DualAxisConstraintPart.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>
#include <Jolt/Math/Vector.h>
#include <Jolt/Math/Matrix.h>
 
JPH_NAMESPACE_BEGIN
 
class DualAxisConstraintPart
{
public:
    using Vec2 = Vector<2>;
    using Mat22 = Matrix<2, 2>;
 
private:
    JPH_INLINE bool             ApplyVelocityStep(Body &ioBody1, Body &ioBody2, Vec3Arg inN1, Vec3Arg inN2, const Vec2 &inLambda) const
    {
        // Apply impulse if delta is not zero
        if (!inLambda.IsZero())
        {
            // Calculate velocity change due to constraint
            //
            // Impulse:
            // P = J^T lambda
            //
            // Euler velocity integration: 
            // v' = v + M^-1 P
            Vec3 impulse = inN1 * inLambda[0] + inN2 * inLambda[1];
            if (ioBody1.IsDynamic())
            {
                MotionProperties *mp1 = ioBody1.GetMotionProperties();
                mp1->SubLinearVelocityStep(mp1->GetInverseMass() * impulse);
                mp1->SubAngularVelocityStep(mInvI1_R1PlusUxN1 * inLambda[0] + mInvI1_R1PlusUxN2 * inLambda[1]);
            }
            if (ioBody2.IsDynamic())
            {
                MotionProperties *mp2 = ioBody2.GetMotionProperties();
                mp2->AddLinearVelocityStep(mp2->GetInverseMass() * impulse);
                mp2->AddAngularVelocityStep(mInvI2_R2xN1 * inLambda[0] + mInvI2_R2xN2 * inLambda[1]);
            }
            return true;
        }
 
        return false;
    }
    
    inline void                 CalculateLagrangeMultiplier(const Body &inBody1, const Body &inBody2, Vec3Arg inN1, Vec3Arg inN2, Vec2 &outLambda) const
    {
        // Calculate lagrange multiplier:
        //
        // lambda = -K^-1 (J v + b)
        Vec3 delta_lin = inBody1.GetLinearVelocity() - inBody2.GetLinearVelocity();
        Vec2 jv;
        jv[0] = inN1.Dot(delta_lin) + mR1PlusUxN1.Dot(inBody1.GetAngularVelocity()) - mR2xN1.Dot(inBody2.GetAngularVelocity());
        jv[1] = inN2.Dot(delta_lin) + mR1PlusUxN2.Dot(inBody1.GetAngularVelocity()) - mR2xN2.Dot(inBody2.GetAngularVelocity());
        outLambda = mEffectiveMass * jv;
    }
 
public:
    inline void                 CalculateConstraintProperties(const Body &inBody1, Mat44Arg inRotation1, Vec3Arg inR1PlusU, const Body &inBody2, Mat44Arg inRotation2, Vec3Arg inR2, Vec3Arg inN1, Vec3Arg inN2)
    {
        JPH_ASSERT(inN1.IsNormalized(1.0e-5f));
        JPH_ASSERT(inN2.IsNormalized(1.0e-5f));
 
        // Calculate properties used during constraint solving
        mR1PlusUxN1 = inR1PlusU.Cross(inN1);
        mR1PlusUxN2 = inR1PlusU.Cross(inN2);
        mR2xN1 = inR2.Cross(inN1);
        mR2xN2 = inR2.Cross(inN2);
 
        // Calculate effective mass: K^-1 = (J M^-1 J^T)^-1, eq 59
        Mat22 inv_effective_mass;
        if (inBody1.IsDynamic())
        {
            const MotionProperties *mp1 = inBody1.GetMotionProperties();
            Mat44 inv_i1 = mp1->GetInverseInertiaForRotation(inRotation1);
            mInvI1_R1PlusUxN1 = inv_i1.Multiply3x3(mR1PlusUxN1);
            mInvI1_R1PlusUxN2 = inv_i1.Multiply3x3(mR1PlusUxN2);
 
            inv_effective_mass(0, 0) = mp1->GetInverseMass() + mR1PlusUxN1.Dot(mInvI1_R1PlusUxN1);
            inv_effective_mass(0, 1) = mR1PlusUxN1.Dot(mInvI1_R1PlusUxN2);
            inv_effective_mass(1, 0) = mR1PlusUxN2.Dot(mInvI1_R1PlusUxN1);
            inv_effective_mass(1, 1) = mp1->GetInverseMass() + mR1PlusUxN2.Dot(mInvI1_R1PlusUxN2);
        }
        else
        {
            JPH_IF_DEBUG(mInvI1_R1PlusUxN1 = Vec3::sNaN();)
            JPH_IF_DEBUG(mInvI1_R1PlusUxN2 = Vec3::sNaN();)
 
            inv_effective_mass = Mat22::sZero();
        }
 
        if (inBody2.IsDynamic())
        {
            const MotionProperties *mp2 = inBody2.GetMotionProperties();
            Mat44 inv_i2 = mp2->GetInverseInertiaForRotation(inRotation2);  
            mInvI2_R2xN1 = inv_i2.Multiply3x3(mR2xN1);
            mInvI2_R2xN2 = inv_i2.Multiply3x3(mR2xN2);
 
            inv_effective_mass(0, 0) += mp2->GetInverseMass() + mR2xN1.Dot(mInvI2_R2xN1);
            inv_effective_mass(0, 1) += mR2xN1.Dot(mInvI2_R2xN2);
            inv_effective_mass(1, 0) += mR2xN2.Dot(mInvI2_R2xN1);
            inv_effective_mass(1, 1) += mp2->GetInverseMass() + mR2xN2.Dot(mInvI2_R2xN2);
        }
        else
        {
            JPH_IF_DEBUG(mInvI2_R2xN1 = Vec3::sNaN();)
            JPH_IF_DEBUG(mInvI2_R2xN2 = Vec3::sNaN();)
        }
 
        if (!mEffectiveMass.SetInversed(inv_effective_mass))
        {
            JPH_ASSERT(false, "Determinant is zero!");
            Deactivate();
        }
    }
 
    inline void                 Deactivate()
    {
        mEffectiveMass.SetZero();
        mTotalLambda.SetZero();
    }
 
    inline bool                 IsActive() const
    {
        return !mEffectiveMass.IsZero();
    }
 
    inline void                 WarmStart(Body &ioBody1, Body &ioBody2, Vec3Arg inN1, Vec3Arg inN2, float inWarmStartImpulseRatio)
    {
        mTotalLambda *= inWarmStartImpulseRatio;
        ApplyVelocityStep(ioBody1, ioBody2, inN1, inN2, mTotalLambda);
    }
 
    inline bool                 SolveVelocityConstraint(Body &ioBody1, Body &ioBody2, Vec3Arg inN1, Vec3Arg inN2)
    {
        Vec2 lambda;
        CalculateLagrangeMultiplier(ioBody1, ioBody2, inN1, inN2, lambda);
        
        // Store accumulated lambda
        mTotalLambda += lambda; 
        
        return ApplyVelocityStep(ioBody1, ioBody2, inN1, inN2, lambda);
    }
    
    inline bool                 SolvePositionConstraint(Body &ioBody1, Body &ioBody2, Vec3Arg inU, Vec3Arg inN1, Vec3Arg inN2, float inBaumgarte) const
    {
        Vec2 c;
        c[0] = inU.Dot(inN1);
        c[1] = inU.Dot(inN2);
        if (!c.IsZero())
        {
            // 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
            Vec2 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.
            Vec3 impulse = inN1 * lambda[0] + inN2 * lambda[1];
            if (ioBody1.IsDynamic())
            {
                ioBody1.SubPositionStep(ioBody1.GetMotionProperties()->GetInverseMass() * impulse);
                ioBody1.SubRotationStep(mInvI1_R1PlusUxN1 * lambda[0] + mInvI1_R1PlusUxN2 * lambda[1]);
            }
            if (ioBody2.IsDynamic())
            {
                ioBody2.AddPositionStep(ioBody2.GetMotionProperties()->GetInverseMass() * impulse);
                ioBody2.AddRotationStep(mInvI2_R2xN1 * lambda[0] + mInvI2_R2xN2 * lambda[1]);
            }
            return true;
        }
 
        return false;
    }
 
    inline void                 SetTotalLambda(const Vec2 &inLambda)
    {
        mTotalLambda = inLambda;
    }
 
    inline const Vec2 &         GetTotalLambda() const
    {
        return mTotalLambda;
    }
 
    void                        SaveState(StateRecorder &inStream) const
    {
        inStream.Write(mTotalLambda);
    }
 
    void                        RestoreState(StateRecorder &inStream)
    {
        inStream.Read(mTotalLambda);
    }
 
private:
    Vec3                        mR1PlusUxN1;
    Vec3                        mR1PlusUxN2;
    Vec3                        mR2xN1;
    Vec3                        mR2xN2;
    Vec3                        mInvI1_R1PlusUxN1;
    Vec3                        mInvI1_R1PlusUxN2;
    Vec3                        mInvI2_R2xN1;
    Vec3                        mInvI2_R2xN2;
    Mat22                       mEffectiveMass;
    Vec2                        mTotalLambda { Vec2::sZero() };
};
 
JPH_NAMESPACE_END