Real-Time Physics Simulation Forum

Re: Quaternion Integration: velocity and acceleration

2013-05-01T06:20:17+00:00

Oh, I found the solution to my problem but thanks.

Code:

//Velocity Verlet//RotationsVector3 newW = iInv * t;Quaternion halfQ= PIKHelper.ScaleQ(q, 0.5f);Quaternion qDot = halfQ * (new Quaternion(w.x, w.y, w.z, 0));float qd = Quaternion.Dot(qDot,qDot)* -2.0f;Quaternion qDotDot = halfQ * (new Quaternion(newW.x, newW.y, newW.z, qd));

Statistics: Posted by SinisterMephisto — Wed May 01, 2013 6:20 am

Re: Quaternion Integration: velocity and acceleration

2013-04-30T10:56:25+00:00

So I use slerp in my engine for animation. The idea between slerp is that you know where you want to go and you want to go somewhere in between. For physics, you don't know where you're going to end up, but you have a deltaAngularVelocity. So you do an Euler integration. I think Bullet does a straight Quaternion integration. Here is what Bullet does:

Code:

btQuaternion dorn (axis.x(),axis.y(),axis.z(),btCos( fAngle*timeStep*btScalar(0.5) ));btQuaternion orn0 = curTrans.getRotation();btQuaternion predictedOrn = dorn * orn0;predictedOrn.normalize();predictedTransform.setRotation(predictedOrn);

This is what I do:

Code:

   MEHVector4 axisAngle = m_angularVelocity;   axisAngle.SetW(0.0);   axisAngle.Normalize();   axisAngle.SetW(m_angularVelocity.Magnitude() * elapsedSecs);   MEHMatrix4 angularMov;   angularMov.ToRotateFromAxisAngle(axisAngle);      MEHVector3 pos = m_worldMat[3];   m_worldMat *= angularMov;   m_worldMat[3] = pos;

HTH,
Mike

Statistics: Posted by mikeshafer — Tue Apr 30, 2013 10:56 am

Quaternion Integration: velocity and acceleration

2013-04-12T18:12:48+00:00

I was wondering how you guys implemented your rotational integrations.
I know most books only talk about the first derivative of orientation and most engines only implement the first.

I saw these functions last night and they were in my head all morning. I am currently on the train home and i though i should just ask before i arrive.

Code:

q'(q,w) = 1/2qw  //W = anglar velocity transformed into quarternion [w,0]. you knew that.

But while going through some of Insomniac's publications on their site I read that
We should not multiply quaternions with scalar values (As quaternions should ideally be unit when we multiply them with other vectors)

Hence 0.5f*q should be

Code:

slerp(Quaternion.Identity, q, 0.5f);

But every one I have seen scaled theirs (Basically a lerp) //I guess the inaccuracy is negligible

Secondly Angular acceleration has me a bit confused.

Code:

//q = orientation//W = anglar velocity transformed into Quarternion [w,dot].//dot = -2w'.w' //. = dot product//w' = q' //first derivativeq"(q,w,w') = 1/2qw

What is the order of operations for -2w'.w'?
Do you use Quaternion.Dot(-2w',w') or -2 * Quaternion.Dot(w',w')?

the final code

Code:

//mimicing s= ut +1/2at^2q(t+dt) = q(t) + q'*dt + 1/2q"dt^2;

Is there really a need for the angular acceleration (Second derivative)?
Would all these lerping and damping that occurs after not increase the amount of error in the system?
If you use the physics for some controlled system would it not save you all that extra control logic if every thing was slerped?

This is probably stupid and I am probably over thinking it.

Statistics: Posted by SinisterMephisto — Fri Apr 12, 2013 6:12 pm