Question

I want my app to be able to detect a device rotation while the device is held horizontally. I could use readings from a compass but I believe yaw values from the gyroscope would be more accurate. Given yaw readings, what would be the best algorithm to determine a 360° rotation (either clockwise or counter-clockwise). And it has to be a full 360°, not just turning the phone 180° in one direction and back 180° in the opposite direction.

Answer 1

Here is an idea assuming that you can obtain the readout in short intervals, and that the yaw can be zeroed at a specific start point. This is different from the other answer, which detects full circles from a continuously adapted start point.

In this approach, we keep comparing the current yaw to the previous yaw, asking whether a checkpoint at 180 degrees, or PI has been passed. Initially, the checkpoint flag cp_pi is NO, and passing it in either direction toggles its state. Note that yaw changes its sign in two places, at the zero point and again at PI to -PI.

Assuming your object has two properties that are persistent between ticks of the detector, BOOL cp_pi; and float prev_yaw;, we consider that d_yaw is less than PI for crossing 0 and larger than PI for crossing at the opposite end of your circle. When crossing the opposite end, we toggle cp_pi. When cp_pi is YES while crossing 0, we are guaranteed to have passed a full circle – since otherwise, cp_pi would have been toggled back to NO:

-(void)tick
{
    float yaw = [self zeroedYaw];
    if ((fabs(yaw) == PI) || (yaw == 0.0f)) return;

    if (yaw * prev_yaw < 0)
    {
        float d_yaw = fabs(yaw - prev_yaw);
        if (d_yaw > PI)
        {
            cp_pi = ! cp_pi;
        }
        else if (cp_pi)
        {
            // fire detection event
        }
    }
    prev_yaw = yaw;
}

Note that in order to make our life easier, we skip the detector function entirely if yaw is sitting right on one of the checkpoints.