RotationQuatConstraintPart.h

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// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)
// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
// SPDX-License-Identifier: MIT
 
#pragma once
 
#include <Jolt/Physics/Body/Body.h>
#include <Jolt/Physics/StateRecorder.h>
 
JPH_NAMESPACE_BEGIN
 
class RotationQuatConstraintPart
{
private:
    JPH_INLINE bool             ApplyVelocityStep(Body &ioBody1, Body &ioBody2, Vec3Arg inLambda) const
    {
        // Apply impulse if delta is not zero
        if (inLambda != Vec3::sZero())
        {
            // Calculate velocity change due to constraint
            //
            // Impulse:
            // P = J^T lambda
            //
            // Euler velocity integration: 
            // v' = v + M^-1 P
            if (ioBody1.IsDynamic())
                ioBody1.GetMotionProperties()->SubAngularVelocityStep(mInvI1_JPT.Multiply3x3(inLambda));
            if (ioBody2.IsDynamic())
                ioBody2.GetMotionProperties()->AddAngularVelocityStep(mInvI2_JPT.Multiply3x3(inLambda));
            return true;
        }
 
        return false;
    }
 
public:
    static Quat                 sGetInvInitialOrientation(const Body &inBody1, const Body &inBody2)
    {
        // q20 = q10 r0 
        // <=> r0 = q10^-1 q20 
        // <=> r0^-1 = q20^-1 q10
        //
        // where:
        //
        // q20 = initial orientation of body 2
        // q10 = initial orientation of body 1
        // r0 = initial rotation rotation from body 1 to body 2
        return inBody2.GetRotation().Conjugated() * inBody1.GetRotation();
    }
 
    inline void                 CalculateConstraintProperties(const Body &inBody1, Mat44Arg inRotation1, const Body &inBody2, Mat44Arg inRotation2, QuatArg inInvInitialOrientation)
    {
        // Calculate: JP = 1/2 A ML(q1^*) MR(q2 r0^*) A^T
        Mat44 jp = (Mat44::sQuatLeftMultiply(0.5f * inBody1.GetRotation().Conjugated()) * Mat44::sQuatRightMultiply(inBody2.GetRotation() * inInvInitialOrientation)).GetRotationSafe();
 
        // Calculate properties used during constraint solving
        Mat44 invi1 = inBody1.IsDynamic()? inBody1.GetMotionProperties()->GetInverseInertiaForRotation(inRotation1) : Mat44::sZero();
        Mat44 invi2 = inBody2.IsDynamic()? inBody2.GetMotionProperties()->GetInverseInertiaForRotation(inRotation2) : Mat44::sZero();
        mInvI1_JPT = invi1.Multiply3x3RightTransposed(jp);
        mInvI2_JPT = invi2.Multiply3x3RightTransposed(jp);
 
        // Calculate effective mass: K^-1 = (J M^-1 J^T)^-1 
        // = (JP * I1^-1 * JP^T + JP * I2^-1 * JP^T)^-1
        // = (JP * (I1^-1 + I2^-1) * JP^T)^-1
        mEffectiveMass = jp.Multiply3x3(invi1 + invi2).Multiply3x3RightTransposed(jp).Inversed3x3();
        mEffectiveMass_JP = mEffectiveMass.Multiply3x3(jp);
    }
 
    inline void                 WarmStart(Body &ioBody1, Body &ioBody2, float inWarmStartImpulseRatio)
    {
        mTotalLambda *= inWarmStartImpulseRatio;
        ApplyVelocityStep(ioBody1, ioBody2, mTotalLambda);
    }
 
    inline bool                 SolveVelocityConstraint(Body &ioBody1, Body &ioBody2)
    {
        // Calculate lagrange multiplier:
        //
        // lambda = -K^-1 (J v + b)
        Vec3 lambda = mEffectiveMass_JP.Multiply3x3(ioBody1.GetAngularVelocity() - ioBody2.GetAngularVelocity());
        mTotalLambda += lambda;
        return ApplyVelocityStep(ioBody1, ioBody2, lambda);
    }
 
    inline bool                 SolvePositionConstraint(Body &ioBody1, Body &ioBody2, QuatArg inInvInitialOrientation, float inBaumgarte) const
    {
        // Calculate constraint equation
        Vec3 c = (ioBody1.GetRotation().Conjugated() * ioBody2.GetRotation() * inInvInitialOrientation).GetXYZ();
        if (c != Vec3::sZero())
        {
            // Calculate lagrange multiplier (lambda) for Baumgarte stabilization:
            //
            // lambda = -K^-1 * beta / dt * C
            //
            // We should divide by inDeltaTime, but we should multiply by inDeltaTime in the Euler step below so they're cancelled out
            Vec3 lambda = -inBaumgarte * mEffectiveMass * c;
 
            // Directly integrate velocity change for one time step
            //
            // Euler velocity integration: 
            // dv = M^-1 P
            //
            // Impulse:
            // P = J^T lambda
            //
            // Euler position integration:
            // x' = x + dv * dt
            //
            // Note we don't accumulate velocities for the stabilization. This is using the approach described in 'Modeling and 
            // Solving Constraints' by Erin Catto presented at GDC 2007. On slide 78 it is suggested to split up the Baumgarte 
            // stabilization for positional drift so that it does not actually add to the momentum. We combine an Euler velocity 
            // integrate + a position integrate and then discard the velocity change.
            if (ioBody1.IsDynamic())
                ioBody1.SubRotationStep(mInvI1_JPT.Multiply3x3(lambda));
            if (ioBody2.IsDynamic())
                ioBody2.AddRotationStep(mInvI2_JPT.Multiply3x3(lambda));
            return true;
        }
 
        return false;
    }
 
    Vec3                        GetTotalLambda() const
    {
        return mTotalLambda;
    }
 
    void                        SaveState(StateRecorder &inStream) const
    {
        inStream.Write(mTotalLambda);
    }
 
    void                        RestoreState(StateRecorder &inStream)
    {
        inStream.Read(mTotalLambda);
    }
 
private:    
    Mat44                       mInvI1_JPT;
    Mat44                       mInvI2_JPT;
    Mat44                       mEffectiveMass;
    Mat44                       mEffectiveMass_JP;
    Vec3                        mTotalLambda { Vec3::sZero() };
};
 
JPH_NAMESPACE_END