///////////////////////////////////////////////////////////////////////////
//
// 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/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
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// its contributors may be used to endorse or promote products derived
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///////////////////////////////////////////////////////////////////////////
//
/// @author Ken Museth
///
/// @file LevelSetMeasure.h

#ifndef OPENVDB_TOOLS_LEVELSETMEASURE_HAS_BEEN_INCLUDED
#define OPENVDB_TOOLS_LEVELSETMEASURE_HAS_BEEN_INCLUDED

#include <openvdb/math/Math.h>
#include <openvdb/Types.h>
#include <openvdb/Grid.h>
#include <openvdb/tree/LeafManager.h>
#include <openvdb/tree/ValueAccessor.h>
#include <openvdb/math/FiniteDifference.h>
#include <openvdb/math/Operators.h>
#include <openvdb/util/NullInterrupter.h>
#include <boost/math/constants/constants.hpp>//for Pi
#include <tbb/parallel_for.h>
#include <tbb/parallel_sort.h>
#include <type_traits>


namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tools {

/// @brief Return the surface area of a narrow-band level set.
///
/// @param grid          a scalar, floating-point grid with one or more disjoint,
///                      closed isosurfaces at the given @a isovalue
/// @param useWorldSpace if true the area is computed in
///                      world space units, else in voxel units.
///
/// @throw TypeError if @a grid is not scalar or not floating-point or not a level set.
template<class GridType>
inline Real
levelSetArea(const GridType& grid, bool useWorldSpace = true);

/// @brief Return the volume of a narrow-band level set surface.
///
/// @param grid          a scalar, floating-point grid with one or more disjoint,
///                      closed isosurfaces at the given @a isovalue
/// @param useWorldSpace if true the volume is computed in
///                      world space units, else in voxel units.
///
/// @throw TypeError if @a grid is not scalar or not floating-point or not a level set.
template<class GridType>
inline Real
levelSetVolume(const GridType& grid, bool useWorldSpace = true);

/// @brief Compute the surface area and volume of a narrow-band level set.
///
/// @param grid          a scalar, floating-point grid with one or more disjoint,
///                      closed isosurfaces at the given @a isovalue
/// @param area          surface area of the level set
/// @param volume        volume of the level set surface
/// @param useWorldSpace if true the area and volume are computed in
///                      world space units, else in voxel units.
///
/// @throw TypeError if @a grid is not scalar or not floating-point or not a level set.
template<class GridType>
inline void
levelSetMeasure(const GridType& grid, Real& area, Real& volume, bool useWorldSpace = true);

/// @brief Compute the surface area and volume of a narrow-band level set.
///
/// @param grid          a scalar, floating-point grid with one or more disjoint,
///                      closed isosurfaces at the given @a isovalue
/// @param area          surface area of the level set
/// @param volume        volume of the level set surface
/// @param avgCurvature  average mean curvature of the level set surface
/// @param useWorldSpace if true the area, volume and curvature are computed in
///                      world space units, else in voxel units.
///
/// @throw TypeError if @a grid is not scalar or not floating-point or not a level set.
template<class GridType>
inline void
levelSetMeasure(const GridType& grid, Real& area, Real& volume, Real& avgCurvature,
                bool useWorldSpace = true);

/// @brief Smeared-out and continuous Dirac Delta function.
template<typename RealT>
class DiracDelta
{
public:
    DiracDelta(RealT eps) : mC(0.5/eps), mD(2*boost::math::constants::pi<RealT>()*mC), mE(eps) {}
    inline RealT operator()(RealT phi) const { return math::Abs(phi) > mE ? 0 : mC*(1+cos(mD*phi)); }
private:
    const RealT mC, mD, mE;
};


/// @brief Multi-threaded computation of surface area, volume and
/// average mean-curvature for narrow band level sets.
///
/// @details To reduce the risk of round-off errors (primarily due to
/// catastrophic cancellation) and guarantee determinism during
/// multi-threading this class is implemented using parallel_for, and
/// delayed reduction of a sorted list.
template<typename GridT, typename InterruptT = util::NullInterrupter>
class LevelSetMeasure
{
public:
    using GridType = GridT;
    using TreeType = typename GridType::TreeType;
    using ValueType = typename TreeType::ValueType;
    using ManagerType = typename tree::LeafManager<const TreeType>;
    static_assert(std::is_floating_point<ValueType>::value,
        "level set measure is supported only for scalar, floating-point grids");

    /// @brief Main constructor from a grid
    /// @param grid The level set to be measured.
    /// @param interrupt Optional interrupter.
    /// @throw RuntimeError if the grid is not a level set.
    LevelSetMeasure(const GridType& grid, InterruptT* interrupt = nullptr);

    LevelSetMeasure(ManagerType& leafs, Real Dx, InterruptT* interrupt);

    /// @brief Re-initialize using the specified grid.
    void reinit(const GridType& grid);

    /// @brief Re-initialize using the specified LeafManager and voxelSize.
    void reinit(ManagerType& leafs, Real dx);

    /// @brief Destructor
    virtual ~LevelSetMeasure() {}

     /// @return the grain-size used for multi-threading
    int getGrainSize() const { return mGrainSize; }

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

    /// @brief Compute the surface area and volume of the level
    /// set. Use the last argument to specify the result in world or
    /// voxel units.
    /// @note This method is faster (about 3x) then the measure method
    /// below that also computes the average mean-curvature.
    void measure(Real& area, Real& volume, bool useWorldUnits = true);

    /// @brief Compute the surface area, volume, and average
    /// mean-curvature of the level set. Use the last argument to
    /// specify the result in world or voxel units.
    /// @note This method is slower (about 3x) then the measure method
    /// above that only computes the area and volume.
    void measure(Real& area, Real& volume, Real& avgMeanCurvature, bool useWorldUnits = true);

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

    const TreeType* mTree;
    ManagerType*    mLeafs;
    InterruptT*     mInterrupter;
    double          mDx;
    double*         mArray;
    int             mGrainSize;

    // @brief Return false if the process was interrupted
    bool checkInterrupter();

    using LeafT = typename TreeType::LeafNodeType;
    using VoxelCIterT = typename LeafT::ValueOnCIter;
    using LeafRange = typename ManagerType::LeafRange;
    using LeafIterT = typename LeafRange::Iterator;

    struct Measure2
    {
        Measure2(LevelSetMeasure* parent) : mParent(parent), mAcc(*mParent->mTree)
        {
            if (parent->mGrainSize>0) {
                tbb::parallel_for(parent->mLeafs->leafRange(parent->mGrainSize), *this);
            } else {
                (*this)(parent->mLeafs->leafRange());
            }
        }
        Measure2(const Measure2& other) : mParent(other.mParent), mAcc(*mParent->mTree) {}
        void operator()(const LeafRange& range) const;
        LevelSetMeasure* mParent;
        typename GridT::ConstAccessor mAcc;
    };
    struct Measure3
    {
        Measure3(LevelSetMeasure* parent) : mParent(parent), mAcc(*mParent->mTree)
        {
            if (parent->mGrainSize>0) {
                tbb::parallel_for(parent->mLeafs->leafRange(parent->mGrainSize), *this);
            } else {
                (*this)(parent->mLeafs->leafRange());
            }
        }
        Measure3(const Measure3& other) : mParent(other.mParent), mAcc(*mParent->mTree) {}
        void operator()(const LeafRange& range) const;
        LevelSetMeasure* mParent;
        typename GridT::ConstAccessor mAcc;
    };
    inline double reduce(double* first, double scale)
    {
        double* last = first + mLeafs->leafCount();
        tbb::parallel_sort(first, last);//reduces catastrophic cancellation
        Real sum = 0.0;
        while(first != last) sum += *first++;
        return scale * sum;
    }

}; // end of LevelSetMeasure class


template<typename GridT, typename InterruptT>
inline
LevelSetMeasure<GridT, InterruptT>::LevelSetMeasure(const GridType& grid, InterruptT* interrupt)
    : mTree(&(grid.tree()))
    , mLeafs(nullptr)
    , mInterrupter(interrupt)
    , mDx(grid.voxelSize()[0])
    , mArray(nullptr)
    , mGrainSize(1)
{
    if (!grid.hasUniformVoxels()) {
         OPENVDB_THROW(RuntimeError,
             "The transform must have uniform scale for the LevelSetMeasure to function");
    }
    if (grid.getGridClass() != GRID_LEVEL_SET) {
        OPENVDB_THROW(RuntimeError,
            "LevelSetMeasure only supports level sets;"
            " try setting the grid class to \"level set\"");
    }
}


template<typename GridT, typename InterruptT>
inline
LevelSetMeasure<GridT, InterruptT>::LevelSetMeasure(
    ManagerType& leafs, Real dx, InterruptT* interrupt)
    : mTree(&(leafs.tree()))
    , mLeafs(&leafs)
    , mInterrupter(interrupt)
    , mDx(dx)
    , mArray(nullptr)
    , mGrainSize(1)
{
}

template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::reinit(const GridType& grid)
{
    if (!grid.hasUniformVoxels()) {
         OPENVDB_THROW(RuntimeError,
             "The transform must have uniform scale for the LevelSetMeasure to function");
    }
    if (grid.getGridClass() != GRID_LEVEL_SET) {
        OPENVDB_THROW(RuntimeError,
            "LevelSetMeasure only supports level sets;"
            " try setting the grid class to \"level set\"");
    }
    mTree = &(grid.tree());
    mLeafs = nullptr;
    mDx = grid.voxelSize()[0];
}


template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::reinit(ManagerType& leafs, Real dx)
{
    mLeafs = &leafs;
    mTree = &(leafs.tree());
    mDx = dx;
}

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


template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::measure(Real& area, Real& volume, bool useWorldUnits)
{
    if (mInterrupter) mInterrupter->start("Measuring level set");


    const bool newLeafs = mLeafs == nullptr;
    if (newLeafs) mLeafs = NewObject<ManagerType>(*mTree);
    const size_t leafCount = mLeafs->leafCount();
    if (leafCount == 0) {
        area = volume = 0;
        return;
    }
    mArray = NewMemory<double>(2*leafCount);

    Measure2 m(this);

    const double dx = useWorldUnits ? mDx : 1.0;
    area = this->reduce(mArray, math::Pow2(dx));
    volume = this->reduce(mArray + leafCount, math::Pow3(dx) / 3.0);

    if (newLeafs) {
        DeleteObject(mLeafs);
        mLeafs = nullptr;
    }
    DeleteMemory(mArray);

    if (mInterrupter) mInterrupter->end();
}


template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::measure(Real& area, Real& volume,
                                            Real& avgMeanCurvature,
                                            bool useWorldUnits)
{
    if (mInterrupter) mInterrupter->start("Measuring level set");

    const bool newLeafs = mLeafs == nullptr;
    if (newLeafs) mLeafs = NewObject<ManagerType>(*mTree);
    const size_t leafCount = mLeafs->leafCount();
    if (leafCount == 0) {
        area = volume = avgMeanCurvature = 0;
        return;
    }
    mArray = NewMemory<double>(3*leafCount);

    Measure3 m(this);

    const double dx = useWorldUnits ? mDx : 1.0;
    area = this->reduce(mArray, math::Pow2(dx));
    volume = this->reduce(mArray + leafCount, math::Pow3(dx) / 3.0);
    avgMeanCurvature = this->reduce(mArray + 2*leafCount, dx/area);

    if (newLeafs) {
        DeleteObject(mLeafs);
        mLeafs = nullptr;
    }
    DeleteMemory(mArray);

    if (mInterrupter) mInterrupter->end();
}


///////////////////////// PRIVATE METHODS //////////////////////


template<typename GridT, typename InterruptT>
inline bool
LevelSetMeasure<GridT, InterruptT>::checkInterrupter()
{
    if (util::wasInterrupted(mInterrupter)) {
        tbb::task::self().cancel_group_execution();
        return false;
    }
    return true;
}

template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::
Measure2::operator()(const LeafRange& range) const
{
    using Vec3T = math::Vec3<ValueType>;
    using Grad = math::ISGradient<math::CD_2ND>;
    mParent->checkInterrupter();
    const Real invDx = 1.0/mParent->mDx;
    const DiracDelta<Real> DD(1.5);
    const size_t leafCount = mParent->mLeafs->leafCount();
    for (LeafIterT leafIter=range.begin(); leafIter; ++leafIter) {
        Real sumA = 0, sumV = 0;//reduce risk of catastrophic cancellation
        for (VoxelCIterT voxelIter = leafIter->cbeginValueOn(); voxelIter; ++voxelIter) {
            const Real dd = DD(invDx * (*voxelIter));
            if (dd > 0.0) {
                const Coord p = voxelIter.getCoord();
                const Vec3T g = invDx*Grad::result(mAcc, p);//voxel units
                sumA += dd * g.dot(g);
                sumV += dd * (g[0]*p[0]+g[1]*p[1]+g[2]*p[2]);
            }
        }
        double* v = mParent->mArray + leafIter.pos();
        *v = sumA;
        v += leafCount;
        *v = sumV;
    }
}

template<typename GridT, typename InterruptT>
inline void
LevelSetMeasure<GridT, InterruptT>::
Measure3::operator()(const LeafRange& range) const
{
    using Vec3T = math::Vec3<ValueType>;
    using Grad = math::ISGradient<math::CD_2ND>;
    using Curv = math::ISMeanCurvature<math::CD_SECOND, math::CD_2ND>;
    mParent->checkInterrupter();
    const Real invDx = 1.0/mParent->mDx;
    const DiracDelta<Real> DD(1.5);
    ValueType alpha, beta;
    const size_t leafCount = mParent->mLeafs->leafCount();
    for (LeafIterT leafIter=range.begin(); leafIter; ++leafIter) {
        Real sumA = 0, sumV = 0, sumC = 0;//reduce risk of catastrophic cancellation
        for (VoxelCIterT voxelIter = leafIter->cbeginValueOn(); voxelIter; ++voxelIter) {
            const Real dd = DD(invDx * (*voxelIter));
            if (dd > 0.0) {
                const Coord p = voxelIter.getCoord();
                const Vec3T g = invDx*Grad::result(mAcc, p);//voxel units
                const Real dA = dd * g.dot(g);
                sumA += dA;
                sumV += dd * (g[0]*p[0]+g[1]*p[1]+g[2]*p[2]);
                Curv::result(mAcc, p, alpha, beta);
                sumC += dA * alpha/(2*math::Pow2(beta))*invDx;
            }
        }
        double* v = mParent->mArray + leafIter.pos();
        *v = sumA;
        v += leafCount;
        *v = sumV;
        v += leafCount;
        *v = sumC;
    }
}


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


//{
/// @cond OPENVDB_LEVEL_SET_MEASURE_INTERNAL

template<class GridT>
inline
typename std::enable_if<std::is_floating_point<typename GridT::ValueType>::value, Real>::type
doLevelSetArea(const GridT& grid, bool useWorldSpace)
{
    Real area, volume;
    LevelSetMeasure<GridT> m(grid);
    m.measure(area, volume, useWorldSpace);
    return area;
}

template<class GridT>
inline
typename std::enable_if<!std::is_floating_point<typename GridT::ValueType>::value, Real>::type
doLevelSetArea(const GridT&, bool)
{
    OPENVDB_THROW(TypeError,
        "level set area is supported only for scalar, floating-point grids");
}

/// @endcond
//}


template<class GridT>
inline Real
levelSetArea(const GridT& grid, bool useWorldSpace)
{
    return doLevelSetArea<GridT>(grid, useWorldSpace);
}


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


//{
/// @cond OPENVDB_LEVEL_SET_MEASURE_INTERNAL

template<class GridT>
inline
typename std::enable_if<std::is_floating_point<typename GridT::ValueType>::value, Real>::type
doLevelSetVolume(const GridT& grid, bool useWorldSpace)
{
    Real area, volume;
    LevelSetMeasure<GridT> m(grid);
    m.measure(area, volume, useWorldSpace);
    return volume;
}

template<class GridT>
inline
typename std::enable_if<!std::is_floating_point<typename GridT::ValueType>::value, Real>::type
doLevelSetVolume(const GridT&, bool)
{
    OPENVDB_THROW(TypeError,
        "level set volume is supported only for scalar, floating-point grids");
}

/// @endcond
//}


template<class GridT>
inline Real
levelSetVolume(const GridT& grid, bool useWorldSpace)
{
    return doLevelSetVolume<GridT>(grid, useWorldSpace);
}


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


//{
/// @cond OPENVDB_LEVEL_SET_MEASURE_INTERNAL

template<class GridT>
inline
typename std::enable_if<std::is_floating_point<typename GridT::ValueType>::value>::type
doLevelSetMeasure(const GridT& grid, Real& area, Real& volume, bool useWorldSpace)
{
    LevelSetMeasure<GridT> m(grid);
    m.measure(area, volume, useWorldSpace);
}

template<class GridT>
inline
typename std::enable_if<!std::is_floating_point<typename GridT::ValueType>::value>::type
doLevelSetMeasure(const GridT&, Real&, Real&, bool)
{
    OPENVDB_THROW(TypeError,
        "level set measure is supported only for scalar, floating-point grids");
}

/// @endcond
//}


template<class GridT>
inline void
levelSetMeasure(const GridT& grid, Real& area, Real& volume, bool useWorldSpace)
{
    doLevelSetMeasure<GridT>(grid, area, volume, useWorldSpace);
}


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


//{
/// @cond OPENVDB_LEVEL_SET_MEASURE_INTERNAL

template<class GridT>
inline
typename std::enable_if<std::is_floating_point<typename GridT::ValueType>::value>::type
doLevelSetMeasure(const GridT& grid, Real& area, Real& volume, Real& avgCurvature,
                  bool useWorldSpace)
{
    LevelSetMeasure<GridT> m(grid);
    m.measure(area, volume, avgCurvature, useWorldSpace);
}

template<class GridT>
inline
typename std::enable_if<!std::is_floating_point<typename GridT::ValueType>::value>::type
doLevelSetMeasure(const GridT&, Real&, Real&, Real&, bool)
{
    OPENVDB_THROW(TypeError,
        "level set measure is supported only for scalar, floating-point grids");
}

/// @endcond
//}


template<class GridT>
inline void
levelSetMeasure(const GridT& grid, Real& area, Real& volume, Real& avgCurvature, bool useWorldSpace)
{
    doLevelSetMeasure<GridT>(grid, area, volume, avgCurvature, useWorldSpace);
}

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

#endif // OPENVDB_TOOLS_LEVELSETMEASURE_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/ )
