Fix fundamental floating point error in Clip.iter_frames

[tburrows13]

This PR has the same effect as #229, but with the (fixed) changes suggested in #210.

Closes #210, #229, #632, #646, #858.

Note that this supersedes half of #634, but at a deeper level. I will edit #634 to remove this half of the fix and leave it solely for the #631 supersample fix.

I'm quite confident in this PR so I will merge in a few days if there are no objections.

Explanation taken from #210:

clip duration = 0.56
fps = 12.5

When this gets written out to frames, we use (in Clip.py's iterframes):

        for t in np.arange(0, self.duration, 1.0/fps):

But numpy gives:

(Pdb) np.arange(0, .56, 1.0/12.5)
array([ 0.  ,  0.08,  0.16,  0.24,  0.32,  0.4 ,  0.48,  0.56])

This means that a composite video clip will try to generate an 8th frame at t=0.56. However, since the individual clips that make up the composite all have end=0.56, none of them is considered to be playing at that time. This results in a black final frame (just the background color, with no clips composited over it).

I don't think this is really a bug in the compositor so much as a result of numerical precision issues resulting in the extra t=0.56 frame being generated. Specifically, numpy says that arange generates a half-open interval [start, end), so in theory the arange array should end at t=0.48, but it doesn't, because the numbers 0.56 and 0.8 cannot be represented perfectly by floating point.

---

• I have provided code that clearly demonstrates the bug and that only works correctly when applying this fix
• I have added suitable tests demonstrating a fixed bug or new/changed feature to the test suite in tests/
• I have properly documented new or changed features in the documentation or in the docstrings
• I have properly explained unusual or unexpected code in the comments around it
• I have formatted my code using black -t py36

[coveralls]

Coverage decreased (-0.01%) to 67.327% when pulling 6058a5e on tburrows13:fix-concatenate-indexerror into b2ed1f6 on Zulko:master.

[tbermudez10]

Hello,

I'm a noob so I dont understand how this solves the problem, or maybe i just dont know how to pull it. Any help would be highly appreciated. Cheers!