iPhone - understanding iPhone rotation

Question

I am banging my head on the wall trying to understand this. See the next picture.

Suppose I have an iPhone resting on a table. At this time the rotation readings thr

Answer 1

I was unable to replicate the same results. Using the (free) Gyroscope app, reporting as roll, pitch, yaw I get (0, 0, 0) for position A, then (-90, 0, 0) for B, (-90, 0, 180) for C (which actually causes the device to face away from me, unlike in your diagram), then (-45, 0, 180) for D.

Even flipping that because you seem to be listing as yaw, roll, pitch, that's still (0, 0, 0) -> (0, -90, 0) -> (180, -90, 0) -> (180, -45, 0). Adding a roll by -90 before reporting would make the pitch and yaw axes parallel, creating gimbal lock as mentioned by faster typers than I.

The basic problem is that any attempt to describe rotation in three axes gives an implicit order of rotations — it's "rotate this much around x, then this much around y, then this much about z". Whatever order you pick, there's always a possibility for the rotation around the first axis to align the other two axes. Orientation is three dimensional, so can be described with three numbers (eg, by using unit quaternions but leaving the fourth term implicit), but not by Euler angles.

EDIT: in reference to your comment above, you can obtain delta movements by registering a handler with -startDeviceMotionUpdatesToQueue:withHandler:. That'll receive a series of CMDeviceMotions, from which you can look at the rotationRate member.

Answer 2

The accelerometer measures the sum of two acceleration vectors: gravity and user acceleration. User acceleration is the acceleration that the user imparts to the device. Because Core Motion is able to track a device’s attitude using both the gyroscope and the accelerometer, it can differentiate between gravity and user acceleration

This might be helpful for you:

an-absolute-degree-measurement

Answer 3

Given the case that you can live with delta movements, you can use "quaternion difference" operation. Let's say you have a previous rotation as quaternion called q1 and the current one q2. Then you can calculate the delta dQ between them so that q2 = q1*dQ is valid. All you have to do is build the inverse of q1 (q1^(-1)) and then you get:

dQ = q1^(-1) * q2

If deviceMotionInterval is high enough, you always have handy small Euler angles without any 90° singularities or other beasty stuff. The possible drawback of this solution might be a slight drift because of error propagation and the lack of feedback from your virtual space. Example: if you have your iPhone on a table showing a cube and then do a sequence of rotations, you might find a angular displacment of the cube when you put the phone back in starting position.

[EDIT:Forgot some part] To get rid of the drifting effect, you "only" need a way to express your last object's real position (q1) as a quaternion i.e. coordinates in your app as displayed on the screen. If you use tools like Unity it might be just reading the appropriate property of an the object. If you don't have easy access to it, you may have the possibility to track this position manually.

If you want to read more about this take a look at 3D math primer for graphics and game development, by Fletcher Dunn,Ian Parberry page 168.

Answer 4

Euler angles are not that precise for decribing arbitrary rotation like quaternions or rotation matrices. There is often more than one set of angles to decribe a rotation and thus it's not unique.

[Edit:] As stated by Harinder core motion converts the angles into canonical representation i.e. there are some constraints - I am not sure but think the pitch angle is limited to [-90;90].

Have a look at Gimbal Lock or some similar articles about the phenomenon.

Answer 5

This question looks relevant:

iphone - core motion range of yaw, pitch and roll