I applied @Hartmut correction of comment #17 and pushed all the changes, using Carnë's cset.
(sorry - I did not notice that the patch # was missing :-().

Thanks guys, and sorry it took 6 years.

Thanks, @Hartmut for the comments.
I have added:
1. Documentation for affine2d, affine3d
2. Input check for outputLimits
3. Some BISTs (including that of comment #14
 
Please review the updated version of affine2d.m affine3d.m
(affine.m left unchanged)

(file #52568, file #52569)

I have had a close look at the three files from comment #13.

This is good in affine2d and affine3d:

• I tested the example code from the Matlab help page. And it produces the same results as this Octave code, at least for bit I could check (mainly the missing imwarp.m reduced my possibilities to compare results.)
• All methods of this class are implemented and they did something reasonably when I tested them with 3 different types of tforms.
• All BIST tests pass, and those cover all input versions of the methods.

This should probably be improved in affine2d and affine3d:

• The help text is not display when doing for example "help affine2d", but this is a different bug, namely bug #61521.
• The help text is a bit too short for my taste. I think it would be nice if it mentioned at least the two possible syntax versions: tform = affine2d() and tform = affine2d(M). (Same for affine3d.)
• The is no input check for the method outputLimits. This leads to an awkard error when doing for example "[x y] = outputLimits(tform)". It should be fairly easy to add this input check to the code of the method, there is a good starting point in the comments of the method outputLimits of the parent class in affine.m. (Same for affine3d.)
• In affine3d there is currently no BIST test to check the method invert. I will propose a test code to add below.

Note: In the parent class affine.m is a method outputLimits that is neither used by affine2d nor by affine3d. Nor is it tested anywhere. We could keep it, to be use later by a 4d child class, or we could delete this method to reduce code maintenance burden. I would tend to keep it.

Here is a small test that could be added as BIST to affine3d to test the invert method there:

%!test
%! a = 23;
%! M = [cosd(a) 0 sind(a) 0;
%!      0       1      0  0;
%!     -sind(a) 0 cosd(a) 0;
%!      0       0      0  1];
%! tform = affine3d (M);
%! tform2 = invert (tform);
%! assert (tform.T * tform2.T, diag([1 1 1 1]), eps);

In total this looks like a very good foundation to move towards the modern geometric transformation functions that Matlab introduced white some years ago. Currently these "naked" classes affine2d and affine3d would not be of not much use to any end user, since the following other functions are also still missing in Octave: imregtform, imregcorr, fitgeotrans, randomAffine2d, randomAffine3d, and mainly imwarp. But after having the two foundation classes of this patch, it would be much easier to also generate the mentioned missing functions as well.

@Avinoam: Could you add the above mentioned missing bits to those code files and then prepare a final patch file? I would very much  like to see this code pushed to the image repo in the next weeks, after those many years of preparation and waiting...

Thanks, @Carne for the file.
The final m-files are attached here.

Some things to correct:
1.  print_usage within classdef constructor breaks subsequent calls to the class (bug #60729)
2. The tolerances in BISTs should not be in the form of e^(-n), but 1e(-n)



(file #51907, file #51908, file #51909)

@Martin: Could you please send the full code (not a patch), so I can check it?

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);

 

I have fixed some problems with affine2d (the inverse was problematic).

Please review.

(file #40380)

What do you mean with?

> It is used in imwarp, and is returned from functions such as imregcorr, imregtform and estimateGeometricTransform.

now the test is actually working...

(file #35664)

affine2d class represents the affine transform of 2d vectors (as of matlab 2013a).
It is used in imwarp, and is returned from functions such as imregcorr, imregtform and estimateGeometricTransform.