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POHow to create a CMRotationMatrix on devices without gyroscope
 

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  1. POHow to create a CMRotationMatrix on devices without gyroscope
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    <p>I want to create an augmented reality view on the iPhone. As a starting point, I took a look at Apple's pARk demo project. There, however, the deviceMotion property is used to get the rotation matrix to do the camera transformation with. But since deviceMotion uses the gyroscope (available on the iPhone 4 and newer) and I want to support the 3GS as well (in fact, a 3GS is my only development device), I cannot use this approach. So I want to create the rotation matrix myself using the data available from the accelerometer and compass.</p> <p>Unfortunately, I lack the math skills to do so myself. Searching around, it seemed to me that <a href="http://rouel-projects.blogspot.de/p/calculations-with-iphones.html" rel="nofollow">this</a> is the most relevant hands-on guide for my problem, but following the implementation there doesn't seem to adapt to my problem (the POI-views only appear momentarily and seemingly more due to device movement than to its heading; I've posted my onDisplayLink method (the only method with major changes) below). I've tried to read up on the relevant math, but at this point I simply don't know enough about it to find an approach on my own or to find the error in my code. Any help, please?</p> <p><em>Edit:</em> I've since recognized that the sensor data should better be stored in doubles than in ints and added a bit of smoothing. Now I can see more clearly how POIs that should appear from the side upon device rotation rather come down from above. Maybe that helps pointing to what's wrong.</p> <pre><code>CMAccelerometerData* orientation = motionManager.accelerometerData; CMAcceleration acceleration = orientation.acceleration; vec4f_t normalizedAccelerometer; vec4f_t normalizedMagnetometer; xG = (acceleration.x * kFilteringFactor) + (xG * (1.0 - kFilteringFactor)); yG = (acceleration.y * kFilteringFactor) + (yG * (1.0 - kFilteringFactor)); zG = (acceleration.z * kFilteringFactor) + (zG * (1.0 - kFilteringFactor)); xB = (heading.x * kFilteringFactor) + (xB * (1.0 - kFilteringFactor)); yB = (heading.y * kFilteringFactor) + (yB * (1.0 - kFilteringFactor)); zB = (heading.z * kFilteringFactor) + (zB * (1.0 - kFilteringFactor)); double accelerometerMagnitude = sqrt(pow(xG, 2) + pow(yG, 2) + pow(zG, 2)); double magnetometerMagnitude = sqrt(pow(xB, 2) + pow(yB, 2) + pow(zB, 2)); normalizedAccelerometer[0] = xG/accelerometerMagnitude; normalizedAccelerometer[1] = yG/accelerometerMagnitude; normalizedAccelerometer[2] = zG/accelerometerMagnitude; normalizedAccelerometer[3] = 1.0f; normalizedMagnetometer[0] = xB/magnetometerMagnitude; normalizedMagnetometer[1] = yB/magnetometerMagnitude; normalizedMagnetometer[2] = zB/magnetometerMagnitude; normalizedMagnetometer[3] = 1.0f; vec4f_t eastDirection; eastDirection[0] = normalizedAccelerometer[1] * normalizedMagnetometer[2] - normalizedAccelerometer[2] * normalizedMagnetometer[1]; eastDirection[1] = normalizedAccelerometer[0] * normalizedMagnetometer[2] - normalizedAccelerometer[2] * normalizedMagnetometer[0]; eastDirection[2] = normalizedAccelerometer[0] * normalizedMagnetometer[1] - normalizedAccelerometer[1] * normalizedMagnetometer[0]; eastDirection[3] = 1.0f; double eastDirectionMagnitude = sqrt(pow(eastDirection[0], 2) + pow(eastDirection[1], 2) + pow(eastDirection[2], 2)); vec4f_t normalizedEastDirection; normalizedEastDirection[0] = eastDirection[0]/eastDirectionMagnitude; normalizedEastDirection[1] = eastDirection[1]/eastDirectionMagnitude; normalizedEastDirection[2] = eastDirection[2]/eastDirectionMagnitude; normalizedEastDirection[3] = 1.0f; vec4f_t northDirection; northDirection[0] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * xB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[0]; northDirection[1] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * yB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[1]; northDirection[2] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * zB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[2]; northDirection[3] = 1.0f; double northDirectionMagnitude; northDirectionMagnitude = sqrt(pow(northDirection[0], 2) + pow(northDirection[1], 2) + pow(northDirection[2], 2)); vec4f_t normalizedNorthDirection; normalizedNorthDirection[0] = northDirection[0]/northDirectionMagnitude; normalizedNorthDirection[1] = northDirection[1]/northDirectionMagnitude; normalizedNorthDirection[2] = northDirection[2]/northDirectionMagnitude; normalizedNorthDirection[3] = 1.0f; CMRotationMatrix r; r.m11 = normalizedEastDirection[0]; r.m21 = normalizedEastDirection[1]; r.m31 = normalizedEastDirection[2]; r.m12 = normalizedNorthDirection[0]; r.m22 = normalizedNorthDirection[1]; r.m32 = normalizedNorthDirection[2]; r.m13 = normalizedAccelerometer[0]; r.m23 = normalizedAccelerometer[1]; r.m33 = normalizedAccelerometer[2]; transformFromCMRotationMatrix(cameraTransform, &amp;r); [self setNeedsDisplay]; </code></pre> <p>When the device is placed on a table and roughly (using Compass.app) pointing to north, I log this data:</p> <pre><code>Accelerometer: x: -0.016692, y: 0.060852, z: -0.998007 Magnetometer: x: -0.016099, y: 0.256711, z: -0.966354 North Direction x: 0.011472, y: 8.561041, z:0.521807 Normalized North Direction x: 0.001338, y: 0.998147, z:0.060838 East Direction x: 0.197395, y: 0.000063, z:-0.003305 Normalized East Direction x: 0.999860, y: 0.000319, z:-0.016742 </code></pre> <p>Does that appear sane?</p> <p><em>Edit 2:</em> I have updated the assignment of r to one that apparently leads me halfway to my goal: when the device is upright, I now see the landmarks near the horizontal plane; however, they are about 90º clock-wards off their expected location. Also, the output after the movement suggested by Beta:</p> <pre><code>Accelerometer: x: 0.074289, y: -0.997192, z: -0.009475 Magnetometer: x: 0.031341, y: -0.986382, z: -0.161458 North Direction x: -1.428996, y: -0.057306, z:-5.172881 Normalized North Direction x: -0.266259, y: -0.010678, z:-0.963842 East Direction x: 0.151658, y: -0.011698, z:-0.042025 Normalized East Direction x: 0.961034, y: -0.074126, z:-0.266305 </code></pre>
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    1. COI don't have means to test your code, but I see some opportunities. Can you verify that `eastDirection` and `northDirection` work as you intended?
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    2. COI'm not sure, so I've added some logged data along with the edit above. Does that help?
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    3. COLooks good; North is +Y and East is +X. You should verify that when you lift up the North edge, rotating about the South edge by 90 degrees, East is still +X and North is -Z. Now, what do you want to do with the rotation matrix, and how will you know when it's working?
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