102e-016
so a.T(3,3) is not 1, and b = affine2d(a.T) fails.
there should be something like
this.T(:,3) = [0; 0; 1];

BTW,  line 72 should be:
this.T = inv (this.T);

 


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