RayTracer.h

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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: Apache-2.0

/// @file RayTracer.h
///
/// @author Ken Museth
///
/// @brief Defines two simple but multithreaded renders, a level-set
/// ray tracer and a volume render. To support these renders we also define
/// perspective and orthographic cameras (both designed to mimic a Houdini camera),
/// a Film class and some rather naive shaders.
///
/// @note These classes are included mainly as reference implementations for
/// ray-tracing of OpenVDB volumes. In other words they are not intended for
/// production-quality rendering, but could be used for fast pre-visualization
/// or as a starting point for a more serious render.

#ifndef OPENVDB_TOOLS_RAYTRACER_HAS_BEEN_INCLUDED
#define OPENVDB_TOOLS_RAYTRACER_HAS_BEEN_INCLUDED

#include <openvdb/Types.h>
#include <openvdb/math/BBox.h>
#include <openvdb/math/Ray.h>
#include <openvdb/math/Math.h>
#include <openvdb/tools/RayIntersector.h>
#include <openvdb/tools/Interpolation.h>
#include <openvdb/util/Assert.h>
#include <openvdb/openvdb.h>
#include <deque>
#include <iostream>
#include <fstream>
#include <limits>
#include <memory>
#include <string>
#include <type_traits>
#include <vector>

namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tools {

// Forward declarations
class BaseCamera;
class BaseShader;

/// @brief Ray-trace a volume.
template<typename GridT>
void rayTrace(const GridT&,
              const BaseShader&,
              BaseCamera&,
              size_t pixelSamples = 1,
              unsigned int seed = 0,
              bool threaded = true);

/// @brief Ray-trace a volume using a given ray intersector.
template<typename GridT, typename IntersectorT>
void rayTrace(const GridT&,
              const IntersectorT&,
              const BaseShader&,
              BaseCamera&,
              size_t pixelSamples = 1,
              unsigned int seed = 0,
              bool threaded = true);


///////////////////////////////LEVEL SET RAY TRACER ///////////////////////////////////////

/// @brief A (very) simple multithreaded ray tracer specifically for narrow-band level sets.
/// @details Included primarily as a reference implementation.
template<typename GridT, typename IntersectorT = tools::LevelSetRayIntersector<GridT> >
class LevelSetRayTracer
{
public:
    using GridType = GridT;
    using Vec3Type = typename IntersectorT::Vec3Type;
    using RayType = typename IntersectorT::RayType;

    /// @brief Constructor based on an instance of the grid to be rendered.
    LevelSetRayTracer(const GridT& grid,
                      const BaseShader& shader,
                      BaseCamera& camera,
                      size_t pixelSamples = 1,
                      unsigned int seed = 0);

    /// @brief Constructor based on an instance of the intersector
    /// performing the ray-intersections.
    LevelSetRayTracer(const IntersectorT& inter,
                      const BaseShader& shader,
                      BaseCamera& camera,
                      size_t pixelSamples = 1,
                      unsigned int seed = 0);

    /// @brief Copy constructor
    LevelSetRayTracer(const LevelSetRayTracer& other);

    /// @brief Destructor
    ~LevelSetRayTracer();

    /// @brief Set the level set grid to be ray-traced
    void setGrid(const GridT& grid);

    /// @brief Set the intersector that performs the actual
    /// intersection of the rays against the narrow-band level set.
    void setIntersector(const IntersectorT& inter);

    /// @brief Set the shader derived from the abstract BaseShader class.
    ///
    /// @note The shader is not assumed to be thread-safe so each
    /// thread will get its only deep copy. For instance it could
    /// contains a ValueAccessor into another grid with auxiliary
    /// shading information. Thus, make sure it is relatively
    /// light-weight and efficient to copy (which is the case for ValueAccesors).
    void setShader(const BaseShader& shader);

    /// @brief Set the camera derived from the abstract BaseCamera class.
    void setCamera(BaseCamera& camera);

    /// @brief Set the number of pixel samples and the seed for
    /// jittered sub-rays. A value larger than one implies
    /// anti-aliasing by jittered super-sampling.
    /// @throw ValueError if pixelSamples is equal to zero.
    void setPixelSamples(size_t pixelSamples, unsigned int seed = 0);

    /// @brief Perform the actual (potentially multithreaded) ray-tracing.
    void render(bool threaded = true) const;

    /// @brief Public method required by tbb::parallel_for.
    /// @warning Never call it directly.
    void operator()(const tbb::blocked_range<size_t>& range) const;

private:
    const bool                          mIsMaster;
    double*                             mRand;
    IntersectorT                        mInter;
    std::unique_ptr<const BaseShader>   mShader;
    BaseCamera*                         mCamera;
    size_t                              mSubPixels;
};// LevelSetRayTracer


///////////////////////////////VOLUME RENDER ///////////////////////////////////////

/// @brief A (very) simple multithreaded volume render specifically for scalar density.
/// @details Included primarily as a reference implementation.
/// @note It will only compile if the IntersectorT is templated on a Grid with a
/// floating-point voxel type.
template <typename IntersectorT, typename SamplerT = tools::BoxSampler>
class VolumeRender
{
public:

    using GridType = typename IntersectorT::GridType;
    using RayType = typename IntersectorT::RayType;
    using ValueType = typename GridType::ValueType;
    using AccessorType = typename GridType::ConstAccessor;
    using SamplerType = tools::GridSampler<AccessorType, SamplerT>;
    static_assert(std::is_floating_point<ValueType>::value,
        "VolumeRender requires a floating-point-valued grid");

    /// @brief Constructor taking an intersector and a base camera.
    VolumeRender(const IntersectorT& inter, BaseCamera& camera);

    /// @brief Copy constructor which creates a thread-safe clone
    VolumeRender(const VolumeRender& other);

    /// @brief Perform the actual (potentially multithreaded) volume rendering.
    void render(bool threaded=true) const;

    /// @brief Set the camera derived from the abstract BaseCamera class.
    void setCamera(BaseCamera& camera) { mCamera = &camera; }

    /// @brief Set the intersector that performs the actual
    /// intersection of the rays against the volume.
    void setIntersector(const IntersectorT& inter);

    /// @brief Set the vector components of a directional light source
    /// @throw ArithmeticError if input is a null vector.
    void setLightDir(Real x, Real y, Real z) { mLightDir = Vec3R(x,y,z).unit(); }

    /// @brief Set the color of the directional light source.
    void setLightColor(Real r, Real g, Real b) { mLightColor = Vec3R(r,g,b); }

    /// @brief Set the integration step-size in voxel units for the primay ray.
    void setPrimaryStep(Real primaryStep) { mPrimaryStep = primaryStep; }

    /// @brief Set the integration step-size in voxel units for the primay ray.
    void setShadowStep(Real shadowStep) { mShadowStep  = shadowStep; }

    /// @brief Set Scattering coefficients.
    void setScattering(Real x, Real y, Real z) { mScattering = Vec3R(x,y,z); }

    /// @brief Set absorption coefficients.
    void setAbsorption(Real x, Real y, Real z) { mAbsorption = Vec3R(x,y,z); }

    /// @brief Set parameter that imitates multi-scattering. A value
    /// of zero implies no multi-scattering.
    void setLightGain(Real gain) { mLightGain = gain; }

    /// @brief Set the cut-off value for density and transmittance.
    void setCutOff(Real cutOff) { mCutOff = cutOff; }

    /// @brief Print parameters, statistics, memory usage and other information.
    /// @param os            a stream to which to write textual information
    /// @param verboseLevel  1: print parameters only; 2: include grid
    ///                      statistics; 3: include memory usage
    void print(std::ostream& os = std::cout, int verboseLevel = 1);

    /// @brief Public method required by tbb::parallel_for.
    /// @warning Never call it directly.
    void operator()(const tbb::blocked_range<size_t>& range) const;

private:

    AccessorType mAccessor;
    BaseCamera*  mCamera;
    std::unique_ptr<IntersectorT> mPrimary, mShadow;
    Real  mPrimaryStep, mShadowStep, mCutOff, mLightGain;
    Vec3R mLightDir, mLightColor, mAbsorption, mScattering;
};//VolumeRender

//////////////////////////////////////// FILM ////////////////////////////////////////

/// @brief A simple class that allows for concurrent writes to pixels in an image,
/// background initialization of the image, and PPM file output.
class Film
{
public:
    /// @brief Floating-point RGBA components in the range [0, 1].
    /// @details This is our preferred representation for color processing.
    struct RGBA
    {
        using ValueT = float;

        RGBA() : r(0), g(0), b(0), a(1) {}
        explicit RGBA(ValueT intensity) : r(intensity), g(intensity), b(intensity), a(1) {}
        RGBA(ValueT _r, ValueT _g, ValueT _b, ValueT _a = static_cast<ValueT>(1.0)):
            r(_r), g(_g), b(_b), a(_a)
        {}
        RGBA(double _r, double _g, double _b, double _a = 1.0)
            : r(static_cast<ValueT>(_r))
            , g(static_cast<ValueT>(_g))
            , b(static_cast<ValueT>(_b))
            , a(static_cast<ValueT>(_a))
        {}

        RGBA  operator* (ValueT scale)  const { return RGBA(r*scale, g*scale, b*scale);}
        RGBA  operator+ (const RGBA& rhs) const { return RGBA(r+rhs.r, g+rhs.g, b+rhs.b);}
        RGBA  operator* (const RGBA& rhs) const { return RGBA(r*rhs.r, g*rhs.g, b*rhs.b);}
        RGBA& operator+=(const RGBA& rhs) { r+=rhs.r; g+=rhs.g; b+=rhs.b; a+=rhs.a; return *this;}

        void over(const RGBA& rhs)
        {
            const float s = rhs.a*(1.0f-a);
            r = a*r+s*rhs.r;
            g = a*g+s*rhs.g;
            b = a*b+s*rhs.b;
            a = a + s;
        }

        ValueT r, g, b, a;
    };


    Film(size_t width, size_t height)
        : mWidth(width), mHeight(height), mSize(width*height), mPixels(new RGBA[mSize])
    {
    }
    Film(size_t width, size_t height, const RGBA& bg)
        : mWidth(width), mHeight(height), mSize(width*height), mPixels(new RGBA[mSize])
    {
        this->fill(bg);
    }

    const RGBA& pixel(size_t w, size_t h) const
    {
        OPENVDB_ASSERT(w < mWidth);
        OPENVDB_ASSERT(h < mHeight);
        return mPixels[w + h*mWidth];
    }

    RGBA& pixel(size_t w, size_t h)
    {
        OPENVDB_ASSERT(w < mWidth);
        OPENVDB_ASSERT(h < mHeight);
        return mPixels[w + h*mWidth];
    }

    void fill(const RGBA& rgb=RGBA(0)) { for (size_t i=0; i<mSize; ++i) mPixels[i] = rgb; }
    void checkerboard(const RGBA& c1=RGBA(0.3f), const RGBA& c2=RGBA(0.6f), size_t size=32)
    {
        RGBA *p = mPixels.get();
        for (size_t j = 0; j < mHeight; ++j) {
            for (size_t i = 0; i < mWidth; ++i, ++p) {
                *p = ((i & size) ^ (j & size)) ? c1 : c2;
            }
        }
    }

    template <typename Type = unsigned char>
    std::unique_ptr<Type[]> convertToBitBuffer(const bool alpha = true) const
    {
        const size_t totalSize = mSize * (alpha ? 4 : 3);
        std::unique_ptr<Type[]> buffer(new Type[totalSize]);
        Type *q = buffer.get();
        const RGBA* p = this->pixels();
        size_t n = mSize;
        while (n--) {
            *q++ = static_cast<Type>(255.0f*(*p).r);
            *q++ = static_cast<Type>(255.0f*(*p).g);
            *q++ = static_cast<Type>(255.0f*(*p).b);
            if(alpha)
                *q++ = static_cast<Type>(255.0f*(*p).a);
            ++p;
        }
        return buffer;
    }

    void savePPM(const std::string& fileName)
    {
        std::string name(fileName);
        if (name.find_last_of(".") == std::string::npos) name.append(".ppm");

        std::ofstream os(name.c_str(), std::ios_base::binary);
        if (!os.is_open()) {
            std::cerr << "Error opening PPM file \"" << name << "\"" << std::endl;
            return;
        }

        auto buf = this->convertToBitBuffer<unsigned char>(/*alpha=*/false);
        unsigned char* tmp = buf.get();

        os << "P6\n" << mWidth << " " << mHeight << "\n255\n";
        os.write(reinterpret_cast<const char*>(&(*tmp)), 3 * mSize * sizeof(unsigned char));
    }

    size_t width()       const { return mWidth; }
    size_t height()      const { return mHeight; }
    size_t numPixels()   const { return mSize; }
    const RGBA* pixels() const { return mPixels.get(); }

private:
    size_t mWidth, mHeight, mSize;
    std::unique_ptr<RGBA[]> mPixels;
};// Film


//////////////////////////////////////// CAMERAS ////////////////////////////////////////

/// Abstract base class for the perspective and orthographic cameras
class BaseCamera
{
public:
    BaseCamera(Film& film, const Vec3R& rotation, const Vec3R& translation,
               double frameWidth, double nearPlane, double farPlane)
        : mFilm(&film)
        , mScaleWidth(frameWidth)
        , mScaleHeight(frameWidth * double(film.height()) / double(film.width()))
    {
        OPENVDB_ASSERT(nearPlane > 0 && farPlane > nearPlane);
        mScreenToWorld.accumPostRotation(math::X_AXIS, rotation[0] * math::pi<double>() / 180.0);
        mScreenToWorld.accumPostRotation(math::Y_AXIS, rotation[1] * math::pi<double>() / 180.0);
        mScreenToWorld.accumPostRotation(math::Z_AXIS, rotation[2] * math::pi<double>() / 180.0);
        mScreenToWorld.accumPostTranslation(translation);
        this->initRay(nearPlane, farPlane);
    }

    virtual ~BaseCamera() {}

    Film::RGBA& pixel(size_t i, size_t j) { return mFilm->pixel(i, j); }

    size_t width()  const { return mFilm->width(); }
    size_t height() const { return mFilm->height(); }

    /// Rotate the camera so its negative z-axis points at xyz and its
    /// y axis is in the plane of the xyz and up vectors. In other
    /// words the camera will look at xyz and use up as the
    /// horizontal direction.
    void lookAt(const Vec3R& xyz, const Vec3R& up = Vec3R(0.0, 1.0, 0.0))
    {
        const Vec3R orig = mScreenToWorld.applyMap(Vec3R(0.0));
        const Vec3R dir  = orig - xyz;
        try {
            Mat4d xform = math::aim<Mat4d>(dir, up);
            xform.postTranslate(orig);
            mScreenToWorld = math::AffineMap(xform);
            this->initRay(mRay.t0(), mRay.t1());
        } catch (...) {}
    }

    Vec3R rasterToScreen(double i, double j, double z) const
    {
        return Vec3R( (2 * i / double(mFilm->width()) - 1)  * mScaleWidth,
                      (1 - 2 * j / double(mFilm->height())) * mScaleHeight, z );
    }

    /// @brief Return a Ray in world space given the pixel indices and
    /// optional offsets in the range [0, 1]. An offset of 0.5 corresponds
    /// to the center of the pixel.
    virtual math::Ray<double> getRay(
        size_t i, size_t j, double iOffset = 0.5, double jOffset = 0.5) const = 0;

protected:
    void initRay(double t0, double t1)
    {
        mRay.setTimes(t0, t1);
        mRay.setEye(mScreenToWorld.applyMap(Vec3R(0.0)));
        mRay.setDir(mScreenToWorld.applyJacobian(Vec3R(0.0, 0.0, -1.0)));
    }

    Film* mFilm;
    double mScaleWidth, mScaleHeight;
    math::Ray<double> mRay;
    math::AffineMap mScreenToWorld;
};// BaseCamera


class PerspectiveCamera: public BaseCamera
{
  public:
    /// @brief Constructor
    /// @param film         film (i.e. image) defining the pixel resolution
    /// @param rotation     rotation in degrees of the camera in world space
    ///                     (applied in x, y, z order)
    /// @param translation  translation of the camera in world-space units,
    ///                     applied after rotation
    /// @param focalLength  focal length of the camera in mm
    ///                     (the default of 50mm corresponds to Houdini's default camera)
    /// @param aperture     width in mm of the frame, i.e., the visible field
    ///                     (the default 41.2136 mm corresponds to Houdini's default camera)
    /// @param nearPlane    depth of the near clipping plane in world-space units
    /// @param farPlane     depth of the far clipping plane in world-space units
    ///
    /// @details If no rotation or translation is provided, the camera is placed
    /// at (0,0,0) in world space and points in the direction of the negative z axis.
    PerspectiveCamera(Film& film,
                      const Vec3R& rotation    = Vec3R(0.0),
                      const Vec3R& translation = Vec3R(0.0),
                      double focalLength = 50.0,
                      double aperture    = 41.2136,
                      double nearPlane   = 1e-3,
                      double farPlane    = std::numeric_limits<double>::max())
        : BaseCamera(film, rotation, translation, 0.5*aperture/focalLength, nearPlane, farPlane)
    {
    }

    ~PerspectiveCamera() override = default;

    /// @brief Return a Ray in world space given the pixel indices and
    /// optional offsets in the range [0,1]. An offset of 0.5 corresponds
    /// to the center of the pixel.
    math::Ray<double> getRay(
        size_t i, size_t j, double iOffset = 0.5, double jOffset = 0.5) const override
    {
        math::Ray<double> ray(mRay);
        Vec3R dir = BaseCamera::rasterToScreen(Real(i) + iOffset, Real(j) + jOffset, -1.0);
        dir = BaseCamera::mScreenToWorld.applyJacobian(dir);
        dir.normalize();
        ray.scaleTimes(1.0/dir.dot(ray.dir()));
        ray.setDir(dir);
        return ray;
    }

    /// @brief Return the horizontal field of view in degrees given a
    /// focal lenth in mm and the specified aperture in mm.
    static double focalLengthToFieldOfView(double length, double aperture)
    {
        return 360.0 / math::pi<double>() * atan(aperture/(2.0*length));
    }
    /// @brief Return the focal length in mm given a horizontal field of
    /// view in degrees and the specified aperture in mm.
    static double fieldOfViewToFocalLength(double fov, double aperture)
    {
        return aperture/(2.0*(tan(fov * math::pi<double>() / 360.0)));
    }
};// PerspectiveCamera


class OrthographicCamera: public BaseCamera
{
public:
    /// @brief Constructor
    /// @param film         film (i.e. image) defining the pixel resolution
    /// @param rotation     rotation in degrees of the camera in world space
    ///                     (applied in x, y, z order)
    /// @param translation  translation of the camera in world-space units,
    ///                     applied after rotation
    /// @param frameWidth   width in of the frame in world-space units
    /// @param nearPlane    depth of the near clipping plane in world-space units
    /// @param farPlane     depth of the far clipping plane in world-space units
    ///
    /// @details If no rotation or translation is provided, the camera is placed
    /// at (0,0,0) in world space and points in the direction of the negative z axis.
    OrthographicCamera(Film& film,
                       const Vec3R& rotation    = Vec3R(0.0),
                       const Vec3R& translation = Vec3R(0.0),
                       double frameWidth = 1.0,
                       double nearPlane  = 1e-3,
                       double farPlane   = std::numeric_limits<double>::max())
        : BaseCamera(film, rotation, translation, 0.5*frameWidth, nearPlane, farPlane)
    {
    }
    ~OrthographicCamera() override = default;

    math::Ray<double> getRay(
        size_t i, size_t j, double iOffset = 0.5, double jOffset = 0.5) const override
    {
        math::Ray<double> ray(mRay);
        Vec3R eye = BaseCamera::rasterToScreen(Real(i) + iOffset, Real(j) + jOffset, 0.0);
        ray.setEye(BaseCamera::mScreenToWorld.applyMap(eye));
        return ray;
    }
};// OrthographicCamera


//////////////////////////////////////// SHADERS ////////////////////////////////////////


/// Abstract base class for the shaders
class BaseShader
{
public:
    using RayT = math::Ray<Real>;
    BaseShader() {}
    BaseShader(const BaseShader&) = default;
    virtual ~BaseShader() = default;
    /// @brief Defines the interface of the virtual function that returns a RGB color.
    /// @param xyz World position of the intersection point.
    /// @param nml Normal in world space at the intersection point.
    /// @param dir Direction of the ray in world space.
    virtual Film::RGBA operator()(const Vec3R& xyz, const Vec3R& nml, const Vec3R& dir) const = 0;
    virtual BaseShader* copy() const = 0;
};


/// @brief Shader that produces a simple matte.
///
/// @details The color can either be constant (if GridT =
/// Film::RGBA which is the default) or defined in a separate Vec3
/// color grid. Use SamplerType to define the order of interpolation
/// (default is zero order, i.e. closes-point).
template<typename GridT = Film::RGBA,
         typename SamplerType = tools::PointSampler>
class MatteShader: public BaseShader
{
public:
    MatteShader(const GridT& grid) : mAcc(grid.getAccessor()), mXform(&grid.transform()) {}
    MatteShader(const MatteShader&) = default;
    ~MatteShader() override = default;
    Film::RGBA operator()(const Vec3R& xyz, const Vec3R&, const Vec3R&) const override
    {
        typename GridT::ValueType v = zeroVal<typename GridT::ValueType>();
        SamplerType::sample(mAcc, mXform->worldToIndex(xyz), v);
        return Film::RGBA(v[0], v[1], v[2]);
    }
    BaseShader* copy() const override { return new MatteShader<GridT, SamplerType>(*this); }

private:
    typename GridT::ConstAccessor mAcc;
    const math::Transform* mXform;
};

// Template specialization using a constant color of the material.
template<typename SamplerType>
class MatteShader<Film::RGBA, SamplerType>: public BaseShader
{
public:
    MatteShader(const Film::RGBA& c = Film::RGBA(1.0f)): mRGBA(c) {}
    MatteShader(const MatteShader&) = default;
    ~MatteShader() override = default;
    Film::RGBA operator()(const Vec3R&, const Vec3R&, const Vec3R&) const override
    {
        return mRGBA;
    }
    BaseShader* copy() const override { return new MatteShader<Film::RGBA, SamplerType>(*this); }

private:
    const Film::RGBA mRGBA;
};


/// @brief Color shader that treats the surface normal (x, y, z) as an
/// RGB color.
///
/// @details The color can either be constant (if GridT =
/// Film::RGBA which is the default) or defined in a separate Vec3
/// color grid. Use SamplerType to define the order of interpolation
/// (default is zero order, i.e. closes-point).
template<typename GridT = Film::RGBA,
         typename SamplerType = tools::PointSampler>
class NormalShader: public BaseShader
{
public:
    NormalShader(const GridT& grid) : mAcc(grid.getAccessor()), mXform(&grid.transform()) {}
    NormalShader(const NormalShader&) = default;
    ~NormalShader() override = default;
    Film::RGBA operator()(const Vec3R& xyz, const Vec3R& normal, const Vec3R&) const override
    {
        typename GridT::ValueType v = zeroVal<typename GridT::ValueType>();
        SamplerType::sample(mAcc, mXform->worldToIndex(xyz), v);
        return Film::RGBA(v[0]*(normal[0]+1.0), v[1]*(normal[1]+1.0), v[2]*(normal[2]+1.0));
    }
    BaseShader* copy() const override { return new NormalShader<GridT, SamplerType>(*this); }

private:
    typename GridT::ConstAccessor mAcc;
    const math::Transform* mXform;
};

// Template specialization using a constant color of the material.
template<typename SamplerType>
class NormalShader<Film::RGBA, SamplerType>: public BaseShader
{
public:
    NormalShader(const Film::RGBA& c = Film::RGBA(1.0f)) : mRGBA(c*0.5f) {}
    NormalShader(const NormalShader&) = default;
    ~NormalShader() override = default;
    Film::RGBA operator()(const Vec3R&, const Vec3R& normal, const Vec3R&) const override
    {
        return mRGBA * Film::RGBA(normal[0] + 1.0, normal[1] + 1.0, normal[2] + 1.0);
    }
    BaseShader* copy() const override { return new NormalShader<Film::RGBA, SamplerType>(*this); }

private:
    const Film::RGBA mRGBA;
};


/// @brief Color shader that treats position (x, y, z) as an RGB color in a
/// cube defined from an axis-aligned bounding box in world space.
///
/// @details The color can either be constant (if GridT =
/// Film::RGBA which is the default) or defined in a separate Vec3
/// color grid. Use SamplerType to define the order of interpolation
/// (default is zero order, i.e. closes-point).
template<typename GridT = Film::RGBA,
         typename SamplerType = tools::PointSampler>
class PositionShader: public BaseShader
{
public:
    PositionShader(const math::BBox<Vec3R>& bbox, const GridT& grid)
        : mMin(bbox.min())
        , mInvDim(1.0/bbox.extents())
        , mAcc(grid.getAccessor())
        , mXform(&grid.transform())
    {
    }
    PositionShader(const PositionShader&) = default;
    ~PositionShader() override = default;
    Film::RGBA operator()(const Vec3R& xyz, const Vec3R&, const Vec3R&) const override
    {
        typename GridT::ValueType v = zeroVal<typename GridT::ValueType>();
        SamplerType::sample(mAcc, mXform->worldToIndex(xyz), v);
        const Vec3R rgb = (xyz - mMin) * mInvDim;
        return Film::RGBA(v[0],v[1],v[2]) * Film::RGBA(rgb[0], rgb[1], rgb[2]);
    }
    BaseShader* copy() const override { return new PositionShader<GridT, SamplerType>(*this); }

private:
    const Vec3R mMin, mInvDim;
    typename GridT::ConstAccessor mAcc;
    const math::Transform* mXform;
};

// Template specialization using a constant color of the material.
template<typename SamplerType>
class PositionShader<Film::RGBA, SamplerType>: public BaseShader
{
public:
    PositionShader(const math::BBox<Vec3R>& bbox, const Film::RGBA& c = Film::RGBA(1.0f))
        : mMin(bbox.min()), mInvDim(1.0/bbox.extents()), mRGBA(c) {}
    PositionShader(const PositionShader&) = default;
    ~PositionShader() override = default;
    Film::RGBA operator()(const Vec3R& xyz, const Vec3R&, const Vec3R&) const override
    {
        const Vec3R rgb = (xyz - mMin)*mInvDim;
        return mRGBA*Film::RGBA(rgb[0], rgb[1], rgb[2]);
    }
    BaseShader* copy() const override { return new PositionShader<Film::RGBA, SamplerType>(*this); }

private:
    const Vec3R mMin, mInvDim;
    const Film::RGBA mRGBA;
};


/// @brief Simple diffuse Lambertian surface shader.
///
/// @details The diffuse color can either be constant (if GridT =
/// Film::RGBA which is the default) or defined in a separate Vec3
/// color grid. Lambertian implies that the (radiant) intensity is
/// directly proportional to the cosine of the angle between the
/// surface normal and the direction of the light source. Use
/// SamplerType to define the order of interpolation (default is
/// zero order, i.e. closes-point).
template<typename GridT = Film::RGBA,
         typename SamplerType = tools::PointSampler>
class DiffuseShader: public BaseShader
{
public:
    DiffuseShader(const GridT& grid): mAcc(grid.getAccessor()), mXform(&grid.transform()) {}
    DiffuseShader(const DiffuseShader&) = default;
    ~DiffuseShader() override = default;
    Film::RGBA operator()(const Vec3R& xyz, const Vec3R& normal, const Vec3R& rayDir) const override
    {
        typename GridT::ValueType v = zeroVal<typename GridT::ValueType>();
        SamplerType::sample(mAcc, mXform->worldToIndex(xyz), v);
        // We take the abs of the dot product corresponding to having
        // light sources at +/- rayDir, i.e., two-sided shading.
        return Film::RGBA(v[0],v[1],v[2])
            * static_cast<Film::RGBA::ValueT>(math::Abs(normal.dot(rayDir)));
    }
    BaseShader* copy() const override { return new DiffuseShader<GridT, SamplerType>(*this); }

private:
    typename GridT::ConstAccessor mAcc;
    const math::Transform* mXform;
};

// Template specialization using a constant color of the material.
template <typename SamplerType>
class DiffuseShader<Film::RGBA, SamplerType>: public BaseShader
{
public:
    DiffuseShader(const Film::RGBA& d = Film::RGBA(1.0f)): mRGBA(d) {}
    DiffuseShader(const DiffuseShader&) = default;
    ~DiffuseShader() override = default;
    Film::RGBA operator()(const Vec3R&, const Vec3R& normal, const Vec3R& rayDir) const override
    {
        // We assume a single directional light source at the camera,
        // so the cosine of the angle between the surface normal and the
        // direction of the light source becomes the dot product of the
        // surface normal and inverse direction of the ray.  We also ignore
        // negative dot products, corresponding to strict one-sided shading.
        //return mRGBA * math::Max(0.0, normal.dot(-rayDir));

        // We take the abs of the dot product corresponding to having
        // light sources at +/- rayDir, i.e., two-sided shading.
        return mRGBA * static_cast<Film::RGBA::ValueT>(math::Abs(normal.dot(rayDir)));
    }
    BaseShader* copy() const override { return new DiffuseShader<Film::RGBA, SamplerType>(*this); }

private:
    const Film::RGBA mRGBA;
};


//////////////////////////////////////// RAYTRACER ////////////////////////////////////////

template<typename GridT>
void rayTrace(const GridT& grid,
              const BaseShader& shader,
              BaseCamera& camera,
              size_t pixelSamples,
              unsigned int seed,
              bool threaded)
{
    LevelSetRayTracer<GridT, tools::LevelSetRayIntersector<GridT> >
        tracer(grid, shader, camera, pixelSamples, seed);
    tracer.render(threaded);
}


template<typename GridT, typename IntersectorT>
void rayTrace(const GridT&,
              const IntersectorT& inter,
              const BaseShader& shader,
              BaseCamera& camera,
              size_t pixelSamples,
              unsigned int seed,
              bool threaded)
{
    LevelSetRayTracer<GridT, IntersectorT> tracer(inter, shader, camera, pixelSamples, seed);
    tracer.render(threaded);
}


//////////////////////////////////////// LevelSetRayTracer ////////////////////////////////////////


template<typename GridT, typename IntersectorT>
inline LevelSetRayTracer<GridT, IntersectorT>::
LevelSetRayTracer(const GridT& grid,
                  const BaseShader& shader,
                  BaseCamera& camera,
                  size_t pixelSamples,
                  unsigned int seed)
    : mIsMaster(true),
      mRand(nullptr),
      mInter(grid),
      mShader(shader.copy()),
      mCamera(&camera)
{
    this->setPixelSamples(pixelSamples, seed);
}

template<typename GridT, typename IntersectorT>
inline LevelSetRayTracer<GridT, IntersectorT>::
LevelSetRayTracer(const IntersectorT& inter,
                  const BaseShader& shader,
                  BaseCamera& camera,
                  size_t pixelSamples,
                  unsigned int seed)
    : mIsMaster(true),
      mRand(nullptr),
      mInter(inter),
      mShader(shader.copy()),
      mCamera(&camera)
{
    this->setPixelSamples(pixelSamples, seed);
}

template<typename GridT, typename IntersectorT>
inline LevelSetRayTracer<GridT, IntersectorT>::
LevelSetRayTracer(const LevelSetRayTracer& other) :
    mIsMaster(false),
    mRand(other.mRand),
    mInter(other.mInter),
    mShader(other.mShader->copy()),
    mCamera(other.mCamera),
    mSubPixels(other.mSubPixels)
{
}

template<typename GridT, typename IntersectorT>
inline LevelSetRayTracer<GridT, IntersectorT>::
~LevelSetRayTracer()
{
    if (mIsMaster) delete [] mRand;
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
setGrid(const GridT& grid)
{
    OPENVDB_ASSERT(mIsMaster);
    mInter = IntersectorT(grid);
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
setIntersector(const IntersectorT& inter)
{
    OPENVDB_ASSERT(mIsMaster);
    mInter = inter;
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
setShader(const BaseShader& shader)
{
    OPENVDB_ASSERT(mIsMaster);
    mShader.reset(shader.copy());
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
setCamera(BaseCamera& camera)
{
    OPENVDB_ASSERT(mIsMaster);
    mCamera = &camera;
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
setPixelSamples(size_t pixelSamples, unsigned int seed)
{
    OPENVDB_ASSERT(mIsMaster);
    if (pixelSamples == 0) {
        OPENVDB_THROW(ValueError, "pixelSamples must be larger than zero!");
    }
    mSubPixels = pixelSamples - 1;
    delete [] mRand;
    if (mSubPixels > 0) {
        mRand = new double[16];
        math::Rand01<double> rand(seed);//offsets for anti-aliaing by jittered super-sampling
        for (size_t i=0; i<16; ++i) mRand[i] = rand();
    } else {
        mRand = nullptr;
    }
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
render(bool threaded) const
{
    tbb::blocked_range<size_t> range(0, mCamera->height());
    threaded ? tbb::parallel_for(range, *this) : (*this)(range);
}

template<typename GridT, typename IntersectorT>
inline void LevelSetRayTracer<GridT, IntersectorT>::
operator()(const tbb::blocked_range<size_t>& range) const
{
    const BaseShader& shader = *mShader;
    Vec3Type xyz, nml;
    const float frac = 1.0f / (1.0f + float(mSubPixels));
    for (size_t j=range.begin(), n=0, je = range.end(); j<je; ++j) {
        for (size_t i=0, ie = mCamera->width(); i<ie; ++i) {
            Film::RGBA& bg = mCamera->pixel(i,j);
            RayType ray = mCamera->getRay(i, j);//primary ray
            Film::RGBA c = mInter.intersectsWS(ray, xyz, nml) ? shader(xyz, nml, ray.dir()) : bg;
            for (size_t k=0; k<mSubPixels; ++k, n +=2 ) {
                ray = mCamera->getRay(i, j, mRand[n & 15], mRand[(n+1) & 15]);
                c += mInter.intersectsWS(ray, xyz, nml) ? shader(xyz, nml, ray.dir()) : bg;
            }//loop over sub-pixels
            bg = c*frac;
        }//loop over image height
    }//loop over image width
}

//////////////////////////////////////// VolumeRender ////////////////////////////////////////

template<typename IntersectorT, typename SampleT>
inline VolumeRender<IntersectorT, SampleT>::
VolumeRender(const IntersectorT& inter, BaseCamera& camera)
    : mAccessor(inter.grid().getConstAccessor())
    , mCamera(&camera)
    , mPrimary(new IntersectorT(inter))
    , mShadow(new IntersectorT(inter))
    , mPrimaryStep(1.0)
    , mShadowStep(3.0)
    , mCutOff(0.005)
    , mLightGain(0.2)
    , mLightDir(Vec3R(0.3, 0.3, 0).unit())
    , mLightColor(0.7, 0.7, 0.7)
    , mAbsorption(0.1)
    , mScattering(1.5)
{
}

template<typename IntersectorT, typename SampleT>
inline VolumeRender<IntersectorT, SampleT>::
VolumeRender(const VolumeRender& other)
    : mAccessor(other.mAccessor)
    , mCamera(other.mCamera)
    , mPrimary(new IntersectorT(*(other.mPrimary)))
    , mShadow(new IntersectorT(*(other.mShadow)))
    , mPrimaryStep(other.mPrimaryStep)
    , mShadowStep(other.mShadowStep)
    , mCutOff(other.mCutOff)
    , mLightGain(other.mLightGain)
    , mLightDir(other.mLightDir)
    , mLightColor(other.mLightColor)
    , mAbsorption(other.mAbsorption)
    , mScattering(other.mScattering)
{
}

template<typename IntersectorT, typename SampleT>
inline void VolumeRender<IntersectorT, SampleT>::
print(std::ostream& os, int verboseLevel)
{
    if (verboseLevel>0) {
        os << "\nPrimary step: " <<  mPrimaryStep
           << "\nShadow step: " << mShadowStep
           << "\nCutoff: " << mCutOff
           << "\nLightGain: " << mLightGain
           << "\nLightDir: " << mLightDir
           << "\nLightColor: " << mLightColor
           << "\nAbsorption: " << mAbsorption
           << "\nScattering: " << mScattering << std::endl;
    }
    mPrimary->print(os, verboseLevel);
}

template<typename IntersectorT, typename SampleT>
inline void VolumeRender<IntersectorT, SampleT>::
setIntersector(const IntersectorT& inter)
{
    mPrimary.reset(new IntersectorT(inter));
    mShadow.reset( new IntersectorT(inter));
}

template<typename IntersectorT, typename SampleT>
inline void VolumeRender<IntersectorT, SampleT>::
render(bool threaded) const
{
    tbb::blocked_range<size_t> range(0, mCamera->height());
    threaded ? tbb::parallel_for(range, *this) : (*this)(range);
}

template<typename IntersectorT, typename SampleT>
inline void VolumeRender<IntersectorT, SampleT>::
operator()(const tbb::blocked_range<size_t>& range) const
{
    SamplerType sampler(mAccessor, mShadow->grid().transform());//light-weight wrapper

    // Any variable prefixed with p (or s) means it's associated with a primary (or shadow) ray
    const Vec3R extinction = -mScattering-mAbsorption, One(1.0);
    const Vec3R albedo = mLightColor*mScattering/(mScattering+mAbsorption);//single scattering
    const Real sGain = mLightGain;//in-scattering along shadow ray
    const Real pStep = mPrimaryStep;//Integration step along primary ray in voxel units
    const Real sStep = mShadowStep;//Integration step along shadow ray in voxel units
    const Real cutoff = mCutOff;//Cutoff for density and transmittance

    // For the sake of completeness we show how to use two different
    // methods (hits/march) in VolumeRayIntersector that produce
    // segments along the ray that intersects active values. Comment out
    // the line below to use VolumeRayIntersector::march instead of
    // VolumeRayIntersector::hits.
#define USE_HITS
#ifdef USE_HITS
    std::vector<typename RayType::TimeSpan> pTS, sTS;
    //std::deque<typename RayType::TimeSpan> pTS, sTS;
#endif

    RayType sRay(Vec3R(0), mLightDir);//Shadow ray
    for (size_t j=range.begin(), je = range.end(); j<je; ++j) {
        for (size_t i=0, ie = mCamera->width(); i<ie; ++i) {
            Film::RGBA& bg = mCamera->pixel(i, j);
            bg.a = bg.r = bg.g = bg.b = 0;
            RayType pRay = mCamera->getRay(i, j);// Primary ray
            if( !mPrimary->setWorldRay(pRay)) continue;
            Vec3R pTrans(1.0), pLumi(0.0);
#ifndef USE_HITS
            Real pT0, pT1;
            while (mPrimary->march(pT0, pT1)) {
                for (Real pT = pStep*ceil(pT0/pStep); pT <= pT1; pT += pStep) {
#else
            mPrimary->hits(pTS);
            for (size_t k=0; k<pTS.size(); ++k) {
                Real pT = pStep*ceil(pTS[k].t0/pStep), pT1=pTS[k].t1;
                for (; pT <= pT1; pT += pStep) {
#endif
                    Vec3R pPos = mPrimary->getWorldPos(pT);
                    const Real density = sampler.wsSample(pPos);
                    if (density < cutoff) continue;
                    const Vec3R dT = math::Exp(extinction * density * pStep);
                    Vec3R sTrans(1.0);
                    sRay.setEye(pPos);
                    if( !mShadow->setWorldRay(sRay)) continue;
#ifndef USE_HITS
                    Real sT0, sT1;
                    while (mShadow->march(sT0, sT1)) {
                        for (Real sT = sStep*ceil(sT0/sStep); sT <= sT1; sT+= sStep) {
#else
                    mShadow->hits(sTS);
                    for (size_t l=0; l<sTS.size(); ++l) {
                        Real sT = sStep*ceil(sTS[l].t0/sStep), sT1=sTS[l].t1;
                        for (; sT <= sT1; sT+= sStep) {
#endif
                            const Real d = sampler.wsSample(mShadow->getWorldPos(sT));
                            if (d < cutoff) continue;
                            sTrans *= math::Exp(extinction * d * sStep/(1.0+sT*sGain));
                            if (sTrans.lengthSqr()<cutoff) goto Luminance;//Terminate sRay
                        }//Integration over shadow segment
                    }// Shadow ray march
                Luminance:
                    pLumi += albedo * sTrans * pTrans * (One-dT);
                    pTrans *= dT;
                    if (pTrans.lengthSqr()<cutoff) goto Pixel;  // Terminate Ray
                }//Integration over primary segment
            }// Primary ray march
        Pixel:
            bg.r = static_cast<Film::RGBA::ValueT>(pLumi[0]);
            bg.g = static_cast<Film::RGBA::ValueT>(pLumi[1]);
            bg.b = static_cast<Film::RGBA::ValueT>(pLumi[2]);
            bg.a = static_cast<Film::RGBA::ValueT>(1.0f - pTrans.sum()/3.0f);
     }//Horizontal pixel scan
   }//Vertical pixel scan
}


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


// Explicit Template Instantiation

#ifdef OPENVDB_USE_EXPLICIT_INSTANTIATION

#ifdef OPENVDB_INSTANTIATE_RAYTRACER
#include <openvdb/util/ExplicitInstantiation.h>
#endif

#define _FUNCTION(TreeT) \
    void rayTrace(const Grid<TreeT>&, const BaseShader&, BaseCamera&, size_t, unsigned int, bool)
OPENVDB_REAL_TREE_INSTANTIATE(_FUNCTION)
#undef _FUNCTION

#define _FUNCTION(TreeT) \
    void rayTrace(const Grid<TreeT>&, const tools::LevelSetRayIntersector<Grid<TreeT>>&, const BaseShader&, BaseCamera&, size_t, unsigned int, bool)
OPENVDB_REAL_TREE_INSTANTIATE(_FUNCTION)
#undef _FUNCTION

OPENVDB_INSTANTIATE_CLASS VolumeRender<tools::VolumeRayIntersector<FloatGrid>, tools::BoxSampler>;
OPENVDB_INSTANTIATE_CLASS VolumeRender<tools::VolumeRayIntersector<DoubleGrid>, tools::BoxSampler>;

#endif // OPENVDB_USE_EXPLICIT_INSTANTIATION


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

#endif // OPENVDB_TOOLS_RAYTRACER_HAS_BEEN_INCLUDED