Rotate model using quaternion

Question

Currently I have this to rotate my 3D model that rotates on it's local axis independent from the world's axis:

// Rotate model with Right Thumbstick
modelRotation -= pController.ThumbSticks.Right.X * mRotSpeed; // float value

What I'm trying to do is rotate the model using quaternion and not by a matrix.

I've searched for tutorials, but have found none that explains thoroughly on how to achieve this. Does anyone know how to I can use quaternions to rotate my model or a complete tutorial?

Answer 1

A quaternion has a vector part and a scalar part. To represent a rotation, a quaternion has to be of unit length. A quaternion that rotates by angle alpha around an axis represented by a normalized vector v is calculated like this:

q = [v*sin(alpha/2), cos(alpha/2)]

The rotation follows the right hand rule.

Now to apply this quaternion to a vector or a point you take your x, y and z and write it as a quaternion. Given a vector v, you can write it in quaternion form as such:

qv = [vx, vy, vz, 0]

Now to transform this vector by a quaternion you premultiply it by the rotation quaternion and postmultiply it by the inverse of the rotation quaternion, as such:

v_rotated = q*qv*q(-1), the (-1) means the quaternion is inversed.

To get an inverse of a quaternion you have to calculate it's conjugate and divide it by the quaternion's length squared, but since our quaternion is of unit length, this just means calculating the conjugate. You calculate the conjugate by negating the vector part of the quaternion.

You do this for every vertex like you would with a matrix.

This is from Jason Gregory's "Game Engine Architecture".

Answer 2

//in the fields section:
Quaternion modelQuat;    

//in the update method:
// Rotate model with Right Thumbstick
    modelRotation -= pController.ThumbSticks.Right.X * mRotSpeed; // float value

    modelQuat = Quaternion.CreateRotationY(modelRotation);


//Later, in the draw call when setting the effect:
    effect.World = Matrix.CreateFromQuaternion(modelQuat);// (and if needed) * Matrix.createTranslation(someLocationVector);

Is this something like what your looking for?