public static void Prestep(ref Vector3Wide tangentX, ref Vector3Wide tangentY, ref Vector3Wide offsetA, ref Vector3Wide offsetB,
ref BodyInertias inertiaA, ref BodyInertias inertiaB,
out TangentFrictionProjection projection)
{
ComputeJacobians(ref tangentX, ref tangentY, ref offsetA, ref offsetB, out var jacobians);
//Compute effective mass matrix contributions.
Triangular2x2Wide.SandwichScale(ref jacobians.LinearA, ref inertiaA.InverseMass, out var linearContributionA);
Triangular2x2Wide.SandwichScale(ref jacobians.LinearA, ref inertiaB.InverseMass, out var linearContributionB);
Triangular3x3Wide.MatrixSandwich(ref jacobians.AngularA, ref inertiaA.InverseInertiaTensor, out var angularContributionA);
Triangular3x3Wide.MatrixSandwich(ref jacobians.AngularB, ref inertiaB.InverseInertiaTensor, out var angularContributionB);
//No softening; this constraint is rigid by design. (It does support a maximum force, but that is distinct from a proper damping ratio/natural frequency.)
Triangular2x2Wide.Add(ref linearContributionA, ref linearContributionB, out var linear);
Triangular2x2Wide.Add(ref angularContributionA, ref angularContributionB, out var angular);
Triangular2x2Wide.Add(ref linear, ref angular, out var inverseEffectiveMass);
Triangular2x2Wide.InvertWithoutOverlap(ref inverseEffectiveMass, out projection.EffectiveMass);
projection.OffsetA = offsetA;
projection.OffsetB = offsetB;
//Note that friction constraints have no bias velocity. They target zero velocity.
}
public static void ComputeCorrectiveImpulse(ref BodyVelocities wsvA, ref BodyVelocities wsvB, ref TangentFrictionProjection data, ref Jacobians jacobians,
ref Vector <float> maximumImpulse, ref Vector2Wide accumulatedImpulse, out Vector2Wide correctiveCSI)
{
Matrix2x3Wide.TransformByTransposeWithoutOverlap(ref wsvA.LinearVelocity, ref jacobians.LinearA, out var csvaLinear);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(ref wsvA.AngularVelocity, ref jacobians.AngularA, out var csvaAngular);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(ref wsvB.LinearVelocity, ref jacobians.LinearA, out var csvbLinear);
Matrix2x3Wide.TransformByTransposeWithoutOverlap(ref wsvB.AngularVelocity, ref 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 bodies.
//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(ref csvbLinear, ref csvaLinear, out var csvLinear);
Vector2Wide.Add(ref csvaAngular, ref csvbAngular, out var csvAngular);
Vector2Wide.Subtract(ref csvLinear, ref csvAngular, out var csv);
Triangular2x2Wide.TransformBySymmetricWithoutOverlap(ref csv, ref data.EffectiveMass, out var csi);
var previousAccumulated = accumulatedImpulse;
Vector2Wide.Add(ref accumulatedImpulse, ref csi, out accumulatedImpulse);
//The maximum force of friction depends upon the normal impulse. The maximum is supplied per iteration.
Vector2Wide.Length(ref 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(ref accumulatedImpulse, ref scale, out accumulatedImpulse);
Vector2Wide.Subtract(ref accumulatedImpulse, ref previousAccumulated, out correctiveCSI);
}
public static void Solve(ref Vector3Wide tangentX, ref Vector3Wide tangentY, ref TangentFrictionProjection projection, ref BodyInertias inertiaA, ref BodyInertias inertiaB, ref Vector <float> maximumImpulse, ref Vector2Wide accumulatedImpulse, ref BodyVelocities wsvA, ref BodyVelocities wsvB)
{
ComputeJacobians(ref tangentX, ref tangentY, ref projection.OffsetA, ref projection.OffsetB, out var jacobians);
ComputeCorrectiveImpulse(ref wsvA, ref wsvB, ref projection, ref jacobians, ref maximumImpulse, ref accumulatedImpulse, out var correctiveCSI);
ApplyImpulse(ref jacobians, ref inertiaA, ref inertiaB, ref correctiveCSI, ref wsvA, ref wsvB);
}
public static void WarmStart(ref Vector3Wide tangentX, ref Vector3Wide tangentY, ref TangentFrictionProjection projection, ref BodyInertias inertiaA, ref BodyInertias inertiaB,
ref Vector2Wide accumulatedImpulse, ref BodyVelocities wsvA, ref BodyVelocities wsvB)
{
ComputeJacobians(ref tangentX, ref tangentY, ref projection.OffsetA, ref projection.OffsetB, 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 inertiaB, ref accumulatedImpulse, ref wsvA, ref wsvB);
}