public static void ComputeCorrectiveImpulse(ref BodyVelocities wsvA, ref BodyVelocities wsvB, ref TangentFriction.Projection data, ref Jacobians jacobians,
ref Vector <float> maximumImpulse, ref Vector2Wide accumulatedImpulse, out Vector2Wide correctiveCSI)
{
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvA.Linear, jacobians.LinearA, out var csvaLinear);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvA.Angular, jacobians.AngularA, out var csvaAngular);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvB.Linear, jacobians.LinearA, out var csvbLinear);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvB.Angular, jacobians.AngularB, out var csvbAngular);
//Note that the velocity in constraint space is (csvaLinear - csvbLinear + csvaAngular + csvbAngular).
//The subtraction there is due to sharing the linear jacobian between both bodies3D.
//In the following, we need to compute the constraint space *violating* velocity- which is the negation of the above velocity in constraint space.
//So, (csvbLinear - csvaLinear - (csvaAngular + csvbAngular)).
Vector2Wide.Subtract(csvbLinear, csvaLinear, out var csvLinear);
Vector2Wide.Add(csvaAngular, csvbAngular, out var csvAngular);
Vector2Wide.Subtract(csvLinear, csvAngular, out var csv);
Symmetric2x2Wide.TransformWithoutOverlap(csv, data.EffectiveMass, out var csi);
var previousAccumulated = accumulatedImpulse;
Vector2Wide.Add(accumulatedImpulse, csi, out accumulatedImpulse);
//The maximum force of friction depends upon the normal impulse. The maximum is supplied per iteration.
Vector2Wide.Length(accumulatedImpulse, out var accumulatedMagnitude);
//Note division by zero guard.
var scale = Vector.Min(Vector <float> .One, maximumImpulse / Vector.Max(new Vector <float>(1e-16f), accumulatedMagnitude));
Vector2Wide.Scale(accumulatedImpulse, scale, out accumulatedImpulse);
Vector2Wide.Subtract(accumulatedImpulse, previousAccumulated, out correctiveCSI);
}
public static void WarmStart(ref Vector3Wide tangentX, ref Vector3Wide tangentY, ref Projection projection, ref BodyInertias inertiaA,
ref Vector2Wide accumulatedImpulse, ref BodyVelocities wsvA)
{
ComputeJacobians(ref tangentX, ref tangentY, ref projection.OffsetA, out var jacobians);
//TODO: If the previous frame and current frame are associated with different time steps, the previous frame's solution won't be a good solution anymore.
//To compensate for this, the accumulated impulse should be scaled if dt changes.
ApplyImpulse(ref jacobians, ref inertiaA, ref accumulatedImpulse, ref wsvA);
}
public static void ApplyImpulse(ref Jacobians jacobians, ref BodyInertias inertiaA,
ref Vector2Wide correctiveImpulse, ref BodyVelocities wsvA)
{
Matrix2x3Wide.Transform(correctiveImpulse, jacobians.LinearA, out var linearImpulseA);
Matrix2x3Wide.Transform(correctiveImpulse, jacobians.AngularA, out var angularImpulseA);
BodyVelocities correctiveVelocityA;
Vector3Wide.Scale(linearImpulseA, inertiaA.InverseMass, out correctiveVelocityA.Linear);
Symmetric3x3Wide.TransformWithoutOverlap(angularImpulseA, inertiaA.InverseInertiaTensor, out correctiveVelocityA.Angular);
Vector3Wide.Add(wsvA.Linear, correctiveVelocityA.Linear, out wsvA.Linear);
Vector3Wide.Add(wsvA.Angular, correctiveVelocityA.Angular, out wsvA.Angular);
}
public static void ApplyImpulse(ref Jacobians jacobians, ref BodyInertias inertiaA, ref BodyInertias inertiaB,
ref Vector2Wide correctiveImpulse, ref BodyVelocities wsvA, ref BodyVelocities wsvB)
{
Matrix2x3Wide.Transform(correctiveImpulse, jacobians.LinearA, out var linearImpulseA);
Matrix2x3Wide.Transform(correctiveImpulse, jacobians.AngularA, out var angularImpulseA);
Matrix2x3Wide.Transform(correctiveImpulse, jacobians.AngularB, out var angularImpulseB);
BodyVelocities correctiveVelocityA, correctiveVelocityB;
Vector3Wide.Scale(linearImpulseA, inertiaA.InverseMass, out correctiveVelocityA.Linear);
Symmetric3x3Wide.TransformWithoutOverlap(angularImpulseA, inertiaA.InverseInertiaTensor, out correctiveVelocityA.Angular);
Vector3Wide.Scale(linearImpulseA, inertiaB.InverseMass, out correctiveVelocityB.Linear);
Symmetric3x3Wide.TransformWithoutOverlap(angularImpulseB, inertiaB.InverseInertiaTensor, out correctiveVelocityB.Angular);
Vector3Wide.Add(wsvA.Linear, correctiveVelocityA.Linear, out wsvA.Linear);
Vector3Wide.Add(wsvA.Angular, correctiveVelocityA.Angular, out wsvA.Angular);
Vector3Wide.Subtract(wsvB.Linear, correctiveVelocityB.Linear, out wsvB.Linear); //note subtract- we based it on the LinearA jacobian.
Vector3Wide.Add(wsvB.Angular, correctiveVelocityB.Angular, out wsvB.Angular);
}
public static void ComputeCorrectiveImpulse(ref BodyVelocities wsvA, ref Projection data, ref Jacobians jacobians,
ref Vector <float> maximumImpulse, ref Vector2Wide accumulatedImpulse, out Vector2Wide correctiveCSI)
{
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvA.Linear, jacobians.LinearA, out var csvaLinear);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(wsvA.Angular, jacobians.AngularA, out var csvaAngular);
Vector2Wide.Add(csvaLinear, csvaAngular, out var csv);
//Required corrective velocity is the negation of the current constraint space velocity.
Symmetric2x2Wide.TransformWithoutOverlap(csv, data.EffectiveMass, out var negativeCSI);
var previousAccumulated = accumulatedImpulse;
Vector2Wide.Subtract(accumulatedImpulse, negativeCSI, out accumulatedImpulse);
//The maximum force of friction depends upon the normal impulse. The maximum is supplied per iteration.
Vector2Wide.Length(accumulatedImpulse, out var accumulatedMagnitude);
//Note division by zero guard.
var scale = Vector.Min(Vector <float> .One, maximumImpulse / Vector.Max(new Vector <float>(1e-16f), accumulatedMagnitude));
Vector2Wide.Scale(accumulatedImpulse, scale, out accumulatedImpulse);
Vector2Wide.Subtract(accumulatedImpulse, previousAccumulated, out correctiveCSI);
}
public static void Solve(ref Vector3Wide tangentX, ref Vector3Wide tangentY,
ref Projection projection, ref BodyInertias inertiaA, ref Vector <float> maximumImpulse, ref Vector2Wide accumulatedImpulse, ref BodyVelocities wsvA)
{
ComputeJacobians(ref tangentX, ref tangentY, ref projection.OffsetA, out var jacobians);
ComputeCorrectiveImpulse(ref wsvA, ref projection, ref jacobians, ref maximumImpulse, ref accumulatedImpulse, out var correctiveCSI);
ApplyImpulse(ref jacobians, ref inertiaA, ref correctiveCSI, ref wsvA);
}
