Quaternions, rotate a model and align with a direction

Question

Suppose you have quaternion that describes the rotation of a 3D Model.

What I want to do is, given an Object (with rotationQuaternion, side vector...), I want to align it to a target point.

For a spaceship, I want the cockpit to point to a target.

Here is some code I have ... It's not doing what I want and I don't know why...

        if (_target._ray.Position != _obj._ray.Position)
        {
            Vector3 vec = Vector3.Normalize(_target._ray.Position - _obj._ray.Position);
            float angle = (float)Math.Acos(Vector3.Dot(vec, _obj._ray.Direction));
            Vector3 cross = Vector3.Cross(vec, _obj._ray.Direction);

            if (cross == Vector3.Zero)
                cross = _obj._side;

            _obj._rotationQuaternion *= Quaternion.CreateFromAxisAngle(cross,angle);
        }
        // Updates direction, up, side vectors and model Matrix
        _obj.UpdateMatrix();

after some time the rotationQuaternion is filled with almost Zero at X,Y,Z and W

Any help? Thanks ;-)

Answer 1

Your code's a bit funky.

if (_target._ray.Position != _obj._ray.Position)
{

This may or may not be correct. Clearly, you've overridden the equals comparator. The correct thing be be doing here would be to ensure that the dot-product between the two (unit-length) rays is close to 1. If the rays have the same origin, then presumably have equal 'positions' means they're the same.

  Vector3 vec = Vector3.Normalize(_target._ray.Position - _obj._ray.Position);

This seems particularly wrong. Unless the minus operator has been overridden in a strange way, subtracting this way doesn't make sense.

Here's pseudocode for what I recommend:

normalize3(targetRay);
normalize3(objectRay);
angleDif = acos(dotProduct(targetRay,objectRay));
if (angleDif!=0) {
  orthoRay = crossProduct(objectRay,targetRay);
  normalize3(orthoRay);
  deltaQ = quaternionFromAxisAngle(orthoRay,angleDif);
  rotationQuaternion = deltaQ*rotationQuaternion;
  normalize4(rotationQuaternion);
}

Two things to note here:

1. Quaternions are not commutative. I've assumed that your quaternions are rotating column vectors; so I put deltaQ on the left. It's not clear what your *= operator is doing.
2. It's important to regularly normalize your quaternions after multiplication. Otherwise small errors accumulate and they drift away from unit length causing all manner of grief.