No, no, no. Wrong again. Please study basic trigonometry and read your own sources. Your own link proves you wrong.
The formula for conversion from quat to ypr involves arctan and arcsin. These functions yield multiple answers.
Additionally your own Wikipedia link explicitly states the existence of multiple answers, and that traditionally atan and asin in programming languages yield only one answer. I quote:
"Note, however, that the arctan and arcsin functions implemented in computer languages only produce results between −π/2 and π/2, and for three rotations between −π/2 and π/2 one does not obtain all possible orientations. To generate all the orientations one needs to replace the arctan functions in computer code by atan2"
Either way you misunderstand the math behind quaternions and you lack a basic grasp of trigonometry. Assuming you read your own Wikipedia link, what I said is categorically true.
The formula for conversion from quat to ypr involves arctan and arcsin. These functions yield multiple answers.
Additionally your own Wikipedia link explicitly states the existence of multiple answers, and that traditionally atan and asin in programming languages yield only one answer. I quote:
"Note, however, that the arctan and arcsin functions implemented in computer languages only produce results between −π/2 and π/2, and for three rotations between −π/2 and π/2 one does not obtain all possible orientations. To generate all the orientations one needs to replace the arctan functions in computer code by atan2"
Either way you misunderstand the math behind quaternions and you lack a basic grasp of trigonometry. Assuming you read your own Wikipedia link, what I said is categorically true.