How to detect iPhone movement in space using accelerometer?

Question

I am trying to make an application that would detect what kind of shape you made with your iPhone using accelerometer. As an example, if you draw a circle with your hand holding the iPhone, the app would be able to redraw it on the screen. This could also work with squares, or even more complicated shapes. The only example of application I've seen doing such a thing is AirPaint (http://vimeo.com/2276713), but it doesn't seems to be able to do it in real time.

My first try is to apply a low-pass filter on the X and Y parameters from the accelerometer, and to make a pointer move toward these values, proportionally to the size of the screen. But this is clearly not enought, I have a very low accuracy, and if I shake the device it also makes the pointer move...

Any ideas about that ? Do you think accelerometer data is enought to do it ? Or should I consider using other data, such as the compass ?

Thanks in advance !

Answer 1

OK I have found something that seems to work, but I still have some problems. Here is how I proceed (admiting the device is hold verticaly) :

1 - I have my default x, y, and z values.
2 - I extract the gravity vector from this data using a low pass filter.
3 - I substract the normalized gravity vector from each x, y, and z, and get the movement acceleration.
4 - Then, I integrate this acceleration value with respect to time, so I get the velocity.
5 - I integrate this velocity again with respect to time, and find a position.

All of the below code is into the accelerometer:didAccelerate: delegate of my controller. I am trying to make a ball moving according to the position i found. Here is my code :

NSTimeInterval interval = 0;
NSDate *now = [NSDate date];
if (previousDate != nil)
{
    interval = [now timeIntervalSinceDate:previousDate];
}
previousDate = now;

//Isolating gravity vector
gravity.x = currentAcceleration.x * kFileringFactor + gravity.x * (1.0 - kFileringFactor);
gravity.y = currentAcceleration.y * kFileringFactor + gravity.y * (1.0 - kFileringFactor);
gravity.z = currentAcceleration.z * kFileringFactor + gravity.z * (1.0 - kFileringFactor);
float gravityNorm = sqrt(gravity.x * gravity.x + gravity.y * gravity.y + gravity.z * gravity.z);

//Removing gravity vector from initial acceleration
filteredAcceleration.x = acceleration.x - gravity.x / gravityNorm;
filteredAcceleration.y = acceleration.y - gravity.y / gravityNorm;
filteredAcceleration.z = acceleration.z - gravity.z / gravityNorm;

//Calculating velocity related to time interval
velocity.x = velocity.x + filteredAcceleration.x * interval;
velocity.y = velocity.y + filteredAcceleration.y * interval;
velocity.z = velocity.z + filteredAcceleration.z * interval;

//Finding position
position.x = position.x + velocity.x * interval * 160;
position.y = position.y + velocity.y * interval * 230;

If I execute this, I get quite good values, I mean I can see the acceleration going into positive or negative values according to the movements I make. But when I try to apply that position to my ball view, I can see it is moving, but with a propencity to go more in one direction than the other. This means, for example, if I draw circles with my device, i will see the ball describing curves towards the top-left corner of the screen. Something like that : http://img685.imageshack.us/i/capturedcran20100422133.png/

Do you have any ideas about what is happening ? Thanks in advance !