public override void Update(float dt)
{
basisA.rotationMatrix = connectionA.orientationMatrix;
basisB.rotationMatrix = connectionB.orientationMatrix;
basisA.ComputeWorldSpaceAxes();
basisB.ComputeWorldSpaceAxes();
if (settings.mode == MotorMode.Servomechanism)
{
Quaternion rotation;
Toolbox.GetQuaternionBetweenNormalizedVectors(ref basisB.primaryAxis, ref basisA.primaryAxis, out rotation);
//Transform b's 'Y' axis so that it is perpendicular with a's 'X' axis for measurement.
Vector3 twistMeasureAxis;
Vector3.Transform(ref basisB.xAxis, 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 basisA.yAxis, out y);
Vector3.Dot(ref twistMeasureAxis, ref basisA.xAxis, out x);
var angle = (float) Math.Atan2(y, x);
//Compute goal velocity.
error = GetDistanceFromGoal(angle);
float absErrorOverDt = Math.Abs(error / dt);
float errorReduction;
settings.servo.springSettings.ComputeErrorReductionAndSoftness(dt, out errorReduction, out usedSoftness);
biasVelocity = Math.Sign(error) * MathHelper.Min(settings.servo.baseCorrectiveSpeed, absErrorOverDt) + error * errorReduction;
biasVelocity = MathHelper.Clamp(biasVelocity, -settings.servo.maxCorrectiveVelocity, settings.servo.maxCorrectiveVelocity);
}
else
{
biasVelocity = settings.velocityMotor.goalVelocity;
usedSoftness = settings.velocityMotor.softness / dt;
error = 0;
}
//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 basisA.primaryAxis, ref basisB.primaryAxis, 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;
//Update the maximum force
ComputeMaxForces(settings.maximumForce, dt);
//****** 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 / (usedSoftness + entryA + entryB);
}
