# How to fly a curve from one heading to another using only roll and pitch.

I have 3 perpendicular vectors representing an object in 3d space...

Heading
Right
Up


...and I would like to be able to 'fly' this object so that it ends up at a specific point and heading using only roll and pitch (no yaw) so that the object follows a smooth flightpath.

This is for spaceship AI.

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I think you need to add a little more detail. What are the dynamics of the object? –  copper.hat Apr 27 '12 at 16:34
Your question is, in mathematical terms, more or less: «given points $A$ and $B$ and orthonormal ordered bases $O_A$ and $O_B$, how do I find a curve going from $A$ to $B$ such that at each of those points its Frenet frame is $O_A$ and $O_B$, respectively, and which is made up of Bezier segments?» –  Mariano Suárez-Alvarez Apr 30 '12 at 19:22
(There are many such curves, so you'd need to add further conditions to make the problem better-posed.) –  Mariano Suárez-Alvarez Apr 30 '12 at 19:24