Maths - Conversion Quaternion to Euler

By: Nobody/Anonymous - nobody
file Quaternion to Euler Angles slight correction  
2006-02-24 07:14

Hello, 
 
First, congratulations on your excellent 3D maths site! It's been really useful, thanks a lot =) 
 
Now, on this page: https://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm 
 
When you consider the singularity at attitude -90 degrees, you ask: 
 
" have I made an error here? in the examples it seems to require: heading = -2 * atan2(x,w) " 
 
Actually, there is a problem with the atan2 arguments. Here: 
 

w = -z = 0.7071(c(1-3)) 
-x = y = 0.7071(s(1-3)) 
 
(...) 
 
w = -z = 0.7071(cos((heading-bank)/2)) 
x = -y = 0.7071(sin((heading-bank)/2)) <-- error 
 
(...) 
 
heading-bank = 2 * atan2(x,w) <-- resulting error 

 
The marked line should read "-x = y = 0.7071(sin((heading-bank)/2))", resulting in  
 
"heading-bank = 2 * atan2(-x,w)" 
or 
"heading-bank = 2 * atan2(y,w)" <-- would be nice to change both (heading+bank) and (heading-bank) expressions to this one 
 
Should work fine then! 
 
Vitor Barata


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