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copied!<ol> <li>In your case we can say rotation of the device is equal to rotation of the device normal (rotation around the normal itself is just ignored like you specified it)</li> <li><a href="http://developer.apple.com/library/ios/#documentation/CoreMotion/Reference/CMAttitude_Class/Reference/Reference.html" rel="nofollow">CMAttitude</a> which you can get via <a href="http://developer.apple.com/library/ios/documentation/CoreMotion/Reference/CMMotionManager_Class/Reference/Reference.html#//apple_ref/occ/instp/CMMotionManager/deviceMotion" rel="nofollow">CMMotionManager.deviceMotion</a> provides the rotation <strong>relative to a reference frame</strong>. Its properties quaternion, roation matrix and Euler angles are just different representations.</li> <li>The reference frame can be specified when you start device motion updates using CMMotionManager's <a href="http://developer.apple.com/library/ios/documentation/CoreMotion/Reference/CMMotionManager_Class/Reference/Reference.html#//apple_ref/occ/instm/CMMotionManager/startDeviceMotionUpdatesUsingReferenceFrame:toQueue:withHandler:" rel="nofollow">startDeviceMotionUpdatesUsingReferenceFrame</a> method. Until iOS 4 you had to use <a href="http://developer.apple.com/library/ios/documentation/CoreMotion/Reference/CMAttitude_Class/Reference/Reference.html#//apple_ref/occ/instm/CMAttitude/multiplyByInverseOfAttitude:" rel="nofollow">multiplyByInverseOfAttitude</a></li> </ol> <p>Putting this together you just have to multiply the quaternion in the <em>right way</em> with the normal vector when the device lies face up on the table. Now we need this <em>right way</em> of quaternion multiplication that represents a rotation: According to <a href="http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation#Rotating_vectors" rel="nofollow">Rotating vectors</a> this is done by:</p> <p><strong>n = q * e * q'</strong> where <strong>q</strong> is the quaternion delivered by CMAttitude [w, (x, y, z)], <strong>q'</strong> is its conjugate [w, (-x, -y, -z)] and <strong>e</strong> is the quaternion representation of the face up normal [0, (0, 0, 1)]. Unfortunately Apple's CMQuaternion is struct and thus you need a small helper class.</p> <pre><code>Quaternion e = [[Quaternion alloc] initWithValues:0 y:0 z:1 w:0]; CMQuaternion cm = deviceMotion.attitude.quaternion; Quaternion quat = [[Quaternion alloc] initWithValues:cm.x y:cm.y z:cm.z w: cm.w]; Quaternion quatConjugate = [[Quaternion alloc] initWithValues:-cm.x y:-cm.y z:-cm.z w: cm.w]; [quat multiplyWithRight:e]; [quat multiplyWithRight:quatConjugate]; // quat.x, .y, .z contain your normal </code></pre> <p>Quaternion.h:</p> <pre><code>@interface Quaternion : NSObject { double w; double x; double y; double z; } @property(readwrite, assign)double w; @property(readwrite, assign)double x; @property(readwrite, assign)double y; @property(readwrite, assign)double z; </code></pre> <p>Quaternion.m:</p> <pre><code>- (Quaternion*) multiplyWithRight:(Quaternion*)q { double newW = w*q.w - x*q.x - y*q.y - z*q.z; double newX = w*q.x + x*q.w + y*q.z - z*q.y; double newY = w*q.y + y*q.w + z*q.x - x*q.z; double newZ = w*q.z + z*q.w + x*q.y - y*q.x; w = newW; x = newX; y = newY; z = newZ; // one multiplication won't denormalise but when multipling again and again // we should assure that the result is normalised return self; } - (id) initWithValues:(double)w2 x:(double)x2 y:(double)y2 z:(double)z2 { if ((self = [super init])) { x = x2; y = y2; z = z2; w = w2; } return self; } </code></pre> <p>I know quaternions are a bit weird at the beginning but once you have got an idea they are really brilliant. It helped me to imagine a quaternion as a rotation around the vector (x, y, z) and w is (cosine of) the angle. </p> <p>If you need to do more with them take a look at <a href="http://code.google.com/p/cocoamath/" rel="nofollow">cocoamath</a> open source project. The classes Quaternion and its extension QuaternionOperations are a good starting point.</p> <p>For the sake of completeness, yes you can do it with matrix multiplication as well:</p> <p><strong>n = M * e</strong></p> <p>But I would prefer the quaternion way it saves you all the trigonometric hassle and performs better.</p>

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