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Line 203: Moreover, typical implementations of [[arcsin]] and [[arccos]], also might have some numerical disadvantages near zero and one. Besides having these problems, some implementations use the equivalent expression<ref>{{cite journal\|last1=Blanco\|first1=Jose-Luis\|title=A tutorial on se (3) transformation parameterizations and on-manifold optimization\|journal=University of Malaga, Tech. Rep\|date=2010\|citeseerx=10.1.1.468.5407}}</ref>: :<math> \theta = \mbox{arcsin} (2(q_0 q_2 - ~~q_3~~ q_1 q_3)) </math> To safely generate all the orientations one needs to replace the arctan functions in computer code by [[atan2]]:

Conversion between quaternions and Euler angles: Difference between revisions