I have not much more to say regarding to the Parallax Scrolling than PFG already did. There is indeed an example in the repository under the test folder and several explanations around the web. I liked this one.
The matter with the background is really easy to solve. This and other related problems can be approached by using modular algebra. I won't go into the details because once shown is very easy to understand.
Imagine that you want to show a compass in your screen. You have a texture 1024x16 representing the cardinal points. Basically all you have is a strip. Letting aside the considerations about the real orientation and such, you have to render it.
Your viewport is 300x400 for example, and you want 200px of the texture on screen (to make it more interesting). You can render it perfectly with a single region until you reach the position (1024-200) = 824. Once you're in this position clearly there is no more texture. But since it is a compass, it's obvious that once you reach the end of it, it has to start again. So this is the answer. Another texture region will do the trick. The range 825-1023 has to be represented by another region. The second region will have a size of (1024-pos) for every value pos>824 && pos<1024
This code is intended to work as real example of a compass. It's very dirty since it works with relative positions all the time due to the conversion between the range (0-3.6) to (0-1024).
spriteBatch.begin();
if (compassorientation<0)
compassorientation = (float) (3.6 - compassorientation%3.6);
else
compassorientation = (float) (compassorientation % 3.6);
if ( compassorientation < ((float)(1024-200)/1024*3.6)){
compass1.setRegion((int)(compassorientation/3.6*1024), 0, 200, 16);
spriteBatch.draw(compass1, 0, (Gdx.graphics.getHeight()/2) -(-250 + compass1.getTexture().getHeight()* (float)1.2), Gdx.graphics.getWidth(), 32 * (float)1.2);
}
else if (compassorientation > ((float)(1024-200)/1024*3.6)) {
compass1.setRegion((int)(compassorientation/3.6*1024), 0, 1024 - (int)(compassorientation/3.6*1024), 16);
spriteBatch.draw(compass1, 0, (Gdx.graphics.getHeight()/2) -(-250 + compass1.getTexture().getHeight()* (float)1.2), compass1.getRegionWidth()/200f * Gdx.graphics.getWidth() , 32 * (float)1.2);
compass2.setRegion(0, 0, 200 - compass1.getRegionWidth(), 16);
spriteBatch.draw(compass2, compass1.getRegionWidth()/200f * Gdx.graphics.getWidth() , (Gdx.graphics.getHeight()/2) -(-250 + compass1.getTexture().getHeight()* (float)1.2), Gdx.graphics.getWidth() - (compass1.getRegionWidth()/200f * Gdx.graphics.getWidth()) , 32 * (float)1.2);
}
spriteBatch.end();