# math - Given a set of Euler Angles, (Pitch, Yaw, Roll) how to find alternate set that describes same 3D orientation?

I have a nice quaternion to euler equation that is sometimes returning a non-intuitive set of angles.

For example:

• Pitch: 129
• Yaw: -85
• Roll: 126

I would like to programatically find alternate rotations such that Pitch and Roll are between -90 and 90. Yaw can be 0 to 360.

[EDIT] Pitch is constrained to -90 to +90 and Roll is constrained to -180 to +180.

Basically, you want to prevent the orientation to go beyond the pole. It is very easy to do that:

First, check if pitch is beyond the pole (i.e. greater than 90° or smaller than -90°). In that case, do the following:

``````add 180° to yaw
set new pitch to 180° - old pitch (or -180° - old pitch in the case of south pole)
``````

This is basically all. You can also adapt the new angles as follows:

``````while(yaw < 0)
yaw += 360
while(yaw > 360)
yaw -= 360
while(roll < -180)
roll += 360
while(roll > 180)
roll -= 360
``````