Computing angles between iPhones
As part of a physiology experiment we want to measure angles between limbs, for instance upper and lower arm, using iPhones. As a test I'm using 2 iPhones, each running the app SensorLog, to record the data.
In my test I take the variables:
motionQuaternionX.R
motionQuaternionY.R
motionQuaternionZ.R
motionQuaternionW.R
from each iPhone and compute the angle between these quaternions using the formula given in:
https://math.stackexchange.com/questions/90081/quaternion-distance?newreg=51f64d6d79e14956861a036db5d72ca6
in Jacobson's comment. It is:
θ=2arccos(q1,q2) (1)
There is also the formula there:
θ=arccos(2⟨q1,q2⟩^2−1) (2)
Where q1 and q2 are the 2 quaternions and the () brackets around them denote a dot product.
In my simple test I have the 2 phones lying flat on a table and rotate one of them through 90 deg till it is standing up on its bottom. I should get 90 deg, but in neither case do I. In (1) I see approx 70 deg, while in (2) I get around 100 deg.
Is this just due to errors in the gyros? And which formula is correct? Also we need to get a consistent 90 deg for 2 phones at right angles whatever the overall orientation of the pair. My result shows that this doesn't hold for either formula. It could be that this whole approach is flawed.
Any advice or pointers would be greatly appreciated.
Thanks
iphone angle quaternions
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
add a comment |
As part of a physiology experiment we want to measure angles between limbs, for instance upper and lower arm, using iPhones. As a test I'm using 2 iPhones, each running the app SensorLog, to record the data.
In my test I take the variables:
motionQuaternionX.R
motionQuaternionY.R
motionQuaternionZ.R
motionQuaternionW.R
from each iPhone and compute the angle between these quaternions using the formula given in:
https://math.stackexchange.com/questions/90081/quaternion-distance?newreg=51f64d6d79e14956861a036db5d72ca6
in Jacobson's comment. It is:
θ=2arccos(q1,q2) (1)
There is also the formula there:
θ=arccos(2⟨q1,q2⟩^2−1) (2)
Where q1 and q2 are the 2 quaternions and the () brackets around them denote a dot product.
In my simple test I have the 2 phones lying flat on a table and rotate one of them through 90 deg till it is standing up on its bottom. I should get 90 deg, but in neither case do I. In (1) I see approx 70 deg, while in (2) I get around 100 deg.
Is this just due to errors in the gyros? And which formula is correct? Also we need to get a consistent 90 deg for 2 phones at right angles whatever the overall orientation of the pair. My result shows that this doesn't hold for either formula. It could be that this whole approach is flawed.
Any advice or pointers would be greatly appreciated.
Thanks
iphone angle quaternions
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
add a comment |
As part of a physiology experiment we want to measure angles between limbs, for instance upper and lower arm, using iPhones. As a test I'm using 2 iPhones, each running the app SensorLog, to record the data.
In my test I take the variables:
motionQuaternionX.R
motionQuaternionY.R
motionQuaternionZ.R
motionQuaternionW.R
from each iPhone and compute the angle between these quaternions using the formula given in:
https://math.stackexchange.com/questions/90081/quaternion-distance?newreg=51f64d6d79e14956861a036db5d72ca6
in Jacobson's comment. It is:
θ=2arccos(q1,q2) (1)
There is also the formula there:
θ=arccos(2⟨q1,q2⟩^2−1) (2)
Where q1 and q2 are the 2 quaternions and the () brackets around them denote a dot product.
In my simple test I have the 2 phones lying flat on a table and rotate one of them through 90 deg till it is standing up on its bottom. I should get 90 deg, but in neither case do I. In (1) I see approx 70 deg, while in (2) I get around 100 deg.
Is this just due to errors in the gyros? And which formula is correct? Also we need to get a consistent 90 deg for 2 phones at right angles whatever the overall orientation of the pair. My result shows that this doesn't hold for either formula. It could be that this whole approach is flawed.
Any advice or pointers would be greatly appreciated.
Thanks
iphone angle quaternions
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
As part of a physiology experiment we want to measure angles between limbs, for instance upper and lower arm, using iPhones. As a test I'm using 2 iPhones, each running the app SensorLog, to record the data.
In my test I take the variables:
motionQuaternionX.R
motionQuaternionY.R
motionQuaternionZ.R
motionQuaternionW.R
from each iPhone and compute the angle between these quaternions using the formula given in:
https://math.stackexchange.com/questions/90081/quaternion-distance?newreg=51f64d6d79e14956861a036db5d72ca6
in Jacobson's comment. It is:
θ=2arccos(q1,q2) (1)
There is also the formula there:
θ=arccos(2⟨q1,q2⟩^2−1) (2)
Where q1 and q2 are the 2 quaternions and the () brackets around them denote a dot product.
In my simple test I have the 2 phones lying flat on a table and rotate one of them through 90 deg till it is standing up on its bottom. I should get 90 deg, but in neither case do I. In (1) I see approx 70 deg, while in (2) I get around 100 deg.
Is this just due to errors in the gyros? And which formula is correct? Also we need to get a consistent 90 deg for 2 phones at right angles whatever the overall orientation of the pair. My result shows that this doesn't hold for either formula. It could be that this whole approach is flawed.
Any advice or pointers would be greatly appreciated.
Thanks
iphone angle quaternions
iphone angle quaternions
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
asked Nov 13 '18 at 3:48
SpottiswoodeSpottiswoode
11
11
add a comment |
add a comment |
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