nh-rep/code/pre_processing/ParametricSample/Mathematics/ParticleSystem.h

// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2021
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13

#pragma once

#include <Mathematics/Vector.h>
#include <vector>

namespace gte
{
    template <int N, typename Real>
    class ParticleSystem
    {
    public:
        // Construction and destruction.  If a particle is to be immovable,
        // set its mass to std::numeric_limits<Real>::max().
        virtual ~ParticleSystem() = default;

        ParticleSystem(int numParticles, Real step)
            :
            mNumParticles(numParticles),
            mMass(numParticles),
            mInvMass(numParticles),
            mPosition(numParticles),
            mVelocity(numParticles),
            mStep(step),
            mHalfStep(step / (Real)2),
            mSixthStep(step / (Real)6),
            mPTmp(numParticles),
            mVTmp(numParticles),
            mPAllTmp(numParticles),
            mVAllTmp(numParticles)
        {
            std::fill(mMass.begin(), mMass.end(), (Real)0);
            std::fill(mInvMass.begin(), mInvMass.end(), (Real)0);
            std::fill(mPosition.begin(), mPosition.end(), Vector<N, Real>::Zero());
            std::fill(mVelocity.begin(), mVelocity.end(), Vector<N, Real>::Zero());
        }

        // Member access.
        inline int GetNumParticles() const
        {
            return mNumParticles;
        }

        void SetMass(int i, Real mass)
        {
            if ((Real)0 < mass && mass < std::numeric_limits<Real>::max())
            {
                mMass[i] = mass;
                mInvMass[i] = (Real)1 / mass;
            }
            else
            {
                mMass[i] = std::numeric_limits<Real>::max();
                mInvMass[i] = (Real)0;
            }
        }

        inline void SetPosition(int i, Vector<N, Real> const& position)
        {
            mPosition[i] = position;
        }

        inline void SetVelocity(int i, Vector<N, Real> const& velocity)
        {
            mVelocity[i] = velocity;
        }

        void SetStep(Real step)
        {
            mStep = step;
            mHalfStep = mStep / (Real)2;
            mSixthStep = mStep / (Real)6;
        }

        inline Real const& GetMass(int i) const
        {
            return mMass[i];
        }

        inline Vector<N, Real> const& GetPosition(int i) const
        {
            return mPosition[i];
        }

        inline Vector<N, Real> const& GetVelocity(int i) const
        {
            return mVelocity[i];
        }

        inline Real GetStep() const
        {
            return mStep;
        }

        // Update the particle positions based on current time and particle
        // state.  The Acceleration(...) function is called in this update
        // for each particle.  This function is virtual so that derived
        // classes can perform pre-update and/or post-update semantics.
        virtual void Update(Real time)
        {
            // Runge-Kutta fourth-order solver.
            Real halfTime = time + mHalfStep;
            Real fullTime = time + mStep;

            // Compute the first step.
            int i;
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPAllTmp[i].d1 = mVelocity[i];
                    mVAllTmp[i].d1 = Acceleration(i, time, mPosition, mVelocity);
                }
            }
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPTmp[i] = mPosition[i] + mHalfStep * mPAllTmp[i].d1;
                    mVTmp[i] = mVelocity[i] + mHalfStep * mVAllTmp[i].d1;
                }
                else
                {
                    mPTmp[i] = mPosition[i];
                    mVTmp[i].MakeZero();
                }
            }

            // Compute the second step.
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPAllTmp[i].d2 = mVTmp[i];
                    mVAllTmp[i].d2 = Acceleration(i, halfTime, mPTmp, mVTmp);
                }
            }
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPTmp[i] = mPosition[i] + mHalfStep * mPAllTmp[i].d2;
                    mVTmp[i] = mVelocity[i] + mHalfStep * mVAllTmp[i].d2;
                }
                else
                {
                    mPTmp[i] = mPosition[i];
                    mVTmp[i].MakeZero();
                }
            }

            // Compute the third step.
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPAllTmp[i].d3 = mVTmp[i];
                    mVAllTmp[i].d3 = Acceleration(i, halfTime, mPTmp, mVTmp);
                }
            }
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPTmp[i] = mPosition[i] + mStep * mPAllTmp[i].d3;
                    mVTmp[i] = mVelocity[i] + mStep * mVAllTmp[i].d3;
                }
                else
                {
                    mPTmp[i] = mPosition[i];
                    mVTmp[i].MakeZero();
                }
            }

            // Compute the fourth step.
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPAllTmp[i].d4 = mVTmp[i];
                    mVAllTmp[i].d4 = Acceleration(i, fullTime, mPTmp, mVTmp);
                }
            }
            for (i = 0; i < mNumParticles; ++i)
            {
                if (mInvMass[i] > (Real)0)
                {
                    mPosition[i] += mSixthStep * (mPAllTmp[i].d1 +
                        (Real)2 * (mPAllTmp[i].d2 + mPAllTmp[i].d3) + mPAllTmp[i].d4);

                    mVelocity[i] += mSixthStep * (mVAllTmp[i].d1 +
                        (Real)2 * (mVAllTmp[i].d2 + mVAllTmp[i].d3) + mVAllTmp[i].d4);
                }
            }
        }

    protected:
        // Callback for acceleration (ODE solver uses x" = F/m) applied to
        // particle i.  The positions and velocities are not necessarily
        // mPosition and mVelocity, because the ODE solver evaluates the
        // impulse function at intermediate positions.
        virtual Vector<N, Real> Acceleration(int i, Real time,
            std::vector<Vector<N, Real>> const& position,
            std::vector<Vector<N, Real>> const& velocity) = 0;

        int mNumParticles;
        std::vector<Real> mMass, mInvMass;
        std::vector<Vector<N, Real>> mPosition, mVelocity;
        Real mStep, mHalfStep, mSixthStep;

        // Temporary storage for the Runge-Kutta differential equation solver.
        struct Temporary
        {
            Vector<N, Real> d1, d2, d3, d4;
        };

        std::vector<Vector<N, Real>> mPTmp, mVTmp;
        std::vector<Temporary> mPAllTmp, mVAllTmp;
    };
}