Whether it’s a texture or rendered directly is basically an implementation detail. You can pre-distort the virtual camera so that it gives the perspective-correct result. Of course, you have to re-render it if the source position changes, but you have to re-render it every frame regardless. Doing it as a texture has some advantages, like being able to lower the resolution more easily.
Still, I think the more common way would be to set up a stencil so that only the mirror surface is rendered, and then change the scene transform to mirror across the plane, and then just render normally. It’s not that costly if you handle the geometry culling, etc. properly.
That’s also the approach that games like Portal use, or in fact any game with large indoor maps. A scene will have regions that represent a portal to a different area (or maybe the same area). There’s a transform that maps the other scene to the current one at the boundary plane. That transform is usually a rigid one, but could include mirroring, scaling, or other kinds of warping.
Anything but a planar mirror is pretty dodgy using this approach, though, since straight lines wouldn’t map to straight lines otherwise.
Not sure. It also depends on what one means by accurate. I’m pretty sure there was a car racing game for the Atari 800 which featured cars with an extremely basic image on the mirror. But there were many car racing games and I am unsure which one - not Pole Position.
By “source position”, you mean the position of the player? In that case, yes, I suppose you could do it that way. It seems a funny way of doing it, to me, but then, I can’t criticize, as I’ve done similarly funny-seeming things in some of my code, and it would work. In a multiplayer environment, you’d need a different texture for each player, but again, nearly everything about what the players see needs to be re-done (at least to some degree) for every player.
It’s probably not the way I’d do it, but it’s not really that wild, and might have some advantages depending on the way the engine is designed. 3D engine writers are pretty comfortable with the various types of projective transforms. Mirroring the viewer across the plane and then setting up a camera projection that takes the perspective of the mirror into account is pretty straightforward for anyone comfortable with 4D homogeneous coordinates.
