OpenGL - "ultra smooth" animation of simple horizontally moving object

Well, this is actually typical separate game-loop behavior. You manage all you physics (movement) related actions in one thread, letting the render thread to do its work. This is actually desirable.

Don´t forget this way of implementation of game loop is to have maximum available frame rate while preserving constant physics speed. At higher FPS, you can not see this effect by any chance, if there is not any other code related problem. Some hooking between framerate and physics for example.

If you want to achieve what you describe as perfect smoothness, you could synchronize your physics engine with VSync. Simply do all your physics BEFORE refresh kicks in, than wait for another.

But this all applies to constant speed objects. If you have object with dynamic speed, you can never know when to draw it to be "in sync". Same problem arises then you want multiple object with different constant speeds.

Also, this is NOT what you want in complex scenes. The whole idea of V-sync is to limit screen tearing effect. You should definitely NOT hook your physics or rendering code to display refresh rate. You want you physics code to run independent of users display refresh rate. This could be REAL pain in multiplayer games for example. For start, look at this page: How A Game Loop Works

EDIT: I say your vision of perfect smoothness is unrealistic. You can mask it using techniques Kevin wrote. But you will always struggle with HW limits as refresh rate, or display pixelation. For example, you have window of 640x480 px. Now, you want your object to move horizontally. You can move your object by vector heading towards bottom right corner, BUT you must increment object coordinates by float number (640/480). But in rendering, you go to integers. So your object moves jagged. No way around this. In small speed, you can notice it. You can blur it, or make it move faster, but never get rid of it...

1. Allow your object to move by fractions of a pixel. In OpenGL, this can be done for your example of a square by drawing the square onto a texture (i.e. a one-pixel or larger border), rather than letting it be just the polygon edge. If you are rendering 2D sprite graphics, then you get this pretty much automatically (but if you have 1:1 pixel art it will be blurred/sharp/blurred as it crosses pixel boundaries).

2. Smooth (antialias) the polygon edge (GL_POLYGON_SMOOTH). The problem with this technique is that it does not work with Z-buffer-based rendering since it causes transparency, but if you are doing a 2D scene you can make sure to always draw back-to-front.

3. Enable multisample/supersample antialiasing, which is more expensive but doesn't have the above problem.

4. Make your object have a sufficiently animated appearance that the pixel shifts aren't easy to notice because there's much more going on at that edge (i.e. it is itself moving in place at much more than 1 pixel/frame).

5. Make your game sufficiently complex and engrossing that players are distracted from looking at the pixels. :)