I used to work on video editing software in a previous job, for all framerate changes it’s done via image/frame interop. (Combining 2 frames to produce a merged in-between frame)
It’s more complicated than just adding 13 additional frames for every 100 frames of the video because that would just cause a weird speed up/slow down situation as the original 29.87 frames would be playing at a slightly faster 30fps rate while the inserted 13 frames would cause a slight gap/delay.
What ends up happening is each frame is rebuilt, with a percentage based formula of how much of the previous and next frame should be used, over the course of this process new extra frames are also introduced but generally speaking most frames of the video have been altered slightly to keep the timing correct.
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