How to get the effect of a roll axis as a sum of yaw and pitch axes?

I have two axes, and I need to add 'roll' to them in a way that would change the yaw/pitch but not actually add a roll third axis. I don't really know what calculations to use for this, and I couldn't really figure out how to do such a thing without adding a third axis.

enter image description here

the red dot in this picture shows an example pitch/yaw, as an example, imagine the yaw is 0 and the pitch is 25. the green circle shows 'fake roll'. how would I apply, using an equation of some sort, 35 degrees of roll to the red dot to move its position to the blue dot's.

thanks in advance, sorry for my improper capitalization.

  • $\begingroup$ If you yaw by $90$ degrees, then the (rotated) pitch axis will align with the original roll axis. $\endgroup$ – David K Apr 5 '15 at 2:09

I'm not sure I understand what rotations you are trying to do. If I understood correctly I think the resulting point will be here:

(sin(25)*cos(35), sin(25)*sin(35))


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