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Billboarding is more general than that, it refers to any 2D sprite that always faces the camera. It's often used at close range for things like particles and grass as well.

Billboards that are used as substitutes for 3D models at long distances are more specifically called "imposters".

Or 'posters ?

BTW I've often noticed these 2D images (which work better than I'd've thought)... but for distant objects (in an open world game where the player can approach them from any direction), is a 3D model ever rendered once to a 2D poster when the player first sees them, then that is reused (until player gets too close; or approaches at too different an angle)?

I'm concerned at the uneven computation required as objects move in/out of range and need to be re-postered. (I prefer steady fps).

Back when I was in games we still called them billboards or more commonly just LODs.

LODs refer to simplified versions of the original mesh. So they are not flat like billboards, and still have the "depth" to them. Think for example, a pine tree with many shapes for branches in the foreground, but in the distant background the entire body of the leaves can just be a simple cone.

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