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But honestly C++ is not the right tool for this, even though you technically can do all of that. I suggest you use something like https://processing.org/ which is quite literally made to do animations and then use OBS or something similar to record your screen into a video.
Manim is made for this. Made by 3Blue1Brown, a YouTuber who makes great mathematical YouTube videos.
STB has a single file header-only library that can write PNG images if you want to keep your dependencies simple at the expense of supporting some exotic formats and features: https://github.com/nothings/stb/blob/master/stb_image_write.h