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Getting quaternion from forward and up

Started by SunTzu Jun 17, 2007 at 3:19 AM 1 replies 3.7k views

Original Post

Jun 17, 2007 at 3:19 AM

I have a (unit) forward vector and a (unit) up vector (known to be orthogonal to one another). How do I get the quaternion that rotates to such an orientation? In other words: there is some quaternion that would transform (0,1,0) into the up vector and (0,0,1) into the forward vector. How do I calculate what that quaternion is? I'm actually implementing this in C#/XNA so have all the .NET and XMA framework functions available (none of them appear to provide this automatically), but I can easily translate from other languages or straight mathematics if required. Quaternions confuse the heck out of me. :-)

DaBookshah

Jun 17, 2007 at 3:36 AM

I'm no expert, and I don't really understand quaternions either, but here's an idea:

You can easily represent the rotation transformation as a 3x3 matrix. If you want to transform (1,0,0) into (a,b,c), (0,1,0) into (d,e,f) and (0,0,1) into (g,h,i), then your matrix is

a d g
b e h
c f i

(in the standard maths notation). Then you just need to convert this orthogonal matrix into a quaternion. Just use google - "quaternion rotation matrix" or "quaternion orthogonal matrix", I turned up this. I think that does it?

SunTzu

Jun 17, 2007 at 3:49 AM

Brilliant. Rate++.

Especially easy as the .NET framework provides Matrix.Forward, Matrix.Up and Matrix.Right as properties, and Quaternion.CreateFromRotationMatrix as well. It was just a question of taking the step from "transform (0,1,0) into the up vector" etc., into "transform (0,1,0) into (d,e,f)... then your matrix is..." etc. Many thanks!

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