///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2012-2017 DreamWorks Animation LLC
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///////////////////////////////////////////////////////////////////////////
//
///////////////////////////////////////////////////////////////////////////
//
/// @author Ken Museth
///
/// @file VelocityFields.h
///
/// @brief Defines two simple wrapper classes for advection velocity
///        fields as well as VelocitySampler and VelocityIntegrator
///
///
/// @details DiscreteField wraps a velocity grid and EnrightField is mostly
///          intended for debugging (it's an analytical divergence free and
///          periodic field). They both share the same API required by the
///          LevelSetAdvection class defined in LevelSetAdvect.h. Thus, any
///          class with this API should work with LevelSetAdvection.
///
/// @warning Note the Field wrapper classes below always assume the velocity
///          is represented in the world-frame of reference. For DiscreteField
///          this implies the input grid must contain velocities in world
///          coordinates.

#ifndef OPENVDB_TOOLS_VELOCITY_FIELDS_HAS_BEEN_INCLUDED
#define OPENVDB_TOOLS_VELOCITY_FIELDS_HAS_BEEN_INCLUDED

#include <tbb/parallel_reduce.h>
#include <openvdb/Platform.h>
#include "Interpolation.h" // for Sampler, etc.
#include <openvdb/math/FiniteDifference.h>
#include <boost/math/constants/constants.hpp>

namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tools {

/// @brief Thin wrapper class for a velocity grid
/// @note Consider replacing BoxSampler with StaggeredBoxSampler
template <typename VelGridT, typename Interpolator = BoxSampler>
class DiscreteField
{
public:
    typedef typename VelGridT::ValueType     VectorType;
    typedef typename VectorType::ValueType   ValueType;
    BOOST_STATIC_ASSERT(boost::is_floating_point<ValueType>::value);

    DiscreteField(const VelGridT &vel)
        : mAccessor(vel.tree())
        , mTransform(&vel.transform())
    {
    }

    /// @brief Copy constructor
    DiscreteField(const DiscreteField& other)
        : mAccessor(other.mAccessor.tree())
        , mTransform(other.mTransform)
    {
    }

    /// @return const reference to the transform between world and index space
    /// @note Use this method to determine if a client grid is
    /// aligned with the coordinate space of the velocity grid.
    const math::Transform& transform() const { return *mTransform; }

    /// @return the interpolated velocity at the world space position xyz
    ///
    /// @warning Not threadsafe since it uses a ValueAccessor! So use
    /// one instance per thread (which is fine since its lightweight).
    inline VectorType operator() (const Vec3d& xyz, ValueType/*dummy time*/) const
    {
        return Interpolator::sample(mAccessor, mTransform->worldToIndex(xyz));
    }

    /// @return the velocity at the coordinate space position ijk
    ///
    /// @warning Not threadsafe since it uses a ValueAccessor! So use
    /// one instance per thread (which is fine since its lightweight).
    inline VectorType operator() (const Coord& ijk, ValueType/*dummy time*/) const
    {
        return mAccessor.getValue(ijk);
    }

private:
    const typename VelGridT::ConstAccessor mAccessor;//Not thread-safe
    const math::Transform*                 mTransform;

}; // end of DiscreteField

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

/// @brief Analytical, divergence-free and periodic velocity field
/// @note Primarily intended for debugging!
/// @warning This analytical velocity only produce meaningful values
/// in the unit box in world space. In other words make sure any level
/// set surface is fully enclosed in the axis aligned bounding box
/// spanning 0->1 in world units.
template <typename ScalarT = float>
class EnrightField
{
public:
    typedef ScalarT             ValueType;
    typedef math::Vec3<ScalarT> VectorType;
    BOOST_STATIC_ASSERT(boost::is_floating_point<ScalarT>::value);

    EnrightField() {}

    /// @return const reference to the identity transform between world and index space
    /// @note Use this method to determine if a client grid is
    /// aligned with the coordinate space of this velocity field
    math::Transform transform() const { return math::Transform(); }

    /// @return the velocity in world units, evaluated at the world
    /// position xyz and at the specified time
    inline VectorType operator() (const Vec3d& xyz, ValueType time) const;

    /// @return the velocity at the coordinate space position ijk
    inline VectorType operator() (const Coord& ijk, ValueType time) const
    {
        return (*this)(ijk.asVec3d(), time);
    }
}; // end of EnrightField

template <typename ScalarT>
inline math::Vec3<ScalarT>
EnrightField<ScalarT>::operator() (const Vec3d& xyz, ValueType time) const
{
    const ScalarT pi = boost::math::constants::pi<ScalarT>();
    const ScalarT phase = pi / ScalarT(3);
    const ScalarT Px =  pi * ScalarT(xyz[0]), Py = pi * ScalarT(xyz[1]), Pz = pi * ScalarT(xyz[2]);
    const ScalarT tr =  math::Cos(ScalarT(time) * phase);
    const ScalarT a  =  math::Sin(ScalarT(2)*Py);
    const ScalarT b  = -math::Sin(ScalarT(2)*Px);
    const ScalarT c  =  math::Sin(ScalarT(2)*Pz);
    return math::Vec3<ScalarT>(
                               tr * ( ScalarT(2) * math::Pow2(math::Sin(Px)) * a * c ),
                               tr * ( b * math::Pow2(math::Sin(Py)) * c ),
                               tr * ( b * a * math::Pow2(math::Sin(Pz)) ));
}


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

/// Class to hold a Vec3 field interpreted as a velocity field.
/// Primarily exists to provide a method(s) that integrate a passive
/// point forward in the velocity field for a single time-step (dt)
template<typename GridT = Vec3fGrid,
         bool Staggered = false,
         size_t Order = 1>
class VelocitySampler
{
public:
    typedef typename GridT::ConstAccessor AccessorType;
    typedef typename GridT::ValueType     ValueType;

    /// @brief Constructor from a grid
    VelocitySampler(const GridT& grid):
        mGrid(&grid),
        mAcc(grid.getAccessor())
    {
    }
    /// @brief Copy-constructor
    VelocitySampler(const VelocitySampler& other):
        mGrid(other.mGrid),
        mAcc(mGrid->getAccessor())
    {
    }
    /// @brief Samples the velocity at world position onto result. Supports both
    /// staggered (i.e. MAC) and collocated velocity grids.
    ///
    /// @return @c true if any one of the sampled values is active.
    ///
    /// @warning Not threadsafe since it uses a ValueAccessor! So use
    /// one instance per thread (which is fine since its lightweight).
    template <typename LocationType>
    inline bool sample(const LocationType& world, ValueType& result) const
    {
        const Vec3R xyz = mGrid->worldToIndex(Vec3R(world[0], world[1], world[2]));
        bool active = Sampler<Order, Staggered>::sample(mAcc, xyz, result);
        return active;
    }

    /// @brief Samples the velocity at world position onto result. Supports both
    /// staggered (i.e. MAC) and co-located velocity grids.
    ///
    /// @warning Not threadsafe since it uses a ValueAccessor! So use
    /// one instance per thread (which is fine since its lightweight).
    template <typename LocationType>
    inline ValueType sample(const LocationType& world) const
    {
        const Vec3R xyz = mGrid->worldToIndex(Vec3R(world[0], world[1], world[2]));
        return Sampler<Order, Staggered>::sample(mAcc, xyz);
    }

private:
    // holding the Grids for the transforms
    const GridT* mGrid; // Velocity vector field
    AccessorType mAcc;
};// end of VelocitySampler class

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

/// @brief Performs Runge-Kutta time integration of variable order in
/// a static velocity field.
///
/// @note Note that the order of the velocity sampling is controlled
/// with the SampleOrder template parameter, which defaults
/// to one, i.e. a tri-linear interpolation kernel.
template<typename GridT = Vec3fGrid,
         bool Staggered = false,
         size_t SampleOrder = 1>
class VelocityIntegrator
{
public:
    typedef typename GridT::ValueType  VecType;
    typedef typename VecType::ValueType ElementType;

    VelocityIntegrator(const GridT& velGrid):
        mVelSampler(velGrid)
    {
    }
    /// @brief Variable order Runge-Kutta time integration for a single time step
    ///
    /// @param dt     Time sub-step for the Runge-Kutte integrator of order OrderRK
    /// @param world  Location in world space coordinates (both input and output)
    template<size_t OrderRK, typename LocationType>
    inline void rungeKutta(const ElementType dt, LocationType& world) const
    {
        BOOST_STATIC_ASSERT(OrderRK <= 4);
        VecType P(static_cast<ElementType>(world[0]),
                  static_cast<ElementType>(world[1]),
                  static_cast<ElementType>(world[2]));
        // Note the if-branching below is optimized away at compile time
        if (OrderRK == 0) {
            return;// do nothing
        } else if (OrderRK == 1) {
            VecType V0;
            mVelSampler.sample(P, V0);
            P =  dt * V0;
        } else if (OrderRK == 2) {
            VecType V0, V1;
            mVelSampler.sample(P, V0);
            mVelSampler.sample(P + ElementType(0.5) * dt * V0, V1);
            P = dt * V1;
        } else if (OrderRK == 3) {
            VecType V0, V1, V2;
            mVelSampler.sample(P, V0);
            mVelSampler.sample(P + ElementType(0.5) * dt * V0, V1);
            mVelSampler.sample(P + dt * (ElementType(2.0) * V1 - V0), V2);
            P = dt * (V0 + ElementType(4.0) * V1 + V2) * ElementType(1.0 / 6.0);
        } else if (OrderRK == 4) {
            VecType V0, V1, V2, V3;
            mVelSampler.sample(P, V0);
            mVelSampler.sample(P + ElementType(0.5) * dt * V0, V1);
            mVelSampler.sample(P + ElementType(0.5) * dt * V1, V2);
            mVelSampler.sample(P + dt * V2, V3);
            P = dt * (V0 + ElementType(2.0) * (V1 + V2) + V3) * ElementType(1.0 / 6.0);
        }
        typedef typename LocationType::ValueType OutType;
        world += LocationType(static_cast<OutType>(P[0]),
                              static_cast<OutType>(P[1]),
                              static_cast<OutType>(P[2]));
    }
private:
    VelocitySampler<GridT, Staggered, SampleOrder> mVelSampler;
};// end of VelocityIntegrator class


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

#endif // OPENVDB_TOOLS_VELOCITY_FIELDS_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/ )
