Lets say you have the acceleration readings in all the 3 dimensions i.e X, Y and Z. How do you infer using the readings the phone was tilted left or right? The readings get generated every 20ms.
I actually want the logic of inferring the tilt from the readings. The tilt needs to be smooth.
A tilt can be detected in a sort of diferent ways. You can take into account 1 axis, 2 axis, or the 3 axis. Depending on how accurate you want it, and how much you feel like fighting with maths.
If you use only one axis, it is quite simple. Think the mobile is completely horizontal, and you move it like this:
using just one axis, lets say, axis x, will be enough, since you can detect accurately a change in that axis position, since even any small movement will do a change in the axis. But, if your application is only reading that axis, and the user has the phone almost vertical, the difference in x axis will be really small even rotating the phone a big angle. Anyways,for applications that only need coarse resolution, a single-axis can be used.
Referring to basic trigonometry, the projection of the gravity vector on the x-axis produces an output acceleration equal to the sine of the angle between the accelerometer x-axis and the horizon. This means that having the values of an axis (those are acceleration values) you can calculate the angle in which the device is.
this means that the value given to you by the sensor, is = to 9,8 * sine of the angle, so doing the maths you can get the actual angle.
But don't worry, you don't even have to do this. Since the values are more or less proportional, as you can see in the table below, you can work directly with the value of the sensor, without taking much care of what angle represents, if you don't need it to be much accurate, since a change in that value means a proportional change in the angle, so with a few test, you will find out how big should be the change in order to be relevant to you.
So, if you take the value over the time, and compare to each other, you can figure out how big the rotation was. For this,
I hope this is good enough for you. For sure you can find some libraries or code snippets to help you out with this, but i think is good, as you say, to know the logic of inferring the tilt from the readings
The pictures was taken from this article, wich i recomend to read if you want to improve the accuracy and consider 2 o 3 axis for the tilt