XNA Help - Slerping the KoolAid

Question

I'm having some SLERP issues and was hoping one of you guys' could help me with your expertise...

(The following code is the Update method of a component whose responsibility is to rotates it's actor towards a given target using SLERP over the course of multiple frames...)

The problem I'm having is that the following causes the actor to rotate on some arbitrary axis when it is facing any direction other than the negative Z axis (works just fine when pointed down negative Z)...

public override void Update(GameTime gameTime)
    {
        if (this.Status == AnimationStatus.Running)
        {
            TransformComponent transformComponent = this.Owner.GetComponent<TransformComponent>();

            Vector3 position = transformComponent.Transform.Translation;

            Vector3 forwardVector = Vector3.Normalize(transformComponent.Transform.Forward);

            float dot = (float)Math.Round(
                Vector3.Dot(
                    forwardVector,
                    Vector3.Normalize(_targetVector)),
                4);

            if (dot == 1)
            {
                this.Status = AnimationStatus.Finished;

                return;
            }

            _targetVector.Normalize();

            Vector3 rotationAxis = 
                Vector3.Normalize(
                    Vector3.Cross(
                        _targetVector,
                        forwardVector));

            float rotationAngle = MathUtilities.GetSignedAngle(
                forwardVector,
                _targetVector);

            _slerpAmount += (float)gameTime.ElapsedGameTime.Milliseconds / 20000f;

            Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);

            Quaternion qEnd = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);

            Quaternion qSlerp = Quaternion.Slerp(
                qStart,
                qStart * qEnd,
                _slerpAmount);

            Matrix rotation = Matrix.CreateFromQuaternion(qSlerp);

            rotation.Translation = position;

            PhysicsComponent physicsComponent = this.Owner.GetComponent<PhysicsComponent>();

            physicsComponent.KinematicMove(rotation);
        }
    }

...and if anyone's curious, here's the GetSignedAngle() method...

public static float GetSignedAngle(
        Vector3 a,
        Vector3 b)
    {
        a.Normalize();

        b.Normalize();

        float theta = (float)Math.Acos(
            Vector3.Dot(
                a,
                b));

        Vector3 normal = Vector3.Normalize(
            Vector3.Cross(
                b,
                a));

        Vector3 v3 = Vector3.Normalize(
            Vector3.Cross(
                a,
                normal));

        if (Vector3.Dot(
            v3,
            b) > 0)
        {
            theta *= -1;
        }

        return theta;
    }

....the really odd thing (and proof that SLERP isn't working as I'd expect it to), is that if I replace the code that performs the SLERP...

_slerpAmount += (float)gameTime.ElapsedGameTime.Milliseconds / 20000f;

            Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);

            Quaternion qEnd = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);

            Quaternion qSlerp = Quaternion.Slerp(
                qStart,
                qStart * qEnd,
                _slerpAmount);

            Matrix rotation = Matrix.CreateFromQuaternion(qSlerp);

...with a regular old rotation transformation like so...

Matrix rotation = transformComponent.Transform *
              Matrix.CreateFromAxisAngle(
                rotationAxis, rotationAngle);

..then the object is rotated correctly (hoever it is instant and so I lose the rotation "animation").

If anyone has any ideas as to how this could be happening or just a suggestion on how I can make this code better please let me know.

EDIT: So I've resolved the issue but I'm not 100% sure why using matrices resolves the issue as I thought concatenating quaternions worked the same way. Here's the updated Slerpage...

Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);

Quaternion qEnd = Quaternion.CreateFromRotationMatrix( transformComponent.Transform * Matrix.CreateFromAxisAngle( rotationAxis, rotationAngle));

Quaternion qSlerp = Quaternion.Slerp( qStart, qEnd, _slerpAmount);

Matrix rotation = Matrix.CreateFromQuaternion(qSlerp);

...so as you can see I'm just converting the rotation axis and angle into a matrix first, transforming the original matrix by the rotation then creating a quaternion. But as Steve pointed out below, this is essentially the same thing I was doing with the quaternions?!?! Does anyone have any insight into this? Thanks again!

Thanks!

Answer 1

your axis and angle represent only the rotation change necessary to go from where you are to where you want to be.

qStart represents where you are.

Your qEnd isn't the goal orientation but only the rotation change necessary to get there.

try:

Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);

Quaternion qChange = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);

Quaternion qEnd = qChange * qStart;//or your favorite method of concatenation 

EDIT sorry, I looked again at your code and saw that you are effectively doing that in the slerp statement already. But it would be worth changing the order that you combine them. In Xna, matrices combine left to right but quaternions combine right to left.