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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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    (There are many such curves, so you'd need to add further conditions to make the problem better-posed.)2012-04-30

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Given a know trajectory in the space, you can introduce for each point three vectors: Tangent, Normal and Binormal vectors. These image should help you visualize them: enter image description hereenter image description here

The condition of having no yaw (i think) should be equivalent that the direction of "Up" should be the same of the direction of the Normal vector. "Heading" and "Right" can be any two orthogonal vector in the plane T-B, but I think that setting T="Heading" and B="Right" should be the most intuitive way of visualizing an airplane.

There you can found reference for how calculate them given the curve: http://en.wikipedia.org/wiki/Differential_geometry_of_curves or http://en.wikipedia.org/wiki/Frenet-Serret_formulas

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    It's totaly possible that my ans$w$er $w$asn't the one that @James requires, I think that he already has find his path (a bezier curve) and now he need to find how to follow it withoyt yaw. If the question was "how to build a smooth path?", he can still use the fact that the problem "find a smooth path with no yaw" it's the same of "find a smooth path", but I don't know what approach suggest him for the latter problem.2012-04-30