RackAndPinionConstraintPart.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 RackAndPinionConstraintPart
{
    JPH_INLINE bool             ApplyVelocityStep(Body &ioBody1, Body &ioBody2, float inLambda) const
    {
        // Apply impulse if delta is not zero
        if (inLambda != 0.0f)
        {
            // Calculate velocity change due to constraint
            //
            // Impulse:
            // P = J^T lambda
            //
            // Euler velocity integration:
            // v' = v + M^-1 P
            ioBody1.GetMotionProperties()->AddAngularVelocityStep(inLambda * mInvI1_A);
            ioBody2.GetMotionProperties()->SubLinearVelocityStep(inLambda * mRatio_InvM2_B);
            return true;
        }
 
        return false;
    }
 
public:
    inline void                 CalculateConstraintProperties(const Body &inBody1, Vec3Arg inWorldSpaceHingeAxis, const Body &inBody2, Vec3Arg inWorldSpaceSliderAxis, float inRatio)
    {
        JPH_ASSERT(inWorldSpaceHingeAxis.IsNormalized(1.0e-4f));
        JPH_ASSERT(inWorldSpaceSliderAxis.IsNormalized(1.0e-4f));
 
        // Calculate: I1^-1 a
        mInvI1_A = inBody1.GetMotionProperties()->MultiplyWorldSpaceInverseInertiaByVector(inBody1.GetRotation(), inWorldSpaceHingeAxis);
 
        // Calculate: r/m2 b
        float inv_m2 = inBody2.GetMotionProperties()->GetInverseMass();
        mRatio_InvM2_B = inRatio * inv_m2 * inWorldSpaceSliderAxis;
 
        // K^-1 = 1 / (J M^-1 J^T) = 1 / (a^T I1^-1 a + 1/m2 * r^2 * b . b)
        float inv_effective_mass = (inWorldSpaceHingeAxis.Dot(mInvI1_A) + inv_m2 * Square(inRatio));
        if (inv_effective_mass == 0.0f)
            Deactivate();
        else
            mEffectiveMass = 1.0f / inv_effective_mass;
    }
 
    inline void                 Deactivate()
    {
        mEffectiveMass = 0.0f;
        mTotalLambda = 0.0f;
    }
 
    inline bool                 IsActive() const
    {
        return mEffectiveMass != 0.0f;
    }
 
    inline void                 WarmStart(Body &ioBody1, Body &ioBody2, float inWarmStartImpulseRatio)
    {
        mTotalLambda *= inWarmStartImpulseRatio;
        ApplyVelocityStep(ioBody1, ioBody2, mTotalLambda);
    }
 
    inline bool                 SolveVelocityConstraint(Body &ioBody1, Vec3Arg inWorldSpaceHingeAxis, Body &ioBody2, Vec3Arg inWorldSpaceSliderAxis, float inRatio)
    {
        // Lagrange multiplier is:
        //
        // lambda = -K^-1 (J v + b)
        float lambda = mEffectiveMass * (inRatio * inWorldSpaceSliderAxis.Dot(ioBody2.GetLinearVelocity()) - inWorldSpaceHingeAxis.Dot(ioBody1.GetAngularVelocity()));
        mTotalLambda += lambda; // Store accumulated impulse
 
        return ApplyVelocityStep(ioBody1, ioBody2, lambda);
    }
 
    float                       GetTotalLambda() const
    {
        return mTotalLambda;
    }
 
    inline bool                 SolvePositionConstraint(Body &ioBody1, Body &ioBody2, float inC, float inBaumgarte) const
    {
        // Only apply position constraint when the constraint is hard, otherwise the velocity bias will fix the constraint
        if (inC != 0.0f)
        {
            // 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
            float lambda = -mEffectiveMass * inBaumgarte * inC;
 
            // 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.AddRotationStep(lambda * mInvI1_A);
            if (ioBody2.IsDynamic())
                ioBody2.SubPositionStep(lambda * mRatio_InvM2_B);
            return true;
        }
 
        return false;
    }
 
    void                        SaveState(StateRecorder &inStream) const
    {
        inStream.Write(mTotalLambda);
    }
 
    void                        RestoreState(StateRecorder &inStream)
    {
        inStream.Read(mTotalLambda);
    }
 
private:
    Vec3                        mInvI1_A;
    Vec3                        mRatio_InvM2_B;
    float                       mEffectiveMass = 0.0f;
    float                       mTotalLambda = 0.0f;
};
 
JPH_NAMESPACE_END