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/// @author Ken Museth
///
/// @file tools/LevelSetAdvect.h
///
/// @brief Hyperbolic advection of narrow-band level sets

#ifndef OPENVDB_TOOLS_LEVEL_SET_ADVECT_HAS_BEEN_INCLUDED
#define OPENVDB_TOOLS_LEVEL_SET_ADVECT_HAS_BEEN_INCLUDED

#include <tbb/parallel_for.h>
#include <tbb/parallel_reduce.h>
#include <openvdb/Platform.h>
#include "LevelSetTracker.h"
#include "VelocityFields.h" // for EnrightField
#include <openvdb/math/FiniteDifference.h>
//#include <openvdb/util/CpuTimer.h>
#include <functional>


namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tools {

/// @brief  Hyperbolic advection of narrow-band level sets in an
/// external velocity field
///
/// The @c FieldType template argument below refers to any functor
/// with the following interface (see tools/VelocityFields.h
/// for examples):
///
/// @code
/// class VelocityField {
///   ...
/// public:
///   openvdb::VectorType operator() (const openvdb::Coord& xyz, ValueType time) const;
///   ...
/// };
/// @endcode
///
/// @note The functor method returns the velocity field at coordinate
/// position xyz of the advection grid, and for the specified
/// time. Note that since the velocity is returned in the local
/// coordinate space of the grid that is being advected, the functor
/// typically depends on the transformation of that grid. This design
/// is chosen for performance reasons. Finally we will assume that the
/// functor method is NOT threadsafe (typically uses a ValueAccessor)
/// and that its lightweight enough that we can copy it per thread.
///
/// The @c InterruptType template argument below refers to any class
/// with the following interface:
/// @code
/// class Interrupter {
///   ...
/// public:
///   void start(const char* name = nullptr) // called when computations begin
///   void end()                             // called when computations end
///   bool wasInterrupted(int percent=-1)    // return true to break computation
///};
/// @endcode
///
/// @note If no template argument is provided for this InterruptType
/// the util::NullInterrupter is used which implies that all
/// interrupter calls are no-ops (i.e. incurs no computational overhead).
///

template<typename GridT,
         typename FieldT     = EnrightField<typename GridT::ValueType>,
         typename InterruptT = util::NullInterrupter>
class LevelSetAdvection
{
public:
    using GridType = GridT;
    using TrackerT = LevelSetTracker<GridT, InterruptT>;
    using LeafRange = typename TrackerT::LeafRange;
    using LeafType = typename TrackerT::LeafType;
    using BufferType = typename TrackerT::BufferType;
    using ValueType = typename TrackerT::ValueType;
    using VectorType = typename FieldT::VectorType;

    /// Main constructor
    LevelSetAdvection(GridT& grid, const FieldT& field, InterruptT* interrupt = nullptr):
        mTracker(grid, interrupt), mField(field),
        mSpatialScheme(math::HJWENO5_BIAS),
        mTemporalScheme(math::TVD_RK2) {}

    virtual ~LevelSetAdvection() {}

    /// @brief Return the spatial finite difference scheme
    math::BiasedGradientScheme getSpatialScheme() const { return mSpatialScheme; }
    /// @brief Set the spatial finite difference scheme
    void setSpatialScheme(math::BiasedGradientScheme scheme) { mSpatialScheme = scheme; }

    /// @brief Return the temporal integration scheme
    math::TemporalIntegrationScheme getTemporalScheme() const { return mTemporalScheme; }
    /// @brief Set the spatial finite difference scheme
    void setTemporalScheme(math::TemporalIntegrationScheme scheme) { mTemporalScheme = scheme; }

    /// @brief Return the spatial finite difference scheme
    math::BiasedGradientScheme getTrackerSpatialScheme() const {
        return mTracker.getSpatialScheme();
    }
    /// @brief Set the spatial finite difference scheme
    void setTrackerSpatialScheme(math::BiasedGradientScheme scheme) {
        mTracker.setSpatialScheme(scheme);
    }
    /// @brief Return the temporal integration scheme
    math::TemporalIntegrationScheme getTrackerTemporalScheme() const {
        return mTracker.getTemporalScheme();
    }
    /// @brief Set the spatial finite difference scheme
    void setTrackerTemporalScheme(math::TemporalIntegrationScheme scheme) {
        mTracker.setTemporalScheme(scheme);
    }

    /// @brief Return The number of normalizations performed per track or
    /// normalize call.
    int  getNormCount() const { return mTracker.getNormCount(); }
    /// @brief Set the number of normalizations performed per track or
    /// normalize call.
    void setNormCount(int n) { mTracker.setNormCount(n); }

    /// @brief Return the grain-size used for multi-threading
    int  getGrainSize() const { return mTracker.getGrainSize(); }
    /// @brief Set the grain-size used for multi-threading.
    /// @note A grain size of 0 or less disables multi-threading!
    void setGrainSize(int grainsize) { mTracker.setGrainSize(grainsize); }

    /// Advect the level set from its current time, time0, to its
    /// final time, time1. If time0>time1 backward advection is performed.
    ///
    /// @return number of CFL iterations used to advect from time0 to time1
    size_t advect(ValueType time0, ValueType time1);

private:
    // disallow copy construction and copy by assinment!
    LevelSetAdvection(const LevelSetAdvection&);// not implemented
    LevelSetAdvection& operator=(const LevelSetAdvection&);// not implemented

    // This templated private struct implements all the level set magic.
    template<typename MapT, math::BiasedGradientScheme SpatialScheme,
             math::TemporalIntegrationScheme TemporalScheme>
    struct Advect
    {
        /// Main constructor
        Advect(LevelSetAdvection& parent);
        /// Shallow copy constructor called by tbb::parallel_for() threads
        Advect(const Advect& other);
        /// Destructor
        virtual ~Advect() { if (mIsMaster) this->clearField(); }
        /// Advect the level set from its current time, time0, to its final time, time1.
        /// @return number of CFL iterations
        size_t advect(ValueType time0, ValueType time1);
        /// Used internally by tbb::parallel_for()
        void operator()(const LeafRange& r) const
        {
            if (mTask) mTask(const_cast<Advect*>(this), r);
            else OPENVDB_THROW(ValueError, "task is undefined - don\'t call this method directly");
        }
        /// method calling tbb
        void cook(const char* msg, size_t swapBuffer = 0);
        /// Sample field and return the CFL time step
        typename GridT::ValueType sampleField(ValueType time0, ValueType time1);
        template <bool Aligned> void sample(const LeafRange& r, ValueType t0, ValueType t1);
        inline void sampleXformed(const LeafRange& r, ValueType t0, ValueType t1)
        {
            this->sample<false>(r, t0, t1);
        }
        inline void sampleAligned(const LeafRange& r, ValueType t0, ValueType t1)
        {
            this->sample<true>(r, t0, t1);
        }
        void clearField();
        // Convex combination of Phi and a forward Euler advection steps:
        // Phi(result) = alpha * Phi(phi) + (1-alpha) * (Phi(0) - dt * Speed(speed)*|Grad[Phi(0)]|);
        template <int Nominator, int Denominator>
        void euler(const LeafRange&, ValueType, Index, Index);
        inline void euler01(const LeafRange& r, ValueType t) {this->euler<0,1>(r, t, 0, 1);}
        inline void euler12(const LeafRange& r, ValueType t) {this->euler<1,2>(r, t, 1, 1);}
        inline void euler34(const LeafRange& r, ValueType t) {this->euler<3,4>(r, t, 1, 2);}
        inline void euler13(const LeafRange& r, ValueType t) {this->euler<1,3>(r, t, 1, 2);}

        LevelSetAdvection& mParent;
        VectorType*        mVelocity;
        size_t*            mOffsets;
        const MapT*        mMap;
        typename std::function<void (Advect*, const LeafRange&)> mTask;
        const bool         mIsMaster;
    }; // end of private Advect struct

    template<math::BiasedGradientScheme SpatialScheme>
    size_t advect1(ValueType time0, ValueType time1);

    template<math::BiasedGradientScheme SpatialScheme,
             math::TemporalIntegrationScheme TemporalScheme>
    size_t advect2(ValueType time0, ValueType time1);

    template<math::BiasedGradientScheme SpatialScheme,
             math::TemporalIntegrationScheme TemporalScheme,
             typename MapType>
    size_t advect3(ValueType time0, ValueType time1);

    TrackerT                        mTracker;
    //each thread needs a deep copy of the field since it might contain a ValueAccessor
    const FieldT                    mField;
    math::BiasedGradientScheme      mSpatialScheme;
    math::TemporalIntegrationScheme mTemporalScheme;

};//end of LevelSetAdvection


template<typename GridT, typename FieldT, typename InterruptT>
inline size_t
LevelSetAdvection<GridT, FieldT, InterruptT>::advect(ValueType time0, ValueType time1)
{
    switch (mSpatialScheme) {
    case math::FIRST_BIAS:
        return this->advect1<math::FIRST_BIAS  >(time0, time1);
    case math::SECOND_BIAS:
        return this->advect1<math::SECOND_BIAS >(time0, time1);
    case math::THIRD_BIAS:
        return this->advect1<math::THIRD_BIAS  >(time0, time1);
    case math::WENO5_BIAS:
        return this->advect1<math::WENO5_BIAS  >(time0, time1);
    case math::HJWENO5_BIAS:
        return this->advect1<math::HJWENO5_BIAS>(time0, time1);
    default:
        OPENVDB_THROW(ValueError, "Spatial difference scheme not supported!");
    }
    return 0;
}


template<typename GridT, typename FieldT, typename InterruptT>
template<math::BiasedGradientScheme SpatialScheme>
inline size_t
LevelSetAdvection<GridT, FieldT, InterruptT>::advect1(ValueType time0, ValueType time1)
{
    switch (mTemporalScheme) {
    case math::TVD_RK1:
        return this->advect2<SpatialScheme, math::TVD_RK1>(time0, time1);
    case math::TVD_RK2:
        return this->advect2<SpatialScheme, math::TVD_RK2>(time0, time1);
    case math::TVD_RK3:
        return this->advect2<SpatialScheme, math::TVD_RK3>(time0, time1);
    default:
        OPENVDB_THROW(ValueError, "Temporal integration scheme not supported!");
    }
    return 0;
}


template<typename GridT, typename FieldT, typename InterruptT>
template<math::BiasedGradientScheme SpatialScheme, math::TemporalIntegrationScheme TemporalScheme>
inline size_t
LevelSetAdvection<GridT, FieldT, InterruptT>::advect2(ValueType time0, ValueType time1)
{
    const math::Transform& trans = mTracker.grid().transform();
    if (trans.mapType() == math::UniformScaleMap::mapType()) {
        return this->advect3<SpatialScheme, TemporalScheme, math::UniformScaleMap>(time0, time1);
    } else if (trans.mapType() == math::UniformScaleTranslateMap::mapType()) {
        return this->advect3<SpatialScheme, TemporalScheme, math::UniformScaleTranslateMap>(
            time0, time1);
    } else if (trans.mapType() == math::UnitaryMap::mapType()) {
        return this->advect3<SpatialScheme, TemporalScheme, math::UnitaryMap    >(time0, time1);
    } else if (trans.mapType() == math::TranslationMap::mapType()) {
        return this->advect3<SpatialScheme, TemporalScheme, math::TranslationMap>(time0, time1);
    } else {
        OPENVDB_THROW(ValueError, "MapType not supported!");
    }
    return 0;
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme,
    typename MapT>
inline size_t
LevelSetAdvection<GridT, FieldT, InterruptT>::advect3(ValueType time0, ValueType time1)
{
    Advect<MapT, SpatialScheme, TemporalScheme> tmp(*this);
    return tmp.advect(time0, time1);
}


///////////////////////////////////////////////////////////////////////


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
Advect(LevelSetAdvection& parent)
    : mParent(parent)
    , mVelocity(nullptr)
    , mOffsets(nullptr)
    , mMap(parent.mTracker.grid().transform().template constMap<MapT>().get())
    , mTask(0)
    , mIsMaster(true)
{
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
Advect(const Advect& other)
    : mParent(other.mParent)
    , mVelocity(other.mVelocity)
    , mOffsets(other.mOffsets)
    , mMap(other.mMap)
    , mTask(other.mTask)
    , mIsMaster(false)
{
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline size_t
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
advect(ValueType time0, ValueType time1)
{
    namespace ph = std::placeholders;

    //util::CpuTimer timer;
    size_t countCFL = 0;
    if ( math::isZero(time0 - time1) ) return countCFL;
    const bool isForward = time0 < time1;
    while ((isForward ? time0<time1 : time0>time1) && mParent.mTracker.checkInterrupter()) {
        /// Make sure we have enough temporal auxiliary buffers
        //timer.start( "\nallocate buffers" );
        mParent.mTracker.leafs().rebuildAuxBuffers(TemporalScheme == math::TVD_RK3 ? 2 : 1);
        //timer.stop();

        const ValueType dt = this->sampleField(time0, time1);
        if ( math::isZero(dt) ) break;//V is essentially zero so terminate

        OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN //switch is resolved at compile-time
        switch(TemporalScheme) {
        case math::TVD_RK1:
            // Perform one explicit Euler step: t1 = t0 + dt
            // Phi_t1(1) = Phi_t0(0) - dt * VdotG_t0(0)
            mTask = std::bind(&Advect::euler01, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 1 such that Phi_t1(0) and Phi_t0(1)
            this->cook("Advecting level set using TVD_RK1", 1);
            break;
        case math::TVD_RK2:
            // Perform one explicit Euler step: t1 = t0 + dt
            // Phi_t1(1) = Phi_t0(0) - dt * VdotG_t0(0)
            mTask = std::bind(&Advect::euler01, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 1 such that Phi_t1(0) and Phi_t0(1)
            this->cook("Advecting level set using TVD_RK1 (step 1 of 2)", 1);

            // Convex combine explict Euler step: t2 = t0 + dt
            // Phi_t2(1) = 1/2 * Phi_t0(1) + 1/2 * (Phi_t1(0) - dt * V.Grad_t1(0))
            mTask = std::bind(&Advect::euler12, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 1 such that Phi_t2(0) and Phi_t1(1)
            this->cook("Advecting level set using TVD_RK1 (step 2 of 2)", 1);
            break;
        case math::TVD_RK3:
            // Perform one explicit Euler step: t1 = t0 + dt
            // Phi_t1(1) = Phi_t0(0) - dt * VdotG_t0(0)
            mTask = std::bind(&Advect::euler01, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 1 such that Phi_t1(0) and Phi_t0(1)
            this->cook("Advecting level set using TVD_RK3 (step 1 of 3)", 1);

            // Convex combine explict Euler step: t2 = t0 + dt/2
            // Phi_t2(2) = 3/4 * Phi_t0(1) + 1/4 * (Phi_t1(0) - dt * V.Grad_t1(0))
            mTask = std::bind(&Advect::euler34, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 2 such that Phi_t2(0) and Phi_t1(2)
            this->cook("Advecting level set using TVD_RK3 (step 2 of 3)", 2);

            // Convex combine explict Euler step: t3 = t0 + dt
            // Phi_t3(2) = 1/3 * Phi_t0(1) + 2/3 * (Phi_t2(0) - dt * V.Grad_t2(0)
            mTask = std::bind(&Advect::euler13, ph::_1, ph::_2, dt);

            // Cook and swap buffer 0 and 2 such that Phi_t3(0) and Phi_t2(2)
            this->cook("Advecting level set using TVD_RK3 (step 3 of 3)", 2);
            break;
        default:
            OPENVDB_THROW(ValueError, "Temporal integration scheme not supported!");
        }//end of compile-time resolved switch
        OPENVDB_NO_UNREACHABLE_CODE_WARNING_END

        time0 += isForward ? dt : -dt;
        ++countCFL;
        mParent.mTracker.leafs().removeAuxBuffers();
        this->clearField();
        /// Track the narrow band
        mParent.mTracker.track();
    }//end wile-loop over time
    return countCFL;//number of CLF propagation steps
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline typename GridT::ValueType
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
sampleField(ValueType time0, ValueType time1)
{
    namespace ph = std::placeholders;

    const int grainSize = mParent.mTracker.getGrainSize();
    const size_t leafCount = mParent.mTracker.leafs().leafCount();
    if (leafCount==0) return ValueType(0.0);

    // Compute the prefix sum of offsets to active voxels
    size_t size=0, voxelCount=mParent.mTracker.leafs().getPrefixSum(mOffsets, size, grainSize);

    // Sample the velocity field
    if (mParent.mField.transform() == mParent.mTracker.grid().transform()) {
        mTask = std::bind(&Advect::sampleAligned, ph::_1, ph::_2, time0, time1);
    } else {
        mTask = std::bind(&Advect::sampleXformed, ph::_1, ph::_2, time0, time1);
    }
    assert(voxelCount == mParent.mTracker.grid().activeVoxelCount());
    mVelocity = NewMemory<VectorType>( voxelCount );
    this->cook("Sampling advection field");

    // Find the extrema of the magnitude of the velocities
    ValueType maxAbsV = 0;
    VectorType* v = mVelocity;
    for (size_t i = 0; i < voxelCount; ++i, ++v) {
        maxAbsV = math::Max(maxAbsV, ValueType(v->lengthSqr()));
    }

    // Compute the CFL number
    if (math::isApproxZero(maxAbsV, math::Delta<ValueType>::value())) return ValueType(0);
#ifndef _MSC_VER // Visual C++ doesn't guarantee thread-safe initialization of local statics
    static
#endif
    const ValueType CFL = (TemporalScheme == math::TVD_RK1 ? ValueType(0.3) :
        TemporalScheme == math::TVD_RK2 ? ValueType(0.9) :
        ValueType(1.0))/math::Sqrt(ValueType(3.0));
    const ValueType dt = math::Abs(time1 - time0), dx = mParent.mTracker.voxelSize();
    return math::Min(dt, ValueType(CFL*dx/math::Sqrt(maxAbsV)));
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
template<bool Aligned>
inline void
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
sample(const LeafRange& range, ValueType time0, ValueType time1)
{
    const bool isForward = time0 < time1;
    using VoxelIterT = typename LeafType::ValueOnCIter;
    const MapT& map = *mMap;
    const FieldT field( mParent.mField );
    mParent.mTracker.checkInterrupter();
    for (typename LeafRange::Iterator leafIter = range.begin(); leafIter; ++leafIter) {
        VectorType* vel = mVelocity + mOffsets[ leafIter.pos() ];
        for (VoxelIterT iter = leafIter->cbeginValueOn(); iter; ++iter, ++vel) {
            const VectorType v = Aligned ? field(iter.getCoord(), time0) ://resolved at compile time
                                 field(map.applyMap(iter.getCoord().asVec3d()), time0);
            *vel = isForward ? v : -v;
        }
    }
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline void
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
clearField()
{
    DeleteMemory(mOffsets);
    DeleteMemory(mVelocity);
    mOffsets = nullptr;
    mVelocity = nullptr;
}


template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
inline void
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
cook(const char* msg, size_t swapBuffer)
{
    mParent.mTracker.startInterrupter( msg );

    const int grainSize   = mParent.mTracker.getGrainSize();
    const LeafRange range = mParent.mTracker.leafs().leafRange(grainSize);

    grainSize == 0 ? (*this)(range) : tbb::parallel_for(range, *this);

    mParent.mTracker.leafs().swapLeafBuffer(swapBuffer, grainSize == 0);

    mParent.mTracker.endInterrupter();
}


// Convex combination of Phi and a forward Euler advection steps:
// Phi(result) = alpha * Phi(phi) + (1-alpha) * (Phi(0) - dt * V.Grad(0));
template<typename GridT, typename FieldT, typename InterruptT>
template<
    typename MapT,
    math::BiasedGradientScheme SpatialScheme,
    math::TemporalIntegrationScheme TemporalScheme>
template <int Nominator, int Denominator>
inline void
LevelSetAdvection<GridT, FieldT, InterruptT>::
Advect<MapT, SpatialScheme, TemporalScheme>::
euler(const LeafRange& range, ValueType dt, Index phiBuffer, Index resultBuffer)
{
    using SchemeT = math::BIAS_SCHEME<SpatialScheme>;
    using StencilT = typename SchemeT::template ISStencil<GridType>::StencilType;
    using VoxelIterT = typename LeafType::ValueOnCIter;
    using GradT = math::GradientBiased<MapT, SpatialScheme>;

    static const ValueType Alpha = ValueType(Nominator)/ValueType(Denominator);
    static const ValueType Beta  = ValueType(1) - Alpha;

    mParent.mTracker.checkInterrupter();
    const MapT& map = *mMap;
    StencilT stencil(mParent.mTracker.grid());
    for (typename LeafRange::Iterator leafIter = range.begin(); leafIter; ++leafIter) {
        const VectorType* vel = mVelocity + mOffsets[ leafIter.pos() ];
        const ValueType* phi = leafIter.buffer(phiBuffer).data();
        ValueType* result = leafIter.buffer(resultBuffer).data();
        for (VoxelIterT voxelIter = leafIter->cbeginValueOn(); voxelIter; ++voxelIter, ++vel) {
            const Index i = voxelIter.pos();
            stencil.moveTo(voxelIter);
            const ValueType a =
                stencil.getValue() - dt * vel->dot(GradT::result(map, stencil, *vel));
            result[i] = Nominator ? Alpha * phi[i] + Beta * a : a;
        }//loop over active voxels in the leaf of the mask
    }//loop over leafs of the level set
}

} // namespace tools
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb

#endif // OPENVDB_TOOLS_LEVEL_SET_ADVECT_HAS_BEEN_INCLUDED

// Copyright (c) 2012-2017 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
