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Yaw is the object turning as if it is spinning on a lazy suzan (one of those spinning plate things you get in chinese restaurants), pitch is pointing the nose up or down, and roll is as if the object is doing a barrel roll.

My question is, do these directly relate to the x, y and z axes? as in, is yaw x, pitch y and roll z? Because If I orient a 3D plane forward using the direct x coordinate system (where z is forward, x is right and y is up) yaw pitch and roll would correspond to the y, x and z axes respectively.

Are they always defined by the axes or are they coordinate system specific?

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Yaw, pitch, and roll are coordinate-system-specific. They're also potentially orientation specific, if the system also allows 'local' mode in addition to 'global' mode.

For instance, I believe that traditionally engineering/architecure use z as the 'up' (out-of-the-page) axis. There are some game engines that do this, as well.

Keep in mind that the actual name of the axis (x, y, z) doesn't really matter - it's what they represent (and the expected order thereof) that does. For instance, if I pass [front, side, up], but I'm talking to something that expects [up, front, side], things aren't going to be the way I expect.

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