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Both so-called "retained" and "immediate" mode graphics libraries continue to exist for most platforms, and you can choose to use whichever one you prefer.
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I have looked it up in the past, and I have looked it up now, but I cannot find a reliable documentation that describes it.

For example, do you know what combination of flags listed here https://documentation.help/SDL/sdlsetvideomode.html would do the trick? Or anything that is not listed there would also help.

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Your post just clicked something from of a deep memory into place.

In the early 80s when the IBM PC hit the scene, Hercules had a graphics card that was amazing and offered better than CGA graphics. I was plinking on it at my dad’s friend’s house, drawing circles and stuff, and on HIS computer the graphics were retained. I had to figure out how to clear the screen, whereas on mine, not having the Hercules card, it wasn’t retained. Never understood what was happening until now.

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It's been a while (over a decade now), but I think SDL allows you to leave the contents on the screen if you don't call the clear function before you render new content. I don't know how well that'd work with resizing a window though.
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I think it works like that if acceleration is no enabled. But even then I think it does not work reliably..I might be missing something though.
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SDL is a relatively high level API and framebuffer style graphics work fine on it. I think there are some edge cases for X11 with non-compositing window manager where you will get interesting glitches if the window moves.
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