public override void Update(float dt)
{
Vector3 aAxisY, aAxisZ;
Vector3 bAxisY;
Matrix3x3.Transform(ref localAxisA, ref connectionA.orientationMatrix, out worldAxisA);
Matrix3x3.Transform(ref aLocalAxisY, ref connectionA.orientationMatrix, out aAxisY);
Matrix3x3.Transform(ref aLocalAxisZ, ref connectionA.orientationMatrix, out aAxisZ);
Matrix3x3.Transform(ref localAxisB, ref connectionB.orientationMatrix, out worldAxisB);
Matrix3x3.Transform(ref bLocalAxisY, ref connectionB.orientationMatrix, out bAxisY);
Quaternion rotation;
Toolbox.GetQuaternionBetweenNormalizedVectors(ref worldAxisB, ref worldAxisA, out rotation);
//Transform b's 'Y' axis so that it is perpendicular with a's 'X' axis for measurement.
Vector3 twistMeasureAxis;
Vector3.Transform(ref bAxisY, ref rotation, out twistMeasureAxis);
//By dotting the measurement vector with a 2d plane's axes, we can get a local X and Y value.
float y, x;
Vector3.Dot(ref twistMeasureAxis, ref aAxisZ, out y);
Vector3.Dot(ref twistMeasureAxis, ref aAxisY, out x);
error = (float) Math.Atan2(y, x);
//Debug.WriteLine("Angle: " + angle);
//The nice thing about this approach is that the jacobian entry doesn't flip.
//Instead, the error can be negative due to the use of Atan2.
//This is important for limits which have a unique high and low value.
//Compute the jacobian.
Vector3.Add(ref worldAxisA, ref worldAxisB, out jacobianB);
if (jacobianB.LengthSquared() < Toolbox.Epsilon)
{
//A nasty singularity can show up if the axes are aligned perfectly.
//In a 'real' situation, this is impossible, so just ignore it.
isActiveInSolver = false;
return;
}
jacobianB.Normalize();
jacobianA.X = -jacobianB.X;
jacobianA.Y = -jacobianB.Y;
jacobianA.Z = -jacobianB.Z;
//****** VELOCITY BIAS ******//
//Compute the correction velocity.
float errorReduction;
springSettings.ComputeErrorReductionAndSoftness(dt, out errorReduction, out softness);
biasVelocity = MathHelper.Clamp(-error * errorReduction, -maxCorrectiveVelocity, maxCorrectiveVelocity);
//****** EFFECTIVE MASS MATRIX ******//
//Connection A's contribution to the mass matrix
float entryA;
Vector3 transformedAxis;
if (connectionA.isDynamic)
{
Matrix3x3.Transform(ref jacobianA, ref connectionA.inertiaTensorInverse, out transformedAxis);
Vector3.Dot(ref transformedAxis, ref jacobianA, out entryA);
}
else
entryA = 0;
//Connection B's contribution to the mass matrix
float entryB;
if (connectionB.isDynamic)
{
Matrix3x3.Transform(ref jacobianB, ref connectionB.inertiaTensorInverse, out transformedAxis);
Vector3.Dot(ref transformedAxis, ref jacobianB, out entryB);
}
else
entryB = 0;
//Compute the inverse mass matrix
velocityToImpulse = 1 / (softness + entryA + entryB);
}
