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Maxim Smolskiy e3ff6ce0cc
Merge pull request #25182 from MaximSmolskiy:increase-decomposeProjectionMatrix-precision-for-small-scales 
Increase decomposeProjectionMatrix precision for small scales #25182 

### Pull Request Readiness Checklist

Fix #23733

It is checked before that `|s| > DBL_EPSILON` (if not, then `s` will be equal to `0`, but `c` will be equal to `1`, then `z` will be equal to `1` and there will be no any problems with small values), so `sqrt(c^2 + s^2) >= |s| > DBL_EPSILON` and thus small values are already taken into account before and there is no need to add `DBL_EPSILON` to `c^2 + s^2` (and I think adding `DBL_EPSILON^2` instead of `DBL_EPSILON` would be more correct).

I ran `Python` script from issue.

`NumPy` and `SciPy` results
```
*Numpy*
P (case 1): 
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]
Numpy, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
Numpy scaled 1e-6, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
P (case 2): 
[[52. -7.  4. 12.]
 [-6. 49. 12.  8.]
 [ 4. 17.  1.  0.]]
Numpy, R.T @ R - I: 
[[-8.88178420e-16 -3.86302608e-16 -2.52050796e-17]
 [-3.86302608e-16 -5.55111512e-16  7.11675423e-18]
 [-2.52050796e-17  7.11675423e-18 -5.55111512e-16]]
Numpy scaled 1e-6, R.T @ R - I: 
[[ 2.22044605e-16 -2.00683644e-16 -1.90063998e-17]
 [-2.00683644e-16  0.00000000e+00  1.16926308e-17]
 [-1.90063998e-17  1.16926308e-17  2.22044605e-16]]

*Scipy*
P (case 1): 
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]
Scipy, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
Scipy scaled 1e-6, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
P (case 2): 
[[52. -7.  4. 12.]
 [-6. 49. 12.  8.]
 [ 4. 17.  1.  0.]]
Scipy, R.T @ R - I: 
[[-1.11022302e-16 -8.74062812e-18 -1.26178867e-17]
 [-8.74062812e-18 -1.11022302e-16  2.07820373e-17]
 [-1.26178867e-17  2.07820373e-17 -1.11022302e-16]]
Scipy scaled 1e-6, R.T @ R - I: 
[[0.00000000e+00 4.04691435e-17 1.12452918e-16]
 [4.04691435e-17 4.44089210e-16 3.74164141e-16]
 [1.12452918e-16 3.74164141e-16 4.44089210e-16]]

*Numpy*
Numpy, P' - P:
 [[ 1.35525272e-20 -9.31736242e-21  8.47032947e-22  3.38813179e-21]
 [-3.38813179e-21  6.77626358e-21  1.69406589e-21  0.00000000e+00]
 [-1.69406589e-21  0.00000000e+00  0.00000000e+00  4.85524279e-22]]

*Scipy*
Scipy, P' - P:
 [[0.00000000e+00 8.47032947e-22 3.38813179e-21 3.38813179e-21]
 [3.38813179e-21 1.35525272e-20 1.52465931e-20 1.52465931e-20]
 [8.47032947e-22 3.38813179e-21 2.54109884e-21 3.39866995e-21]]
```

`OpenCV` results before
```
*OpenCV*
P (case 1): 
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]
OpenCV, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
OpenCV scaled 1e-6, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
P (case 2): 
[[52. -7.  4. 12.]
 [-6. 49. 12.  8.]
 [ 4. 17.  1.  0.]]
OpenCV, R.T @ R - I: 
[[ 2.22044605e-16 -9.12253504e-17 -2.20527203e-19]
 [-9.12253504e-17  0.00000000e+00 -9.12405093e-18]
 [-2.20527203e-19 -9.12405093e-18  2.22044605e-16]]
OpenCV scaled 1e-6, R.T @ R - I: 
[[-1.28197013e-06  1.30450769e-07  7.67357467e-09]
 [ 1.30450769e-07 -1.52141637e-06 -9.92455574e-09]
 [ 7.67357467e-09 -9.92455574e-09 -1.35328272e-06]]

*OpenCV*
OpenCV, P' - P:
 [[-6.75449076e-11  1.73936564e-11 -4.94463312e-12 -1.61106020e-11]
 [ 1.41759913e-11 -7.54512016e-11 -1.67717374e-11 -9.74644390e-12]
 [-2.90254385e-12 -2.53521998e-11 -1.49130587e-12  4.00724440e-13]]
```

`OpenCV` results after
```
*OpenCV*
P (case 1): 
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]
OpenCV, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
OpenCV scaled 1e-6, R.T @ R - I: 
[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]
P (case 2): 
[[52. -7.  4. 12.]
 [-6. 49. 12.  8.]
 [ 4. 17.  1.  0.]]
OpenCV, R.T @ R - I: 
[[ 2.22044605e-16 -9.12253504e-17 -2.20527203e-19]
 [-9.12253504e-17  0.00000000e+00 -9.12405093e-18]
 [-2.20527203e-19 -9.12405093e-18  2.22044605e-16]]
OpenCV scaled 1e-6, R.T @ R - I: 
[[ 0.00000000e+00  4.36198333e-17 -2.66855078e-17]
 [ 4.36198333e-17  2.22044605e-16  3.17216400e-17]
 [-2.66855078e-17  3.17216400e-17 -2.22044605e-16]]

*OpenCV*
OpenCV, P' - P:
 [[ 6.77626358e-21  0.00000000e+00 -8.47032947e-22  1.69406589e-21]
 [-1.69406589e-21  6.77626358e-21  0.00000000e+00  3.38813179e-21]
 [ 8.47032947e-22  3.38813179e-21  2.11758237e-22  1.45657284e-21]]
```

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake
2024-03-27 12:43:56 +03:00
..
calib3d Merge pull request #25182 from MaximSmolskiy:increase-decomposeProjectionMatrix-precision-for-small-scales 2024-03-27 12:43:56 +03:00
core Merge pull request #24893 from chacha21:cart_polar_inplace 2024-03-26 15:38:17 +03:00
dnn Merge pull request #25238 from fengyuentau:optimized_const 2024-03-26 15:09:51 +03:00
features2d Merge pull request #25042 from mshabunin:doc-upgrade 2024-03-05 16:19:45 +03:00
flann Merge pull request #25024 from vrabaud:neon 2024-02-20 11:29:23 +03:00
gapi core: Rename cv::float16_t to cv::hfloat (#25217) 2024-03-21 23:44:19 +03:00
highgui Backport some highgui changes from #22754 2024-03-05 17:49:01 +03:00
imgcodecs Fix: 6 typos 2024-03-26 02:32:54 +01:00
imgproc Fix bug in maskBoundingRect 2024-03-08 03:25:40 +03:00
java doc: fix formulas in JavaDoc broken after Doxygen upgrade 2024-03-11 23:47:23 +03:00
js Merge pull request #25084 from EDVTAZ:emscripten-3.1.54-compat 2024-02-26 10:30:56 +03:00
ml Partially back-port #25075 to 4.x 2024-03-05 12:15:39 +03:00
objc Merge pull request #24136 from komakai:visionos_support 2023-12-20 15:35:10 +03:00
objdetect Merge pull request #25042 from mshabunin:doc-upgrade 2024-03-05 16:19:45 +03:00
photo Merge pull request #25042 from mshabunin:doc-upgrade 2024-03-05 16:19:45 +03:00
python fix [use hasattr("cv2", "name") ,but first param is 'character string', 2024-02-23 22:02:43 +08:00
stitching Partially back-port #25075 to 4.x 2024-03-05 12:15:39 +03:00
ts Partially back-port #25075 to 4.x 2024-03-05 12:15:39 +03:00
video Merge pull request #25042 from mshabunin:doc-upgrade 2024-03-05 16:19:45 +03:00
videoio Merge pull request #25189 from klatism:ios-build-fixes 2024-03-27 10:05:32 +03:00
world cmake: use /INCREMENTAL:NO with MSVS 2015 2023-12-07 19:46:27 +00:00