InternalNode.h

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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: Apache-2.0
//
/// @file InternalNode.h
///
/// @brief Internal table nodes for OpenVDB trees

#ifndef OPENVDB_TREE_INTERNALNODE_HAS_BEEN_INCLUDED
#define OPENVDB_TREE_INTERNALNODE_HAS_BEEN_INCLUDED

#include <openvdb/Platform.h>
#include <openvdb/util/NodeMasks.h>
#include <openvdb/util/Assert.h>
#include <openvdb/io/Compression.h> // for io::readCompressedValues(), etc.
#include <openvdb/math/Math.h> // for math::isExactlyEqual(), etc.
#include <openvdb/version.h>
#include <openvdb/Types.h>
#include "Iterator.h"
#include "NodeUnion.h"
#include <tbb/parallel_for.h>
#include <memory>
#include <type_traits>


namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tree {

template<typename, Index, typename> struct SameInternalConfig; // forward declaration


template<typename _ChildNodeType, Index Log2Dim>
class InternalNode
{
public:
    using ChildNodeType = _ChildNodeType;
    using LeafNodeType = typename ChildNodeType::LeafNodeType;
    using ValueType = typename ChildNodeType::ValueType;
    using BuildType = typename ChildNodeType::BuildType;
    using UnionType = NodeUnion<ValueType, ChildNodeType>;
    using NodeMaskType = util::NodeMask<Log2Dim>;

    static const Index
        LOG2DIM      = Log2Dim,                        // log2 of tile count in one dimension
        TOTAL        = Log2Dim + ChildNodeType::TOTAL, // log2 of voxel count in one dimension
        DIM          = 1 << TOTAL,                     // total voxel count in one dimension
        NUM_VALUES   = 1 << (3 * Log2Dim),             // total voxel count represented by this node
        LEVEL        = 1 + ChildNodeType::LEVEL;       // level 0 = leaf
    static const Index64
        NUM_VOXELS   = uint64_t(1) << (3 * TOTAL);     // total voxel count represented by this node

    /// @brief ValueConverter<T>::Type is the type of an InternalNode having the same
    /// child hierarchy and dimensions as this node but a different value type, T.
    template<typename OtherValueType>
    struct ValueConverter {
        using Type = InternalNode<typename ChildNodeType::template ValueConverter<
            OtherValueType>::Type, Log2Dim>;
    };

    /// @brief SameConfiguration<OtherNodeType>::value is @c true if and only if OtherNodeType
    /// is the type of an InternalNode with the same dimensions as this node and whose
    /// ChildNodeType has the same configuration as this node's ChildNodeType.
    template<typename OtherNodeType>
    struct SameConfiguration {
        static const bool value =
            SameInternalConfig<ChildNodeType, Log2Dim, OtherNodeType>::value;
    };


    /// @brief Default constructor
    /// @warning The resulting InternalNode is uninitialized
    InternalNode() {}

    /// @brief Constructor of an InternalNode with dense inactive tiles of the specified value.
    /// @param offValue Background value used for inactive values
    explicit InternalNode(const ValueType& offValue);

    /// @brief Constructs an InternalNode with dense tiles
    /// @param origin    The location in index space of the fist tile value
    /// @param fillValue Value assigned to all the tiles
    /// @param active    State assigned to all the tiles
    InternalNode(const Coord& origin, const ValueType& fillValue, bool active = false);

    InternalNode(PartialCreate, const Coord&, const ValueType& fillValue, bool active = false);

    /// @brief Deep copy constructor
    ///
    /// @note This method is multi-threaded!
    InternalNode(const InternalNode&);

    /// @brief Value conversion copy constructor
    ///
    /// @note This method is multi-threaded!
    template<typename OtherChildNodeType>
    explicit InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other);

    /// @brief Topology copy constructor
    ///
    /// @note This method is multi-threaded!
    template<typename OtherChildNodeType>
    InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                 const ValueType& background, TopologyCopy);

    /// @brief Topology copy constructor
    ///
    /// @note This method is multi-threaded!
    template<typename OtherChildNodeType>
    InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                 const ValueType& offValue, const ValueType& onValue, TopologyCopy);

    ~InternalNode();

protected:
    using MaskOnIterator = typename NodeMaskType::OnIterator;
    using MaskOffIterator = typename NodeMaskType::OffIterator;
    using MaskDenseIterator = typename NodeMaskType::DenseIterator;

    // Type tags to disambiguate template instantiations
    struct ValueOn {}; struct ValueOff {}; struct ValueAll {};
    struct ChildOn {}; struct ChildOff {}; struct ChildAll {};

    // The following class templates implement the iterator interfaces specified in Iterator.h
    // by providing getItem(), setItem() and/or modifyItem() methods.

    // Sparse iterator that visits child nodes of an InternalNode
    template<typename NodeT, typename ChildT, typename MaskIterT, typename TagT>
    struct ChildIter: public SparseIteratorBase<
        MaskIterT, ChildIter<NodeT, ChildT, MaskIterT, TagT>, NodeT, ChildT>
    {
        ChildIter() {}
        ChildIter(const MaskIterT& iter, NodeT* parent): SparseIteratorBase<
            MaskIterT, ChildIter<NodeT, ChildT, MaskIterT, TagT>, NodeT, ChildT>(iter, parent) {}

        ChildT& getItem(Index pos) const
        {
            OPENVDB_ASSERT(this->parent().isChildMaskOn(pos));
            return *(this->parent().getChildNode(pos));
        }

        // Note: setItem() can't be called on const iterators.
        void setItem(Index pos, const ChildT& c) const { this->parent().resetChildNode(pos, &c); }

        // Note: modifyItem() isn't implemented, since it's not useful for child node pointers.
    };// ChildIter

    // Sparse iterator that visits tile values of an InternalNode
    template<typename NodeT, typename ValueT, typename MaskIterT, typename TagT>
    struct ValueIter: public SparseIteratorBase<
        MaskIterT, ValueIter<NodeT, ValueT, MaskIterT, TagT>, NodeT, ValueT>
    {
        ValueIter() {}
        ValueIter(const MaskIterT& iter, NodeT* parent): SparseIteratorBase<
            MaskIterT, ValueIter<NodeT, ValueT, MaskIterT, TagT>, NodeT, ValueT>(iter, parent) {}

        const ValueT& getItem(Index pos) const { return this->parent().mNodes[pos].getValue(); }

        // Note: setItem() can't be called on const iterators.
        void setItem(Index pos, const ValueT& v) const { this->parent().mNodes[pos].setValue(v); }

        // Note: modifyItem() can't be called on const iterators.
        template<typename ModifyOp>
        void modifyItem(Index pos, const ModifyOp& op) const
        {
            op(this->parent().mNodes[pos].getValue());
        }
    };// ValueIter

    // Dense iterator that visits both tiles and child nodes of an InternalNode
    template<typename NodeT, typename ChildT, typename ValueT, typename TagT>
    struct DenseIter: public DenseIteratorBase<
        MaskDenseIterator, DenseIter<NodeT, ChildT, ValueT, TagT>, NodeT, ChildT, ValueT>
    {
        using BaseT = DenseIteratorBase<MaskDenseIterator, DenseIter, NodeT, ChildT, ValueT>;
        using NonConstValueT = typename BaseT::NonConstValueType;

        DenseIter() {}
        DenseIter(const MaskDenseIterator& iter, NodeT* parent):
            DenseIteratorBase<MaskDenseIterator, DenseIter, NodeT, ChildT, ValueT>(iter, parent) {}

        bool getItem(Index pos, ChildT*& child, NonConstValueT& value) const
        {
            if (this->parent().isChildMaskOn(pos)) {
                child = this->parent().getChildNode(pos);
                return true;
            }
            child = nullptr;
            value = this->parent().mNodes[pos].getValue();
            return false;
        }

        // Note: setItem() can't be called on const iterators.
        void setItem(Index pos, ChildT* child) const
        {
            this->parent().resetChildNode(pos, child);
        }

        // Note: unsetItem() can't be called on const iterators.
        void unsetItem(Index pos, const ValueT& value) const
        {
            this->parent().unsetChildNode(pos, value);
        }
    };// DenseIter

public:
    // Iterators (see Iterator.h for usage)
    using ChildOnIter = ChildIter<InternalNode, ChildNodeType, MaskOnIterator, ChildOn>;
    using ChildOnCIter = ChildIter<const InternalNode,const ChildNodeType,MaskOnIterator,ChildOn>;
    using ChildOffIter = ValueIter<InternalNode, const ValueType, MaskOffIterator, ChildOff>;
    using ChildOffCIter = ValueIter<const InternalNode,const ValueType,MaskOffIterator,ChildOff>;
    using ChildAllIter = DenseIter<InternalNode, ChildNodeType, ValueType, ChildAll>;
    using ChildAllCIter = DenseIter<const InternalNode,const ChildNodeType, ValueType, ChildAll>;

    using ValueOnIter = ValueIter<InternalNode, const ValueType, MaskOnIterator, ValueOn>;
    using ValueOnCIter = ValueIter<const InternalNode, const ValueType, MaskOnIterator, ValueOn>;
    using ValueOffIter = ValueIter<InternalNode, const ValueType, MaskOffIterator, ValueOff>;
    using ValueOffCIter = ValueIter<const InternalNode,const ValueType,MaskOffIterator,ValueOff>;
    using ValueAllIter = ValueIter<InternalNode, const ValueType, MaskOffIterator, ValueAll>;
    using ValueAllCIter = ValueIter<const InternalNode,const ValueType,MaskOffIterator,ValueAll>;

    ChildOnCIter  cbeginChildOn()  const { return ChildOnCIter(mChildMask.beginOn(), this); }
    ChildOffCIter cbeginChildOff() const { return ChildOffCIter(mChildMask.beginOff(), this); }
    ChildAllCIter cbeginChildAll() const { return ChildAllCIter(mChildMask.beginDense(), this); }
    ChildOnCIter   beginChildOn()  const { return cbeginChildOn(); }
    ChildOffCIter  beginChildOff() const { return cbeginChildOff(); }
    ChildAllCIter  beginChildAll() const { return cbeginChildAll(); }
    ChildOnIter    beginChildOn()  { return ChildOnIter(mChildMask.beginOn(), this); }
    ChildOffIter   beginChildOff() { return ChildOffIter(mChildMask.beginOff(), this); }
    ChildAllIter   beginChildAll() { return ChildAllIter(mChildMask.beginDense(), this); }

    ValueOnCIter  cbeginValueOn()  const { return ValueOnCIter(mValueMask.beginOn(), this); }
    /// @warning This iterator will also visit child nodes so use isChildMaskOn to skip them!
    ValueOffCIter cbeginValueOff() const { return ValueOffCIter(mValueMask.beginOff(), this); }
    ValueAllCIter cbeginValueAll() const { return ValueAllCIter(mChildMask.beginOff(), this); }
    ValueOnCIter   beginValueOn()  const { return cbeginValueOn(); }
    /// @warning This iterator will also visit child nodes so use isChildMaskOn to skip them!
    ValueOffCIter  beginValueOff() const { return cbeginValueOff(); }
    ValueAllCIter  beginValueAll() const { return cbeginValueAll(); }
    ValueOnIter    beginValueOn()  { return ValueOnIter(mValueMask.beginOn(), this); }
    /// @warning This iterator will also visit child nodes so use isChildMaskOn to skip them!
    ValueOffIter   beginValueOff() { return ValueOffIter(mValueMask.beginOff(), this); }
    ValueAllIter   beginValueAll() { return ValueAllIter(mChildMask.beginOff(), this); }


    /// @return The dimension of this InternalNode
    /// @details The number of voxels in one coordinate direction covered by this node
    static Index dim() { return DIM; }
    /// @return The level of this node
    /// @details Level 0 is by definition the level of the leaf nodes
    static Index getLevel() { return LEVEL; }
    /// @brief Populated an std::vector with the dimension of all the
    /// nodes in the branch starting with this node.
    static void getNodeLog2Dims(std::vector<Index>& dims);
    /// @return The dimension of the child nodes of this node.
    /// @details The number of voxels in one coordinate direction
    /// covered by a child node of this node.
    static Index getChildDim() { return ChildNodeType::DIM; }

    /// Return the linear table offset of the given global or local coordinates.
    static Index coordToOffset(const Coord& xyz);
    /// @brief Return the local coordinates for a linear table offset,
    /// where offset 0 has coordinates (0, 0, 0).
    static void offsetToLocalCoord(Index n, Coord& xyz);
    /// Return the global coordinates for a linear table offset.
    Coord offsetToGlobalCoord(Index n) const;

    /// Return the grid index coordinates of this node's local origin.
    const Coord& origin() const { return mOrigin; }
    /// Set the grid index coordinates of this node's local origin.
    void setOrigin(const Coord& origin) { mOrigin = origin; }

    /// Return the transient data value.
    Index32 transientData() const { return mTransientData; }
    /// Set the transient data value.
    void setTransientData(Index32 transientData) { mTransientData = transientData; }

    Index64 leafCount() const;
    Index64 nonLeafCount() const;
    void nodeCount(std::vector<Index64> &vec) const;
    OPENVDB_DEPRECATED_MESSAGE("Use input type std::vector<Index64> for nodeCount.")
    void nodeCount(std::vector<Index32> &vec) const;
    Index32 childCount() const;
    Index64 onVoxelCount() const;
    Index64 offVoxelCount() const;
    Index64 onLeafVoxelCount() const;
    Index64 offLeafVoxelCount() const;
    Index64 onTileCount() const;

    /// Return the total amount of memory in bytes occupied by this node and its children.
    Index64 memUsage() const;

    /// @brief Expand the specified bounding box so that it includes the active tiles
    /// of this internal node as well as all the active values in its child nodes.
    /// If visitVoxels is false LeafNodes will be approximated as dense, i.e. with all
    /// voxels active. Else the individual active voxels are visited to produce a tight bbox.
    void evalActiveBoundingBox(CoordBBox& bbox, bool visitVoxels = true) const;

    /// @brief Return the bounding box of this node, i.e., the full index space
    /// spanned by the node regardless of its content.
    CoordBBox getNodeBoundingBox() const { return CoordBBox::createCube(mOrigin, DIM); }

    /// @return True if this node contains no child nodes.
    bool isEmpty() const { return mChildMask.isOff(); }

    /// Return @c true if all of this node's table entries have the same active state
    /// and the same constant value to within the given tolerance,
    /// and return that value in @a firstValue and the active state in @a state.
    ///
    /// @note This method also returns @c false if this node contains any child nodes.
    bool isConstant(ValueType& firstValue, bool& state,
                    const ValueType& tolerance = zeroVal<ValueType>()) const;

    /// Return @c true if all of this node's tables entries have
    /// the same active @a state and the range of its values satisfy
    /// (@a maxValue - @a minValue) <= @a tolerance.
    ///
    /// @param minValue  Is updated with the minimum of all values IF method
    ///                  returns @c true. Else the value is undefined!
    /// @param maxValue  Is updated with the maximum of all values IF method
    ///                  returns @c true. Else the value is undefined!
    /// @param state     Is updated with the state of all values IF method
    ///                  returns @c true. Else the value is undefined!
    /// @param tolerance The tolerance used to determine if values are
    ///                  approximately constant.
    ///
    /// @note This method also returns @c false if this node contains any child nodes.
    bool isConstant(ValueType& minValue, ValueType& maxValue,
                    bool& state, const ValueType& tolerance = zeroVal<ValueType>()) const;

    /// Return @c true if this node has no children and only contains inactive values.
    bool isInactive() const { return this->isChildMaskOff() && this->isValueMaskOff(); }

    /// Return @c true if the voxel at the given coordinates is active.
    bool isValueOn(const Coord& xyz) const;
    /// Return @c true if the voxel at the given offset is active.
    bool isValueOn(Index offset) const { OPENVDB_ASSERT(offset < NUM_VALUES); return mValueMask.isOn(offset); }
    /// Return @c true if the voxel at the given coordinates is inactive.
    bool isValueOff(const Coord& xyz) const;
    /// Return @c true if the voxel at the given offset is inactive.
    bool isValueOff(Index offset) const { OPENVDB_ASSERT(offset < NUM_VALUES); return mValueMask.isOff(offset); }

    /// Return @c true if this node or any of its child nodes have any active tiles.
    bool hasActiveTiles() const;

    const ValueType& getValue(const Coord& xyz) const;
    bool probeValue(const Coord& xyz, ValueType& value) const;

    /// @brief Return the level of the tree (0 = leaf) at which the value
    /// at the given coordinates resides.
    Index getValueLevel(const Coord& xyz) const;

    /// @brief If the first entry in this node's table is a tile, return the tile's value.
    /// Otherwise, return the result of calling getFirstValue() on the child.
    const ValueType& getFirstValue() const;
    /// @brief If the last entry in this node's table is a tile, return the tile's value.
    /// Otherwise, return the result of calling getLastValue() on the child.
    const ValueType& getLastValue() const;

    /// Set the active state of the voxel at the given coordinates but don't change its value.
    void setActiveState(const Coord& xyz, bool on);
    /// Set the value of the voxel at the given coordinates but don't change its active state.
    void setValueOnly(const Coord& xyz, const ValueType& value);
    /// Mark the voxel at the given coordinates as active but don't change its value.
    void setValueOn(const Coord& xyz);
    /// Set the value of the voxel at the given coordinates and mark the voxel as active.
    void setValueOn(const Coord& xyz, const ValueType& value);
    /// Mark the voxel at the given coordinates as inactive but don't change its value.
    void setValueOff(const Coord& xyz);
    /// Set the value of the voxel at the given coordinates and mark the voxel as inactive.
    void setValueOff(const Coord& xyz, const ValueType& value);

    /// @brief Apply a functor to the value of the voxel at the given coordinates
    /// and mark the voxel as active.
    template<typename ModifyOp>
    void modifyValue(const Coord& xyz, const ModifyOp& op);
    /// Apply a functor to the voxel at the given coordinates.
    template<typename ModifyOp>
    void modifyValueAndActiveState(const Coord& xyz, const ModifyOp& op);

    /// Return the value of the voxel at the given coordinates and, if necessary, update
    /// the accessor with pointers to the nodes along the path from the root node to
    /// the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    const ValueType& getValueAndCache(const Coord& xyz, AccessorT&) const;

    /// Return @c true if the voxel at the given coordinates is active and, if necessary,
    /// update the accessor with pointers to the nodes along the path from the root node
    /// to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    bool isValueOnAndCache(const Coord& xyz, AccessorT&) const;

    /// Change the value of the voxel at the given coordinates and mark it as active.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    void setValueAndCache(const Coord& xyz, const ValueType& value, AccessorT&);

    /// Set the value of the voxel at the given coordinate but preserves its active state.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    void setValueOnlyAndCache(const Coord& xyz, const ValueType& value, AccessorT&);

    /// @brief Apply a functor to the value of the voxel at the given coordinates
    /// and mark the voxel as active.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename ModifyOp, typename AccessorT>
    void modifyValueAndCache(const Coord& xyz, const ModifyOp& op, AccessorT&);

    /// Apply a functor to the voxel at the given coordinates.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename ModifyOp, typename AccessorT>
    void modifyValueAndActiveStateAndCache(const Coord& xyz, const ModifyOp& op, AccessorT&);

    /// Change the value of the voxel at the given coordinates and mark it as inactive.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    void setValueOffAndCache(const Coord& xyz, const ValueType& value, AccessorT&);

    /// Set the active state of the voxel at the given coordinates without changing its value.
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    void setActiveStateAndCache(const Coord& xyz, bool on, AccessorT&);

    /// Return, in @a value, the value of the voxel at the given coordinates and,
    /// if necessary, update the accessor with pointers to the nodes along
    /// the path from the root node to the node containing the voxel.
    /// @return @c true if the voxel at the given coordinates is active
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    bool probeValueAndCache(const Coord& xyz, ValueType& value, AccessorT&) const;

    /// @brief Return the level of the tree (0 = leaf) at which the value
    /// at the given coordinates resides.
    ///
    /// If necessary, update the accessor with pointers to the nodes along the path
    /// from the root node to the node containing the voxel.
    /// @note Used internally by ValueAccessor.
    template<typename AccessorT>
    Index getValueLevelAndCache(const Coord& xyz, AccessorT&) const;

    /// Mark all values (both tiles and voxels) as active.
    void setValuesOn();

    //
    // I/O
    //
    void writeTopology(std::ostream&, bool toHalf = false) const;
    void readTopology(std::istream&, bool fromHalf = false);
    void writeBuffers(std::ostream&, bool toHalf = false) const;
    void readBuffers(std::istream&, bool fromHalf = false);
    void readBuffers(std::istream&, const CoordBBox&, bool fromHalf = false);


    //
    // Unsafe methods
    //
    // WARNING: For improved performance, these unsafe methods do not check the value or
    // child masks. If used incorrectly, at best they will leave the InternalNode in an
    // invalid state and at worst cause the application to crash. Always use the safer
    // alternative method(s) unless you really know what you're doing.
    // Enabling OpenVDB asserts will catch where assumptions are incorrectly invalidated.

    /// @brief Return the tile value at offset.
    /// @note Use getValue(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    const ValueType& getValueUnsafe(Index offset) const;
    /// @brief Return the tile value and active state at offset.
    /// @note Use probeValue(const Coord&, ValueType&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    bool getValueUnsafe(Index offset, ValueType& value) const;

    /// @brief Return the child node at offset.
    /// @note Use probeChild(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    ChildNodeType* getChildUnsafe(Index offset);
    /// @brief Return the child node at offset.
    /// @note Use probeConstChild(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    const ChildNodeType* getConstChildUnsafe(Index offset) const;
    /// @brief Return the child node at offset.
    /// @note Use probeChild(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    const ChildNodeType* getChildUnsafe(Index offset) const;

    /// @brief Set the tile active state at offset but don't change its value.
    /// @note Use setActiveState(const Coord&, bool) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setActiveStateUnsafe(Index offset, bool on);
    /// @brief Set the tile value at offset but don't change its value.
    /// @note Use setValueOnly(const Coord&, const ValueType&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueOnlyUnsafe(Index offset, const ValueType& value);
    /// @brief Mark the tile active at offset but don't change its value.
    /// @note Use setValueOn(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueOnUnsafe(Index offset);
    /// @brief Set the tile value at offset and mark the voxel as active.
    /// @note Use setValueOn(const Coord&, const ValueType&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueOnUnsafe(Index offset, const ValueType& value);
    /// @brief Mark the tile inactive at offset but don't change its value.
    /// @note Use setValueOff(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueOffUnsafe(Index offset);
    /// @brief Set the tile value at offset and mark the voxel as inactive.
    /// @note Use setValueOff(const Coord&, const ValueType&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueOffUnsafe(Index offset, const ValueType& value);

    /// @brief Set the active/inactive value mask.
    /// @note Use setValueOn(const Coord&)/setValueOff(const Coord&) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setValueMaskUnsafe(const NodeMaskType& mask);

    /// @brief Replace a tile at offset with the given child node.
    /// @note Use addChild(ChildNodeType*) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void setChildUnsafe(Index offset, ChildNodeType* child);
    /// @brief Replace a child node at offset with the given child node.
    /// @note Use addChild(ChildNodeType*) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void resetChildUnsafe(Index offset, ChildNodeType* child);
    /// @brief Replace a child node at offset with the given value and active state.
    /// @note Use addChild(ChildNodeType*) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    ChildNodeType* stealChildUnsafe(Index offset, const ValueType& value, bool active);
    /// @brief Delete a child node at offset and replace with the given value and active state.
    /// @note Use addTile(Index, const ValueType&, bool) for a safer alternative.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    void deleteChildUnsafe(Index offset, const ValueType& value, bool active);

    //
    // Aux methods
    //

    /// Change the sign of all the values represented in this node and its child nodes.
    void negate();

    /// @brief Set all voxels within a given axis-aligned box to a constant value.
    /// @param bbox    inclusive coordinates of opposite corners of an axis-aligned box
    /// @param value   the value to which to set voxels within the box
    /// @param active  if true, mark voxels within the box as active,
    ///                otherwise mark them as inactive
    /// @note This operation generates a sparse, but not always optimally sparse,
    /// representation of the filled box. Follow fill operations with a prune()
    /// operation for optimal sparseness.
    void fill(const CoordBBox& bbox, const ValueType& value, bool active = true);

    /// @brief Set all voxels within a given axis-aligned box to a constant value
    /// and ensure that those voxels are all represented at the leaf level.
    /// @param bbox    inclusive coordinates of opposite corners of an axis-aligned box.
    /// @param value   the value to which to set voxels within the box.
    /// @param active  if true, mark voxels within the box as active,
    ///                otherwise mark them as inactive.
    /// @sa voxelizeActiveTiles()
    void denseFill(const CoordBBox& bbox, const ValueType& value, bool active = true);

    /// @brief Densify active tiles, i.e., replace them with leaf-level active voxels.
    /// @param threaded if true, this operation is multi-threaded (over the internal nodes).
    /// @sa denseFill()
    void voxelizeActiveTiles(bool threaded = true);

    /// @brief Copy into a dense grid the values of the voxels that lie within
    /// a given bounding box.
    /// @param bbox   inclusive bounding box of the voxels to be copied into the dense grid
    /// @param dense  dense grid with a stride in @e z of one (see tools::Dense
    ///               in tools/Dense.h for the required API)
    /// @note @a bbox is assumed to be identical to or contained in the coordinate domains
    /// of both the dense grid and this node, i.e., no bounds checking is performed.
    template<typename DenseT>
    void copyToDense(const CoordBBox& bbox, DenseT& dense) const;

    /// @brief Efficiently merge another tree into this tree using one of several schemes.
    /// @warning This operation cannibalizes the other tree.
    template<MergePolicy Policy>
    void merge(InternalNode& other, const ValueType& background, const ValueType& otherBackground);

    /// @brief Merge, using one of several schemes, this node (and its descendants)
    /// with a tile of the same dimensions and the given value and active state.
    template<MergePolicy Policy> void merge(const ValueType& tileValue, bool tileActive);

    /// @brief Union this branch's set of active values with the other branch's
    /// active values.  The value type of the other branch can be different.
    /// @details The resulting state of a value is active if the corresponding value
    /// was already active OR if it is active in the other tree.  Also, a resulting
    /// value maps to a voxel if the corresponding value already mapped to a voxel
    /// OR if it is a voxel in the other tree.  Thus, a resulting value can only
    /// map to a tile if the corresponding value already mapped to a tile
    /// AND if it is a tile value in other tree.
    ///
    /// Specifically, active tiles and voxels in this branch are not changed, and
    /// tiles or voxels that were inactive in this branch but active in the other branch
    /// are marked as active in this branch but left with their original values.
    template<typename OtherChildNodeType>
    void topologyUnion(const InternalNode<OtherChildNodeType, Log2Dim>& other, const bool preserveTiles = false);

    /// @brief Intersects this tree's set of active values with the active values
    /// of the other tree, whose @c ValueType may be different.
    /// @details The resulting state of a value is active only if the corresponding
    /// value was already active AND if it is active in the other tree. Also, a
    /// resulting value maps to a voxel if the corresponding value
    /// already mapped to an active voxel in either of the two grids
    /// and it maps to an active tile or voxel in the other grid.
    ///
    /// @note This operation can delete branches in this grid if they
    /// overlap with inactive tiles in the other grid. Likewise active
    /// voxels can be turned into inactive voxels resulting in leaf
    /// nodes with no active values. Thus, it is recommended to
    /// subsequently call prune.
    template<typename OtherChildNodeType>
    void topologyIntersection(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                              const ValueType& background);

    /// @brief Difference this node's set of active values with the active values
    /// of the other node, whose @c ValueType may be different. So a
    /// resulting voxel will be active only if the original voxel is
    /// active in this node and inactive in the other node.
    ///
    /// @details The last dummy argument is required to match the signature
    /// for InternalNode::topologyDifference.
    ///
    /// @note This operation modifies only active states, not
    /// values. Also note that this operation can result in all voxels
    /// being inactive so consider subsequently calling prune.
    template<typename OtherChildNodeType>
    void topologyDifference(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                            const ValueType& background);

    template<typename CombineOp>
    void combine(InternalNode& other, CombineOp&);
    template<typename CombineOp>
    void combine(const ValueType& value, bool valueIsActive, CombineOp&);

    template<typename CombineOp, typename OtherNodeType /*= InternalNode*/>
    void combine2(const InternalNode& other0, const OtherNodeType& other1, CombineOp&);
    template<typename CombineOp, typename OtherNodeType /*= InternalNode*/>
    void combine2(const ValueType& value, const OtherNodeType& other, bool valIsActive, CombineOp&);
    template<typename CombineOp, typename OtherValueType>
    void combine2(const InternalNode& other, const OtherValueType&, bool valIsActive, CombineOp&);

    /// Set all voxels that lie outside the given axis-aligned box to the background.
    void clip(const CoordBBox&, const ValueType& background);

    /// @brief Reduce the memory footprint of this tree by replacing with tiles
    /// any nodes whose values are all the same (optionally to within a tolerance)
    /// and have the same active state.
    void prune(const ValueType& tolerance = zeroVal<ValueType>());

    /// @brief Add the specified leaf to this node, possibly creating a child branch
    /// in the process.  If the leaf node already exists, replace it.
    void addLeaf(LeafNodeType* leaf);

    /// @brief Same as addLeaf() except, if necessary, update the accessor with pointers
    /// to the nodes along the path from the root node to the node containing the coordinate.
    template<typename AccessorT>
    void addLeafAndCache(LeafNodeType* leaf, AccessorT&);

    /// @brief Return a pointer to the node of type @c NodeT that contains voxel (x, y, z)
    /// and replace it with a tile of the specified value and state.
    /// If no such node exists, leave the tree unchanged and return @c nullptr.
    ///
    /// @note The caller takes ownership of the node and is responsible for deleting it.
    ///
    /// @warning Since this method potentially removes nodes and branches of the tree,
    /// it is important to clear the caches of all ValueAccessors associated with this tree.
    template<typename NodeT>
    NodeT* stealNode(const Coord& xyz, const ValueType& value, bool state);

    /// @brief Add the given child node at this level deducing the offset from it's origin.
    /// If a child node with this offset already exists, delete the old node and add the
    /// new node in its place (i.e. ownership of the new child node is transferred to
    /// this InternalNode)
    /// @return @c true if inserting the child has been successful, otherwise the caller
    /// retains ownership of the node and is responsible for deleting it.
    bool addChild(ChildNodeType* child);

    /// @brief Add a tile at the specified tree level that contains voxel (x, y, z),
    /// possibly creating a parent branch or deleting a child branch in the process.
    void addTile(Index level, const Coord& xyz, const ValueType& value, bool state);

    /// @brief Delete any existing child branch at the specified offset and add a tile.
    void addTile(Index offset, const ValueType& value, bool state);

    /// @brief Same as addTile() except, if necessary, update the accessor with pointers
    /// to the nodes along the path from the root node to the node containing (x, y, z).
    template<typename AccessorT>
    void addTileAndCache(Index level, const Coord& xyz, const ValueType&, bool state, AccessorT&);

    //@{
    /// @brief Return a pointer to the node that contains voxel (x, y, z).
    /// If no such node exists, return nullptr.
    template<typename NodeType> NodeType* probeNode(const Coord& xyz);
    template<typename NodeType> const NodeType* probeConstNode(const Coord& xyz) const;
    template<typename NodeType> const NodeType* probeNode(const Coord& xyz) const { return this->probeConstNode<NodeType>(xyz); }
    //@}

    //@{
    /// @brief Return a pointer to the child node that contains voxel (x, y, z).
    /// If no such node exists, return nullptr.
    ChildNodeType* probeChild(const Coord& xyz);
    const ChildNodeType* probeConstChild(const Coord& xyz) const;
    const ChildNodeType* probeChild(const Coord& xyz) const { return this->probeConstChild(xyz); }
    //@}

    //@{
    /// @brief Return a pointer to the child node that contains voxel (x, y, z).
    /// If no such node exists, return nullptr.
    ChildNodeType* probeChild(const Coord& xyz, ValueType& value, bool& active);
    const ChildNodeType* probeConstChild(const Coord& xyz, ValueType& value, bool& active) const;
    const ChildNodeType* probeChild(const Coord& xyz, ValueType& value, bool& active) const  { return this->probeConstChild(xyz, value, active); }
    //@}

    //@{
    /// @brief Return a pointer to the child node for a specific offset.
    /// If no such node exists, return nullptr.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    /// @note Out-of-bounds memory access attempts will wrap around using modulo indexing.
    ChildNodeType* probeChildUnsafe(Index offset);
    const ChildNodeType* probeConstChildUnsafe(Index offset) const;
    const ChildNodeType* probeChildUnsafe(Index offset) const { return this->probeConstChildUnsafe(offset); }
    //@}

    //@{
    /// @brief Return a pointer to the child node for a specific offset.
    /// If no such node exists, return nullptr.
    /// @warning This method should only be used by experts seeking low-level optimizations.
    /// @note Out-of-bounds memory access attempts will wrap around using modulo indexing.
    ChildNodeType* probeChildUnsafe(Index offset, ValueType& value, bool& active);
    const ChildNodeType* probeConstChildUnsafe(Index offset, ValueType& value, bool& active) const;
    const ChildNodeType* probeChildUnsafe(Index offset, ValueType& value, bool& active) const { return this->probeConstChildUnsafe(offset, value, active); }
    //@}

    //@{
    /// @brief Same as probeNode() except, if necessary, update the accessor with pointers
    /// to the nodes along the path from the root node to the node containing (x, y, z).
    template<typename NodeType, typename AccessorT>
    NodeType* probeNodeAndCache(const Coord& xyz, AccessorT&);
    template<typename NodeType, typename AccessorT>
    const NodeType* probeConstNodeAndCache(const Coord& xyz, AccessorT&) const;
    //@}

    //@{
    /// @brief Return a pointer to the leaf node that contains voxel (x, y, z).
    /// If no such node exists, return @c nullptr.
    LeafNodeType* probeLeaf(const Coord& xyz);
    const LeafNodeType* probeConstLeaf(const Coord& xyz) const;
    const LeafNodeType* probeLeaf(const Coord& xyz) const;
    //@}

    //@{
    /// @brief Same as probeLeaf() except, if necessary, update the accessor with pointers
    /// to the nodes along the path from the root node to the node containing (x, y, z).
    template<typename AccessorT>
    LeafNodeType* probeLeafAndCache(const Coord& xyz, AccessorT& acc);
    template<typename AccessorT>
    const LeafNodeType* probeConstLeafAndCache(const Coord& xyz, AccessorT& acc) const;
    template<typename AccessorT>
    const LeafNodeType* probeLeafAndCache(const Coord& xyz, AccessorT& acc) const;
    //@}

    /// @brief Return the leaf node that contains voxel (x, y, z).
    /// If no such node exists, create one, but preserve the values and
    /// active states of all voxels.
    ///
    /// @details Use this method to preallocate a static tree topology
    /// over which to safely perform multithreaded processing.
    LeafNodeType* touchLeaf(const Coord& xyz);

    /// @brief Same as touchLeaf() except, if necessary, update the accessor with pointers
    /// to the nodes along the path from the root node to the node containing the coordinate.
    template<typename AccessorT>
    LeafNodeType* touchLeafAndCache(const Coord& xyz, AccessorT&);

    //@{
    /// @brief Adds all nodes of a certain type to a container with the following API:
    /// @code
    /// struct ArrayT {
    ///    using value_type = ...;// defines the type of nodes to be added to the array
    ///    void push_back(value_type nodePtr);// method that add nodes to the array
    /// };
    /// @endcode
    /// @details An example of a wrapper around a c-style array is:
    /// @code
    /// struct MyArray {
    ///    using value_type = LeafType*;
    ///    value_type* ptr;
    ///    MyArray(value_type* array) : ptr(array) {}
    ///    void push_back(value_type leaf) { *ptr++ = leaf; }
    ///};
    /// @endcode
    /// @details An example that constructs a list of pointer to all leaf nodes is:
    /// @code
    /// std::vector<const LeafNodeType*> array;//most std contains have the required API
    /// array.reserve(tree.leafCount());//this is a fast preallocation.
    /// tree.getNodes(array);
    /// @endcode
    template<typename ArrayT>
    void getNodes(ArrayT& array);
    template<typename ArrayT>
    void getNodes(ArrayT& array) const;
    //@}

    /// @brief Steals all nodes of a certain type from the tree and
    /// adds them to a container with the following API:
    /// @code
    /// struct ArrayT {
    ///    using value_type = ...;// defines the type of nodes to be added to the array
    ///    void push_back(value_type nodePtr);// method that add nodes to the array
    /// };
    /// @endcode
    /// @details An example of a wrapper around a c-style array is:
    /// @code
    /// struct MyArray {
    ///    using value_type = LeafType*;
    ///    value_type* ptr;
    ///    MyArray(value_type* array) : ptr(array) {}
    ///    void push_back(value_type leaf) { *ptr++ = leaf; }
    ///};
    /// @endcode
    /// @details An example that constructs a list of pointer to all leaf nodes is:
    /// @code
    /// std::vector<const LeafNodeType*> array;//most std contains have the required API
    /// array.reserve(tree.leafCount());//this is a fast preallocation.
    /// tree.stealNodes(array);
    /// @endcode
    template<typename ArrayT>
    void stealNodes(ArrayT& array, const ValueType& value, bool state);

    /// @brief Change inactive tiles or voxels with value oldBackground to newBackground
    /// or -oldBackground to -newBackground. Active values are unchanged.
    void resetBackground(const ValueType& oldBackground, const ValueType& newBackground);

    /// @brief Return @c true if the given tree branch has the same node and active value
    /// topology as this tree branch (but possibly a different @c ValueType).
    template<typename OtherChildNodeType, Index OtherLog2Dim>
    bool hasSameTopology(const InternalNode<OtherChildNodeType, OtherLog2Dim>* other) const;

protected:
    //@{
    /// Allow iterators to call mask accessor methods (setValueMask(), setChildMask(), etc.).
    /// @todo Make mask accessors public?
    friend class IteratorBase<MaskOnIterator, InternalNode>;
    friend class IteratorBase<MaskOffIterator, InternalNode>;
    friend class IteratorBase<MaskDenseIterator, InternalNode>;
    //@}

    /// @brief During topology-only construction, access is needed
    /// to protected/private members of other template instances.
    template<typename, Index> friend class InternalNode;

    // Mask accessors
public:
    bool isValueMaskOn(Index n) const { return mValueMask.isOn(n); }
    bool isValueMaskOn() const { return mValueMask.isOn(); }
    bool isValueMaskOff(Index n) const { return mValueMask.isOff(n); }
    bool isValueMaskOff() const { return mValueMask.isOff(); }
    bool isChildMaskOn(Index n) const { return mChildMask.isOn(n); }
    bool isChildMaskOff(Index n) const { return mChildMask.isOff(n); }
    bool isChildMaskOff() const { return mChildMask.isOff(); }
    const NodeMaskType& getValueMask() const { return mValueMask; }
    const NodeMaskType& getChildMask() const { return mChildMask; }
    NodeMaskType getValueOffMask() const
    {
        NodeMaskType mask = mValueMask;
        mask |= mChildMask;
        mask.toggle();
        return mask;
    }
    const UnionType* getTable() const { return mNodes; }
protected:
    //@{
    /// Use a mask accessor to ensure consistency between the child and value masks;
    /// i.e., the value mask should always be off wherever the child mask is on.
    void setValueMask(Index n, bool on) { mValueMask.set(n, mChildMask.isOn(n) ? false : on); }
    //@}

    void makeChildNodeEmpty(Index n, const ValueType& value);
    void setChildNode(  Index i, ChildNodeType* child);//assumes a tile
    void resetChildNode(Index i, ChildNodeType* child);//checks for an existing child
    ChildNodeType* unsetChildNode(Index i, const ValueType& value);

    ///@{
    /// @brief Returns a pointer to the child node at the linear offset n.
    /// @warning This protected method assumes that a child node exists at
    /// the specified linear offset!
    ChildNodeType* getChildNode(Index n);
    const ChildNodeType* getChildNode(Index n) const;
    ///@}

    ///@{
    /// @brief Protected member classes for recursive multi-threading
    struct VoxelizeActiveTiles;
    template<typename OtherInternalNode> struct DeepCopy;
    template<typename OtherInternalNode> struct TopologyCopy1;
    template<typename OtherInternalNode> struct TopologyCopy2;
    template<typename OtherInternalNode> struct TopologyUnion;
    template<typename OtherInternalNode> struct TopologyDifference;
    template<typename OtherInternalNode> struct TopologyIntersection;
    ///@}

    UnionType mNodes[NUM_VALUES];
    NodeMaskType mChildMask, mValueMask;
    /// Global grid index coordinates (x,y,z) of the local origin of this node
    Coord mOrigin;
    /// Transient data (not serialized)
    Index32 mTransientData = 0;
}; // class InternalNode


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


//@{
/// Helper metafunction used to implement InternalNode::SameConfiguration
/// (which, as an inner class, can't be independently specialized)
template<typename ChildT1, Index Dim1, typename NodeT2>
struct SameInternalConfig {
    static const bool value = false;
};

template<typename ChildT1, Index Dim1, typename ChildT2>
struct SameInternalConfig<ChildT1, Dim1, InternalNode<ChildT2, Dim1> > {
    static const bool value = ChildT1::template SameConfiguration<ChildT2>::value;
};
//@}


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


template<typename ChildT, Index Log2Dim>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const ValueType& background)
{
    for (Index i = 0; i < NUM_VALUES; ++i) mNodes[i].setValue(background);
}


template<typename ChildT, Index Log2Dim>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const Coord& origin, const ValueType& val, bool active):
    mOrigin(origin[0] & ~(DIM - 1), // zero out the low-order bits
            origin[1] & ~(DIM - 1),
            origin[2] & ~(DIM - 1))
{
    if (active) mValueMask.setOn();
    for (Index i = 0; i < NUM_VALUES; ++i) mNodes[i].setValue(val);
}


// For InternalNodes, the PartialCreate constructor is identical to its
// non-PartialCreate counterpart.
template<typename ChildT, Index Log2Dim>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(PartialCreate,
    const Coord& origin, const ValueType& val, bool active)
    : mOrigin(origin[0] & ~(DIM-1), origin[1] & ~(DIM-1), origin[2] & ~(DIM-1))
{
    if (active) mValueMask.setOn();
    for (Index i = 0; i < NUM_VALUES; ++i) mNodes[i].setValue(val);
}

template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::DeepCopy
{
    DeepCopy(const OtherInternalNode* source, InternalNode* target) : s(source), t(target) {
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//serial
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (s->mChildMask.isOff(i)) {
                t->mNodes[i].setValue(ValueType(s->mNodes[i].getValue()));
            } else {
                t->mNodes[i].setChild(new ChildNodeType(*(s->mNodes[i].getChild())));
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
};// DeepCopy

template<typename ChildT, Index Log2Dim>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const InternalNode& other)
    : mChildMask(other.mChildMask)
    , mValueMask(other.mValueMask)
    , mOrigin(other.mOrigin)
    , mTransientData(other.mTransientData)
{
    DeepCopy<InternalNode<ChildT, Log2Dim> > tmp(&other, this);
}


// Copy-construct from a node with the same configuration but a different ValueType.
template<typename ChildT, Index Log2Dim>
template<typename OtherChildNodeType>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other)
    : mChildMask(other.mChildMask)
    , mValueMask(other.mValueMask)
    , mOrigin(other.mOrigin)
    , mTransientData(other.mTransientData)
{
    DeepCopy<InternalNode<OtherChildNodeType, Log2Dim> > tmp(&other, this);
}

template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::TopologyCopy1
{
    TopologyCopy1(const OtherInternalNode* source, InternalNode* target,
                  const ValueType& background) : s(source), t(target), b(background) {
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//serial
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (s->isChildMaskOn(i)) {
                t->mNodes[i].setChild(new ChildNodeType(*(s->mNodes[i].getChild()),
                                                        b, TopologyCopy()));
            } else {
                t->mNodes[i].setValue(b);
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
    const ValueType &b;
};// TopologyCopy1

template<typename ChildT, Index Log2Dim>
template<typename OtherChildNodeType>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                                            const ValueType& background, TopologyCopy)
    : mChildMask(other.mChildMask)
    , mValueMask(other.mValueMask)
    , mOrigin(other.mOrigin)
    , mTransientData(other.mTransientData)
{
    TopologyCopy1<InternalNode<OtherChildNodeType, Log2Dim> > tmp(&other, this, background);
}

template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::TopologyCopy2
{
    TopologyCopy2(const OtherInternalNode* source, InternalNode* target,
                  const ValueType& offValue, const ValueType& onValue)
        : s(source), t(target), offV(offValue), onV(onValue) {
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (s->isChildMaskOn(i)) {
                t->mNodes[i].setChild(new ChildNodeType(*(s->mNodes[i].getChild()),
                                                        offV, onV, TopologyCopy()));
            } else {
                t->mNodes[i].setValue(s->isValueMaskOn(i) ? onV : offV);
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
    const ValueType &offV, &onV;
 };// TopologyCopy2

template<typename ChildT, Index Log2Dim>
template<typename OtherChildNodeType>
inline
InternalNode<ChildT, Log2Dim>::InternalNode(const InternalNode<OtherChildNodeType, Log2Dim>& other,
                                            const ValueType& offValue,
                                            const ValueType& onValue, TopologyCopy)
    : mChildMask(other.mChildMask)
    , mValueMask(other.mValueMask)
    , mOrigin(other.mOrigin)
    , mTransientData(other.mTransientData)
{
    TopologyCopy2<InternalNode<OtherChildNodeType, Log2Dim> > tmp(&other, this, offValue, onValue);
}


template<typename ChildT, Index Log2Dim>
inline
InternalNode<ChildT, Log2Dim>::~InternalNode()
{
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        delete mNodes[iter.pos()].getChild();
    }
}


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


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::leafCount() const
{
    if (ChildNodeType::getLevel() == 0) return mChildMask.countOn();
    Index64 sum = 0;
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        sum += iter->leafCount();
    }
    return sum;
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::nodeCount(std::vector<Index64> &vec) const
{
    OPENVDB_ASSERT(vec.size() > ChildNodeType::LEVEL);
    const auto count = mChildMask.countOn();
    if (ChildNodeType::LEVEL > 0 && count > 0) {
        for (auto iter = this->cbeginChildOn(); iter; ++iter) iter->nodeCount(vec);
    }
    vec[ChildNodeType::LEVEL] += count;
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::nodeCount(std::vector<Index32> &vec) const
{
    OPENVDB_ASSERT(vec.size() > ChildNodeType::LEVEL);
    const auto count = mChildMask.countOn();
    if (ChildNodeType::LEVEL > 0 && count > 0) {
        for (auto iter = this->cbeginChildOn(); iter; ++iter) {
            OPENVDB_NO_DEPRECATION_WARNING_BEGIN
            iter->nodeCount(vec);
            OPENVDB_NO_DEPRECATION_WARNING_END
        }
    }
    vec[ChildNodeType::LEVEL] += count;
}


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::nonLeafCount() const
{
    Index64 sum = 1;
    if (ChildNodeType::getLevel() == 0) return sum;
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        sum += iter->nonLeafCount();
    }
    return sum;
}


template<typename ChildT, Index Log2Dim>
inline Index32
InternalNode<ChildT, Log2Dim>::childCount() const
{
    return this->getChildMask().countOn();
}


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::onVoxelCount() const
{
    Index64 sum = ChildT::NUM_VOXELS * mValueMask.countOn();
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        sum += iter->onVoxelCount();
    }
    return sum;
}


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::offVoxelCount() const
{
    Index64 sum = ChildT::NUM_VOXELS * (NUM_VALUES-mValueMask.countOn()-mChildMask.countOn());
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        sum += iter->offVoxelCount();
    }
    return sum;
}


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::onLeafVoxelCount() const
{
    Index64 sum = 0;
    for (ChildOnCIter iter = this->beginChildOn(); iter; ++iter) {
        sum += mNodes[iter.pos()].getChild()->onLeafVoxelCount();
    }
    return sum;
}


template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::offLeafVoxelCount() const
{
    Index64 sum = 0;
    for (ChildOnCIter iter = this->beginChildOn(); iter; ++iter) {
        sum += mNodes[iter.pos()].getChild()->offLeafVoxelCount();
    }
    return sum;
}

template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::onTileCount() const
{
    Index64 sum = mValueMask.countOn();
    for (ChildOnCIter iter = this->cbeginChildOn(); LEVEL>1 && iter; ++iter) {
        sum += iter->onTileCount();
    }
    return sum;
}

template<typename ChildT, Index Log2Dim>
inline Index64
InternalNode<ChildT, Log2Dim>::memUsage() const
{
    Index64 sum = NUM_VALUES * sizeof(UnionType) + mChildMask.memUsage()
                + mValueMask.memUsage() + sizeof(mOrigin);
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        sum += iter->memUsage();
    }
    return sum;
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::evalActiveBoundingBox(CoordBBox& bbox, bool visitVoxels) const
{
    if (bbox.isInside(this->getNodeBoundingBox())) return;

    for (ValueOnCIter i = this->cbeginValueOn(); i; ++i) {
        bbox.expand(i.getCoord(), ChildT::DIM);
    }
    for (ChildOnCIter i = this->cbeginChildOn(); i; ++i) {
        i->evalActiveBoundingBox(bbox, visitVoxels);
    }
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::prune(const ValueType& tolerance)
{
    bool state = false;
    ValueType value = zeroVal<ValueType>();
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        const Index i = iter.pos();
        ChildT* child = mNodes[i].getChild();
        child->prune(tolerance);
        if (child->isConstant(value, state, tolerance)) {
            delete child;
            mChildMask.setOff(i);
            mValueMask.set(i, state);
            mNodes[i].setValue(value);
        }
     }
}


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


template<typename ChildT, Index Log2Dim>
template<typename NodeT>
inline NodeT*
InternalNode<ChildT, Log2Dim>::stealNode(const Coord& xyz, const ValueType& value, bool state)
{
    if ((NodeT::LEVEL == ChildT::LEVEL && !(std::is_same<NodeT, ChildT>::value)) ||
         NodeT::LEVEL >  ChildT::LEVEL) return nullptr;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) return nullptr;
    ChildT* child = mNodes[n].getChild();
    if (std::is_same<NodeT, ChildT>::value) {
        mChildMask.setOff(n);
        mValueMask.set(n, state);
        mNodes[n].setValue(value);
    }
    return (std::is_same<NodeT, ChildT>::value)
        ? reinterpret_cast<NodeT*>(child)
        : child->template stealNode<NodeT>(xyz, value, state);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT, Index Log2Dim>
template<typename NodeT>
inline NodeT*
InternalNode<ChildT, Log2Dim>::probeNode(const Coord& xyz)
{
    if ((NodeT::LEVEL == ChildT::LEVEL && !(std::is_same<NodeT, ChildT>::value)) ||
         NodeT::LEVEL >  ChildT::LEVEL) return nullptr;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) return nullptr;
    ChildT* child = mNodes[n].getChild();
    return (std::is_same<NodeT, ChildT>::value)
           ? reinterpret_cast<NodeT*>(child)
           : child->template probeNode<NodeT>(xyz);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


template<typename ChildT, Index Log2Dim>
template<typename NodeT, typename AccessorT>
inline NodeT*
InternalNode<ChildT, Log2Dim>::probeNodeAndCache(const Coord& xyz, AccessorT& acc)
{
    if ((NodeT::LEVEL == ChildT::LEVEL && !(std::is_same<NodeT, ChildT>::value)) ||
         NodeT::LEVEL >  ChildT::LEVEL) return nullptr;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) return nullptr;
    ChildT* child = mNodes[n].getChild();
    acc.insert(xyz, child);
    return (std::is_same<NodeT, ChildT>::value)
           ? reinterpret_cast<NodeT*>(child)
           : child->template probeNodeAndCache<NodeT>(xyz, acc);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


template<typename ChildT, Index Log2Dim>
template<typename NodeT>
inline const NodeT*
InternalNode<ChildT, Log2Dim>::probeConstNode(const Coord& xyz) const
{
    if ((NodeT::LEVEL == ChildT::LEVEL && !(std::is_same<NodeT, ChildT>::value)) ||
         NodeT::LEVEL >  ChildT::LEVEL) return nullptr;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) return nullptr;
    const ChildT* child = mNodes[n].getChild();
    return (std::is_same<NodeT, ChildT>::value)
            ? reinterpret_cast<const NodeT*>(child)
            : child->template probeConstNode<NodeT>(xyz);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


template<typename ChildT, Index Log2Dim>
template<typename NodeT, typename AccessorT>
inline const NodeT*
InternalNode<ChildT, Log2Dim>::probeConstNodeAndCache(const Coord& xyz, AccessorT& acc) const
{
    if ((NodeT::LEVEL == ChildT::LEVEL && !(std::is_same<NodeT, ChildT>::value)) ||
         NodeT::LEVEL >  ChildT::LEVEL) return nullptr;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) return nullptr;
    const ChildT* child = mNodes[n].getChild();
    acc.insert(xyz, child);
    return (std::is_same<NodeT, ChildT>::value)
            ? reinterpret_cast<const NodeT*>(child)
            : child->template probeConstNodeAndCache<NodeT>(xyz, acc);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::probeChild(const Coord& xyz)
{
    const Index n = this->coordToOffset(xyz);
    return this->probeChildUnsafe(n);
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::probeConstChild(const Coord& xyz) const
{
    const Index n = this->coordToOffset(xyz);
    return this->probeConstChildUnsafe(n);
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::probeChild(const Coord& xyz, ValueType& value, bool& active)
{
    const Index n = this->coordToOffset(xyz);
    return this->probeChildUnsafe(n, value, active);
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::probeConstChild(const Coord& xyz, ValueType& value, bool& active) const
{
    const Index n = this->coordToOffset(xyz);
    return this->probeConstChildUnsafe(n, value, active);
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::probeChildUnsafe(Index offset)
{
    OPENVDB_ASSERT(offset < NUM_VALUES);
    if (mChildMask.isOn(offset))    return mNodes[offset].getChild();
    return nullptr;
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::probeConstChildUnsafe(Index offset) const
{
    OPENVDB_ASSERT(offset < NUM_VALUES);
    if (mChildMask.isOn(offset))    return mNodes[offset].getChild();
    return nullptr;
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::probeChildUnsafe(Index offset, ValueType& value, bool& active)
{
    OPENVDB_ASSERT(offset < NUM_VALUES);
    if (mChildMask.isOn(offset))    return mNodes[offset].getChild();
    value = mNodes[offset].getValue();
    active = mValueMask.isOn(offset);
    return nullptr;
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::probeConstChildUnsafe(Index offset, ValueType& value, bool& active) const
{
    OPENVDB_ASSERT(offset < NUM_VALUES);
    if (mChildMask.isOn(offset))    return mNodes[offset].getChild();
    value = mNodes[offset].getValue();
    active = mValueMask.isOn(offset);
    return nullptr;
}


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


template<typename ChildT, Index Log2Dim>
inline typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::probeLeaf(const Coord& xyz)
{
    return this->template probeNode<LeafNodeType>(xyz);
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::probeLeafAndCache(const Coord& xyz, AccessorT& acc)
{
    return this->template probeNodeAndCache<LeafNodeType>(xyz, acc);
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline const typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::probeLeafAndCache(const Coord& xyz, AccessorT& acc) const
{
    return this->probeConstLeafAndCache(xyz, acc);
}


template<typename ChildT, Index Log2Dim>
inline const typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::probeConstLeaf(const Coord& xyz) const
{
    return this->template probeConstNode<LeafNodeType>(xyz);
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline const typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::probeConstLeafAndCache(const Coord& xyz, AccessorT& acc) const
{
    return this->template probeConstNodeAndCache<LeafNodeType>(xyz, acc);
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::addLeaf(LeafNodeType* leaf)
{
    OPENVDB_ASSERT(leaf != nullptr);
    const Coord& xyz = leaf->origin();
    const Index n = this->coordToOffset(xyz);
    ChildT* child = nullptr;
    if (mChildMask.isOff(n)) {
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, mNodes[n].getValue(), mValueMask.isOn(n));
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        this->setChildNode(n, child);
    } else {
        if (ChildT::LEVEL>0) {
            child = mNodes[n].getChild();
        } else {
            delete mNodes[n].getChild();
            child = reinterpret_cast<ChildT*>(leaf);
            mNodes[n].setChild(child);
        }
    }
    child->addLeaf(leaf);
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::addLeafAndCache(LeafNodeType* leaf, AccessorT& acc)
{
    OPENVDB_ASSERT(leaf != nullptr);
    const Coord& xyz = leaf->origin();
    const Index n = this->coordToOffset(xyz);
    ChildT* child = nullptr;
    if (mChildMask.isOff(n)) {
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, mNodes[n].getValue(), mValueMask.isOn(n));
            acc.insert(xyz, child);//we only cache internal nodes
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        this->setChildNode(n, child);
    } else {
        if (ChildT::LEVEL>0) {
            child = mNodes[n].getChild();
            acc.insert(xyz, child);//we only cache internal nodes
        } else {
            delete mNodes[n].getChild();
            child = reinterpret_cast<ChildT*>(leaf);
            mNodes[n].setChild(child);
        }
    }
    child->addLeafAndCache(leaf, acc);
}


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


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::addChild(ChildT* child)
{
    OPENVDB_ASSERT(child);
    const Coord& xyz = child->origin();
    // verify that the child belongs in this internal node
    if (Coord((xyz & ~(DIM-1))) != this->origin())  return false;
    // compute the offset and insert the child node
    const Index n = this->coordToOffset(xyz);
    // this also deletes an existing child node
    this->resetChildNode(n, child);
    return true;
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::addTile(Index n, const ValueType& value, bool state)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    this->makeChildNodeEmpty(n, value);
    mValueMask.set(n, state);
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::addTile(Index level, const Coord& xyz,
                                       const ValueType& value, bool state)
{
    if (LEVEL >= level) {
        const Index n = this->coordToOffset(xyz);
        if (mChildMask.isOff(n)) {// tile case
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, mNodes[n].getValue(), mValueMask.isOn(n));
                this->setChildNode(n, child);
                child->addTile(level, xyz, value, state);
            } else {
                mValueMask.set(n, state);
                mNodes[n].setValue(value);
            }
        } else {// child branch case
            ChildT* child = mNodes[n].getChild();
            if (LEVEL > level) {
                child->addTile(level, xyz, value, state);
            } else {
                delete child;
                mChildMask.setOff(n);
                mValueMask.set(n, state);
                mNodes[n].setValue(value);
            }
        }
    }
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::addTileAndCache(Index level, const Coord& xyz,
    const ValueType& value, bool state, AccessorT& acc)
{
    if (LEVEL >= level) {
        const Index n = this->coordToOffset(xyz);
        if (mChildMask.isOff(n)) {// tile case
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, mNodes[n].getValue(), mValueMask.isOn(n));
                this->setChildNode(n, child);
                acc.insert(xyz, child);
                child->addTileAndCache(level, xyz, value, state, acc);
            } else {
                mValueMask.set(n, state);
                mNodes[n].setValue(value);
            }
        } else {// child branch case
            ChildT* child = mNodes[n].getChild();
            if (LEVEL > level) {
                acc.insert(xyz, child);
                child->addTileAndCache(level, xyz, value, state, acc);
            } else {
                delete child;
                mChildMask.setOff(n);
                mValueMask.set(n, state);
                mNodes[n].setValue(value);
            }
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
inline typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::touchLeaf(const Coord& xyz)
{
    const Index n = this->coordToOffset(xyz);
    ChildT* child = nullptr;
    if (mChildMask.isOff(n)) {
        child = new ChildT(xyz, mNodes[n].getValue(), mValueMask.isOn(n));
        this->setChildNode(n, child);
    } else {
        child = mNodes[n].getChild();
    }
    return child->touchLeaf(xyz);
}


template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline typename ChildT::LeafNodeType*
InternalNode<ChildT, Log2Dim>::touchLeafAndCache(const Coord& xyz, AccessorT& acc)
{
    const Index n = this->coordToOffset(xyz);
    if (mChildMask.isOff(n)) {
        this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), mValueMask.isOn(n)));
    }
    acc.insert(xyz, mNodes[n].getChild());
    return mNodes[n].getChild()->touchLeafAndCache(xyz, acc);
}


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


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::isConstant(ValueType& firstValue, bool& state,
                                          const ValueType& tolerance) const
{
    if (!mChildMask.isOff() || !mValueMask.isConstant(state)) return false;// early termination

    firstValue = mNodes[0].getValue();
    for (Index i = 1; i < NUM_VALUES; ++i) {
        if (!math::isApproxEqual(mNodes[i].getValue(), firstValue, tolerance)) {
            return false; // early termination
        }
    }
    return true;
}


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


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::isConstant(ValueType& minValue,
                                          ValueType& maxValue,
                                          bool& state,
                                          const ValueType& tolerance) const
{

    if (!mChildMask.isOff() || !mValueMask.isConstant(state)) return false;// early termination
    minValue = maxValue = mNodes[0].getValue();
    for (Index i = 1; i < NUM_VALUES; ++i) {
        const ValueType& v = mNodes[i].getValue();
        if (v < minValue) {
            if ((maxValue - v) > tolerance) return false;// early termination
            minValue = v;
        } else if (v > maxValue) {
            if ((v - minValue) > tolerance) return false;// early termination
            maxValue = v;
        }
    }
    return true;
}


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


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::hasActiveTiles() const
{
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    const bool anyActiveTiles = !mValueMask.isOff();
    if (LEVEL==1 || anyActiveTiles) return anyActiveTiles;
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        if (iter->hasActiveTiles()) return true;
    }
    return false;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::isValueOn(const Coord& xyz) const
{
    const Index n = this->coordToOffset(xyz);
    return this->isChildMaskOff(n) ? this->isValueMaskOn(n)
        : mNodes[n].getChild()->isValueOn(xyz);
}

template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::isValueOff(const Coord& xyz) const
{
    const Index n = this->coordToOffset(xyz);
    return this->isChildMaskOff(n) ? this->isValueMaskOn(n)
        : mNodes[n].getChild()->isValueOff(xyz);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline bool
InternalNode<ChildT, Log2Dim>::isValueOnAndCache(const Coord& xyz, AccessorT& acc) const
{
    const Index n = this->coordToOffset(xyz);
    if (this->isChildMaskOff(n)) return this->isValueMaskOn(n);
    acc.insert(xyz, mNodes[n].getChild());
    return mNodes[n].getChild()->isValueOnAndCache(xyz, acc);
}


template<typename ChildT, Index Log2Dim>
inline const typename ChildT::ValueType&
InternalNode<ChildT, Log2Dim>::getValue(const Coord& xyz) const
{
    const Index n = this->coordToOffset(xyz);
    return this->isChildMaskOff(n) ? mNodes[n].getValue()
        :  mNodes[n].getChild()->getValue(xyz);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline const typename ChildT::ValueType&
InternalNode<ChildT, Log2Dim>::getValueAndCache(const Coord& xyz, AccessorT& acc) const
{
    const Index n = this->coordToOffset(xyz);
    if (this->isChildMaskOn(n)) {
        acc.insert(xyz, mNodes[n].getChild());
        return mNodes[n].getChild()->getValueAndCache(xyz, acc);
    }
    return mNodes[n].getValue();
}


template<typename ChildT, Index Log2Dim>
inline Index
InternalNode<ChildT, Log2Dim>::getValueLevel(const Coord& xyz) const
{
    const Index n = this->coordToOffset(xyz);
    return this->isChildMaskOff(n) ? LEVEL : mNodes[n].getChild()->getValueLevel(xyz);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline Index
InternalNode<ChildT, Log2Dim>::getValueLevelAndCache(const Coord& xyz, AccessorT& acc) const
{
    const Index n = this->coordToOffset(xyz);
    if (this->isChildMaskOn(n)) {
        acc.insert(xyz, mNodes[n].getChild());
        return mNodes[n].getChild()->getValueLevelAndCache(xyz, acc);
    }
    return LEVEL;
}


template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::probeValue(const Coord& xyz, ValueType& value) const
{
    const Index n = this->coordToOffset(xyz);
    if (this->isChildMaskOff(n)) {
        value = mNodes[n].getValue();
        return this->isValueMaskOn(n);
    }
    return mNodes[n].getChild()->probeValue(xyz, value);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline bool
InternalNode<ChildT, Log2Dim>::probeValueAndCache(const Coord& xyz,
    ValueType& value, AccessorT& acc) const
{
    const Index n = this->coordToOffset(xyz);
    if (this->isChildMaskOn(n)) {
        acc.insert(xyz, mNodes[n].getChild());
        return mNodes[n].getChild()->probeValueAndCache(xyz, value, acc);
    }
    value = mNodes[n].getValue();
    return this->isValueMaskOn(n);
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOff(const Coord& xyz)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild && this->isValueMaskOn(n)) {
        // If the voxel belongs to a constant tile that is active,
        // a child subtree must be constructed.
        hasChild = true;
        this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), /*active=*/true));
    }
    if (hasChild) mNodes[n].getChild()->setValueOff(xyz);
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOn(const Coord& xyz)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild && !this->isValueMaskOn(n)) {
        // If the voxel belongs to a constant tile that is inactive,
        // a child subtree must be constructed.
        hasChild = true;
        this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), /*active=*/false));
    }
    if (hasChild) mNodes[n].getChild()->setValueOn(xyz);
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOff(const Coord& xyz, const ValueType& value)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool active = this->isValueMaskOn(n);
        if (active || !math::isExactlyEqual(mNodes[n].getValue(), value)) {
            // If the voxel belongs to a tile that is either active or that
            // has a constant value that is different from the one provided,
            // a child subtree must be constructed.
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) mNodes[n].getChild()->setValueOff(xyz, value);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::setValueOffAndCache(const Coord& xyz,
    const ValueType& value, AccessorT& acc)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool active = this->isValueMaskOn(n);
        if (active || !math::isExactlyEqual(mNodes[n].getValue(), value)) {
            // If the voxel belongs to a tile that is either active or that
            // has a constant value that is different from the one provided,
            // a child subtree must be constructed.
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) {
        ChildT* child = mNodes[n].getChild();
        acc.insert(xyz, child);
        child->setValueOffAndCache(xyz, value, acc);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOn(const Coord& xyz, const ValueType& value)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool active = this->isValueMaskOn(n); // tile's active state
        if (!active || !math::isExactlyEqual(mNodes[n].getValue(), value)) {
            // If the voxel belongs to a tile that is either inactive or that
            // has a constant value that is different from the one provided,
            // a child subtree must be constructed.
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) mNodes[n].getChild()->setValueOn(xyz, value);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::setValueAndCache(const Coord& xyz,
    const ValueType& value, AccessorT& acc)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool active = this->isValueMaskOn(n);
        if (!active || !math::isExactlyEqual(mNodes[n].getValue(), value)) {
            // If the voxel belongs to a tile that is either inactive or that
            // has a constant value that is different from the one provided,
            // a child subtree must be constructed.
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) {
        acc.insert(xyz, mNodes[n].getChild());
        mNodes[n].getChild()->setValueAndCache(xyz, value, acc);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOnly(const Coord& xyz, const ValueType& value)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild && !math::isExactlyEqual(mNodes[n].getValue(), value)) {
        // If the voxel has a tile value that is different from the one provided,
        // a child subtree must be constructed.
        const bool active = this->isValueMaskOn(n);
        hasChild = true;
        this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
    }
    if (hasChild) mNodes[n].getChild()->setValueOnly(xyz, value);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::setValueOnlyAndCache(const Coord& xyz,
                                                    const ValueType& value, AccessorT& acc)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild && !math::isExactlyEqual(mNodes[n].getValue(), value)) {
        // If the voxel has a tile value that is different from the one provided,
        // a child subtree must be constructed.
        const bool active = this->isValueMaskOn(n);
        hasChild = true;
        this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
    }
    if (hasChild) {
        acc.insert(xyz, mNodes[n].getChild());
        mNodes[n].getChild()->setValueOnlyAndCache(xyz, value, acc);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setActiveState(const Coord& xyz, bool on)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        if (on != this->isValueMaskOn(n)) {
            // If the voxel belongs to a tile with the wrong active state,
            // then a child subtree must be constructed.
            // 'on' is the voxel's new state, therefore '!on' is the tile's current state
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), !on));
        }
    }
    if (hasChild) mNodes[n].getChild()->setActiveState(xyz, on);
}

template<typename ChildT, Index Log2Dim>
template<typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::setActiveStateAndCache(const Coord& xyz, bool on, AccessorT& acc)
{
    const Index n = this->coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        if (on != this->isValueMaskOn(n)) {
            // If the voxel belongs to a tile with the wrong active state,
            // then a child subtree must be constructed.
            // 'on' is the voxel's new state, therefore '!on' is the tile's current state
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), !on));
        }
    }
    if (hasChild) {
        ChildT* child = mNodes[n].getChild();
        acc.insert(xyz, child);
        child->setActiveStateAndCache(xyz, on, acc);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValuesOn()
{
    mValueMask = !mChildMask;
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        mNodes[iter.pos()].getChild()->setValuesOn();
    }
}


template<typename ChildT, Index Log2Dim>
template<typename ModifyOp>
inline void
InternalNode<ChildT, Log2Dim>::modifyValue(const Coord& xyz, const ModifyOp& op)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        // Need to create a child if the tile is inactive,
        // in order to activate voxel (x, y, z).
        const bool active = this->isValueMaskOn(n);
        bool createChild = !active;
        if (!createChild) {
            // Need to create a child if applying the functor
            // to the tile value produces a different value.
            const ValueType& tileVal = mNodes[n].getValue();
            ValueType modifiedVal = tileVal;
            op(modifiedVal);
            createChild = !math::isExactlyEqual(tileVal, modifiedVal);
        }
        if (createChild) {
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) mNodes[n].getChild()->modifyValue(xyz, op);
}

template<typename ChildT, Index Log2Dim>
template<typename ModifyOp, typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::modifyValueAndCache(const Coord& xyz, const ModifyOp& op,
    AccessorT& acc)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        // Need to create a child if the tile is inactive,
        // in order to activate voxel (x, y, z).
        const bool active = this->isValueMaskOn(n);
        bool createChild = !active;
        if (!createChild) {
            // Need to create a child if applying the functor
            // to the tile value produces a different value.
            const ValueType& tileVal = mNodes[n].getValue();
            ValueType modifiedVal = tileVal;
            op(modifiedVal);
            createChild = !math::isExactlyEqual(tileVal, modifiedVal);
        }
        if (createChild) {
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, mNodes[n].getValue(), active));
        }
    }
    if (hasChild) {
        ChildNodeType* child = mNodes[n].getChild();
        acc.insert(xyz, child);
        child->modifyValueAndCache(xyz, op, acc);
    }
}


template<typename ChildT, Index Log2Dim>
template<typename ModifyOp>
inline void
InternalNode<ChildT, Log2Dim>::modifyValueAndActiveState(const Coord& xyz, const ModifyOp& op)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool tileState = this->isValueMaskOn(n);
        const ValueType& tileVal = mNodes[n].getValue();
        bool modifiedState = !tileState;
        ValueType modifiedVal = tileVal;
        op(modifiedVal, modifiedState);
        // Need to create a child if applying the functor to the tile
        // produces a different value or active state.
        if (modifiedState != tileState || !math::isExactlyEqual(modifiedVal, tileVal)) {
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, tileVal, tileState));
        }
    }
    if (hasChild) mNodes[n].getChild()->modifyValueAndActiveState(xyz, op);
}

template<typename ChildT, Index Log2Dim>
template<typename ModifyOp, typename AccessorT>
inline void
InternalNode<ChildT, Log2Dim>::modifyValueAndActiveStateAndCache(
    const Coord& xyz, const ModifyOp& op, AccessorT& acc)
{
    const Index n = InternalNode::coordToOffset(xyz);
    bool hasChild = this->isChildMaskOn(n);
    if (!hasChild) {
        const bool tileState = this->isValueMaskOn(n);
        const ValueType& tileVal = mNodes[n].getValue();
        bool modifiedState = !tileState;
        ValueType modifiedVal = tileVal;
        op(modifiedVal, modifiedState);
        // Need to create a child if applying the functor to the tile
        // produces a different value or active state.
        if (modifiedState != tileState || !math::isExactlyEqual(modifiedVal, tileVal)) {
            hasChild = true;
            this->setChildNode(n, new ChildNodeType(xyz, tileVal, tileState));
        }
    }
    if (hasChild) {
        ChildNodeType* child = mNodes[n].getChild();
        acc.insert(xyz, child);
        child->modifyValueAndActiveStateAndCache(xyz, op, acc);
    }
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::clip(const CoordBBox& clipBBox, const ValueType& background)
{
    CoordBBox nodeBBox = this->getNodeBoundingBox();
    if (!clipBBox.hasOverlap(nodeBBox)) {
        // This node lies completely outside the clipping region.  Fill it with background tiles.
        this->fill(nodeBBox, background, /*active=*/false);
    } else if (clipBBox.isInside(nodeBBox)) {
        // This node lies completely inside the clipping region.  Leave it intact.
        return;
    }

    // This node isn't completely contained inside the clipping region.
    // Clip tiles and children, and replace any that lie outside the region
    // with background tiles.

    for (Index pos = 0; pos < NUM_VALUES; ++pos) {
        const Coord xyz = this->offsetToGlobalCoord(pos); // tile or child origin
        CoordBBox tileBBox(xyz, xyz.offsetBy(ChildT::DIM - 1)); // tile or child bounds
        if (!clipBBox.hasOverlap(tileBBox)) {
            // This table entry lies completely outside the clipping region.
            // Replace it with a background tile.
            this->makeChildNodeEmpty(pos, background);
            mValueMask.setOff(pos);
        } else if (!clipBBox.isInside(tileBBox)) {
            // This table entry does not lie completely inside the clipping region
            // and must be clipped.
            if (this->isChildMaskOn(pos)) {
                mNodes[pos].getChild()->clip(clipBBox, background);
            } else {
                // Replace this tile with a background tile, then fill the clip region
                // with the tile's original value.  (This might create a child branch.)
                tileBBox.intersect(clipBBox);
                const ValueType val = mNodes[pos].getValue();
                const bool on = this->isValueMaskOn(pos);
                mNodes[pos].setValue(background);
                mValueMask.setOff(pos);
                this->fill(tileBBox, val, on);
            }
        } else {
            // This table entry lies completely inside the clipping region.  Leave it intact.
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::fill(const CoordBBox& bbox, const ValueType& value, bool active)
{
    auto clippedBBox = this->getNodeBoundingBox();
    clippedBBox.intersect(bbox);
    if (!clippedBBox) return;

    // Iterate over the fill region in axis-aligned, tile-sized chunks.
    // (The first and last chunks along each axis might be smaller than a tile.)
    Coord xyz, tileMin, tileMax;
    for (int x = clippedBBox.min().x(); x <= clippedBBox.max().x(); x = tileMax.x() + 1) {
        xyz.setX(x);
        for (int y = clippedBBox.min().y(); y <= clippedBBox.max().y(); y = tileMax.y() + 1) {
            xyz.setY(y);
            for (int z = clippedBBox.min().z(); z <= clippedBBox.max().z(); z = tileMax.z() + 1) {
                xyz.setZ(z);

                // Get the bounds of the tile that contains voxel (x, y, z).
                const Index n = this->coordToOffset(xyz);
                tileMin = this->offsetToGlobalCoord(n);
                tileMax = tileMin.offsetBy(ChildT::DIM - 1);

                if (xyz != tileMin || Coord::lessThan(clippedBBox.max(), tileMax)) {
                    // If the box defined by (xyz, clippedBBox.max()) doesn't completely enclose
                    // the tile to which xyz belongs, create a child node (or retrieve
                    // the existing one).
                    ChildT* child = nullptr;
                    if (this->isChildMaskOff(n)) {
                        // Replace the tile with a newly-created child that is initialized
                        // with the tile's value and active state.
                        child = new ChildT{xyz, mNodes[n].getValue(), this->isValueMaskOn(n)};
                        this->setChildNode(n, child);
                    } else {
                        child = mNodes[n].getChild();
                    }

                    // Forward the fill request to the child.
                    if (child) {
                        const Coord tmp = Coord::minComponent(clippedBBox.max(), tileMax);
                        child->fill(CoordBBox(xyz, tmp), value, active);
                    }

                } else {
                    // If the box given by (xyz, clippedBBox.max()) completely encloses
                    // the tile to which xyz belongs, create the tile (if it
                    // doesn't already exist) and give it the fill value.
                    this->makeChildNodeEmpty(n, value);
                    mValueMask.set(n, active);
                }
            }
        }
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::denseFill(const CoordBBox& bbox, const ValueType& value, bool active)
{
    auto clippedBBox = this->getNodeBoundingBox();
    clippedBBox.intersect(bbox);
    if (!clippedBBox) return;

    // Iterate over the fill region in axis-aligned, tile-sized chunks.
    // (The first and last chunks along each axis might be smaller than a tile.)
    Coord xyz, tileMin, tileMax;
    for (int x = clippedBBox.min().x(); x <= clippedBBox.max().x(); x = tileMax.x() + 1) {
        xyz.setX(x);
        for (int y = clippedBBox.min().y(); y <= clippedBBox.max().y(); y = tileMax.y() + 1) {
            xyz.setY(y);
            for (int z = clippedBBox.min().z(); z <= clippedBBox.max().z(); z = tileMax.z() + 1) {
                xyz.setZ(z);

                // Get the table index of the tile that contains voxel (x, y, z).
                const auto n = this->coordToOffset(xyz);

                // Retrieve the child node at index n, or replace the tile at index n with a child.
                ChildT* child = nullptr;
                if (this->isChildMaskOn(n)) {
                    child = mNodes[n].getChild();
                } else {
                    // Replace the tile with a newly-created child that is filled
                    // with the tile's value and active state.
                    child = new ChildT{xyz, mNodes[n].getValue(), this->isValueMaskOn(n)};
                    this->setChildNode(n, child);
                }

                // Get the bounds of the tile that contains voxel (x, y, z).
                tileMin = this->offsetToGlobalCoord(n);
                tileMax = tileMin.offsetBy(ChildT::DIM - 1);

                // Forward the fill request to the child.
                child->denseFill(CoordBBox{xyz, clippedBBox.max()}, value, active);
            }
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
template<typename DenseT>
inline void
InternalNode<ChildT, Log2Dim>::copyToDense(const CoordBBox& bbox, DenseT& dense) const
{
    using DenseValueType = typename DenseT::ValueType;

    const size_t xStride = dense.xStride(), yStride = dense.yStride(), zStride = dense.zStride();
    const Coord& min = dense.bbox().min();
    for (Coord xyz = bbox.min(), max; xyz[0] <= bbox.max()[0]; xyz[0] = max[0] + 1) {
        for (xyz[1] = bbox.min()[1]; xyz[1] <= bbox.max()[1]; xyz[1] = max[1] + 1) {
            for (xyz[2] = bbox.min()[2]; xyz[2] <= bbox.max()[2]; xyz[2] = max[2] + 1) {
                const Index n = this->coordToOffset(xyz);
                // Get max coordinates of the child node that contains voxel xyz.
                max = this->offsetToGlobalCoord(n).offsetBy(ChildT::DIM-1);

                // Get the bbox of the interection of bbox and the child node
                CoordBBox sub(xyz, Coord::minComponent(bbox.max(), max));

                if (this->isChildMaskOn(n)) {//is a child
                    mNodes[n].getChild()->copyToDense(sub, dense);
                } else {//a tile value
                    const ValueType value = mNodes[n].getValue();
                    sub.translate(-min);
                    DenseValueType* a0 = dense.data() + zStride*sub.min()[2];
                    for (Int32 x=sub.min()[0], ex=sub.max()[0]+1; x<ex; ++x) {
                        DenseValueType* a1 = a0 + x*xStride;
                        for (Int32 y=sub.min()[1], ey=sub.max()[1]+1; y<ey; ++y) {
                            DenseValueType* a2 = a1 + y*yStride;
                            for (Int32 z = sub.min()[2], ez = sub.max()[2]+1;
                                z < ez; ++z, a2 += zStride)
                            {
                                *a2 = DenseValueType(value);
                            }
                        }
                    }
                }
            }
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::writeTopology(std::ostream& os, bool toHalf) const
{
    mChildMask.save(os);
    mValueMask.save(os);

    {
        // Copy all of this node's values into an array.
        std::unique_ptr<ValueType[]> valuePtr(new ValueType[NUM_VALUES]);
        ValueType* values = valuePtr.get();
        const ValueType zero = zeroVal<ValueType>();
        for (Index i = 0; i < NUM_VALUES; ++i) {
            values[i] = (mChildMask.isOff(i) ? mNodes[i].getValue() : zero);
        }
        // Compress (optionally) and write out the contents of the array.
        io::writeCompressedValues(os, values, NUM_VALUES, mValueMask, mChildMask, toHalf);
    }
    // Write out the child nodes in order.
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        iter->writeTopology(os, toHalf);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::readTopology(std::istream& is, bool fromHalf)
{
    io::checkFormatVersion(is);

    const ValueType background = (!io::getGridBackgroundValuePtr(is) ? zeroVal<ValueType>()
        : *static_cast<const ValueType*>(io::getGridBackgroundValuePtr(is)));

    mChildMask.load(is);
    mValueMask.load(is);

    const bool oldVersion =
        (io::getFormatVersion(is) < OPENVDB_FILE_VERSION_NODE_MASK_COMPRESSION);
    const Index numValues = (oldVersion ? mChildMask.countOff() : NUM_VALUES);
    {
        // Read in (and uncompress, if necessary) all of this node's values
        // into a contiguous array.
        std::unique_ptr<ValueType[]> valuePtr(new ValueType[numValues]);
        ValueType* values = valuePtr.get();
        io::readCompressedValues(is, values, numValues, mValueMask, fromHalf);

        // Copy values from the array into this node's table.
        if (oldVersion) {
            Index n = 0;
            for (ValueAllIter iter = this->beginValueAll(); iter; ++iter) {
                mNodes[iter.pos()].setValue(values[n++]);
            }
            OPENVDB_ASSERT(n == numValues);
        } else {
            for (ValueAllIter iter = this->beginValueAll(); iter; ++iter) {
                mNodes[iter.pos()].setValue(values[iter.pos()]);
            }
        }
    }

    // Read in all child nodes and insert them into the table at their proper locations.
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        ChildNodeType* child = new ChildNodeType(PartialCreate(), iter.getCoord(), background);
        mNodes[iter.pos()].setChild(child);
        child->readTopology(is, fromHalf);
    }
}


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


template<typename ChildT, Index Log2Dim>
inline const typename ChildT::ValueType&
InternalNode<ChildT, Log2Dim>::getFirstValue() const
{
    return (this->isChildMaskOn(0) ? mNodes[0].getChild()->getFirstValue() : mNodes[0].getValue());
}


template<typename ChildT, Index Log2Dim>
inline const typename ChildT::ValueType&
InternalNode<ChildT, Log2Dim>::getLastValue() const
{
    const Index n = NUM_VALUES - 1;
    return (this->isChildMaskOn(n) ? mNodes[n].getChild()->getLastValue() : mNodes[n].getValue());
}


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


template<typename ChildT, Index Log2Dim>
inline const typename ChildT::ValueType&
InternalNode<ChildT, Log2Dim>::getValueUnsafe(Index n) const
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    return mNodes[n].getValue();
}

template<typename ChildT, Index Log2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::getValueUnsafe(Index n, ValueType& value) const
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    value = mNodes[n].getValue();
    return mValueMask.isOn(n);
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::getChildUnsafe(Index n)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOn(n));
    return mNodes[n].getChild();
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::getConstChildUnsafe(Index n) const
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOn(n));
    return mNodes[n].getChild();
}

template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::getChildUnsafe(Index n) const
{
    return this->getConstChildUnsafe(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setActiveStateUnsafe(Index n, bool on)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mValueMask.set(n, on);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOnlyUnsafe(Index n, const ValueType& value)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mNodes[n].setValue(value);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOnUnsafe(Index n)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mValueMask.setOn(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOnUnsafe(Index n, const ValueType& value)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mNodes[n].setValue(value);
    mValueMask.setOn(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOffUnsafe(Index n)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mValueMask.setOff(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueOffUnsafe(Index n, const ValueType& value)
{
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mNodes[n].setValue(value);
    mValueMask.setOff(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setValueMaskUnsafe(const NodeMaskType& mask)
{
    OPENVDB_ASSERT(mChildMask.isOff());
    mValueMask = mask;
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setChildUnsafe(Index n, ChildNodeType* child)
{
    // replace tile with child
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOff(n));
    mNodes[n].setChild(child);
    mChildMask.setOn(n);
    mValueMask.setOff(n);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::resetChildUnsafe(Index n, ChildNodeType* child)
{
    // replace child with child
    OPENVDB_ASSERT(child);
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOn(n));
    delete mNodes[n].getChild();
    mNodes[n].setChild(child);
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::stealChildUnsafe(Index n, const ValueType& value, bool active)
{
    // replace child with tile (and return child)
    OPENVDB_ASSERT(n < NUM_VALUES);
    OPENVDB_ASSERT(mChildMask.isOn(n));
    auto* child = mNodes[n].getChild();
    mChildMask.setOff(n);
    mValueMask.set(n, active);
    mNodes[n].setValue(value);
    return child;
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::deleteChildUnsafe(Index n, const ValueType& value, bool active)
{
    // replace child with tile (and delete child)
    delete this->stealChildUnsafe(n, value, active);
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::negate()
{
    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (this->isChildMaskOn(i)) {
            mNodes[i].getChild()->negate();
        } else {
            mNodes[i].setValue(math::negative(mNodes[i].getValue()));
        }
    }

}


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


template<typename ChildT, Index Log2Dim>
struct InternalNode<ChildT, Log2Dim>::VoxelizeActiveTiles
{
    VoxelizeActiveTiles(InternalNode &node) : mNode(&node) {
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//single thread for debugging
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);

        node.mChildMask |= node.mValueMask;
        node.mValueMask.setOff();
    }
    void operator()(const tbb::blocked_range<Index> &r) const
    {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (mNode->mChildMask.isOn(i)) {// Loop over node's child nodes
                mNode->mNodes[i].getChild()->voxelizeActiveTiles(true);
            } else if (mNode->mValueMask.isOn(i)) {// Loop over node's active tiles
                const Coord &ijk = mNode->offsetToGlobalCoord(i);
                ChildNodeType *child = new ChildNodeType(ijk, mNode->mNodes[i].getValue(), true);
                child->voxelizeActiveTiles(true);
                mNode->mNodes[i].setChild(child);
            }
        }
    }
    InternalNode* mNode;
};// VoxelizeActiveTiles

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::voxelizeActiveTiles(bool threaded)
{
    if (threaded) {
        VoxelizeActiveTiles tmp(*this);
    } else {
        for (ValueOnIter iter = this->beginValueOn(); iter; ++iter) {
            this->setChildNode(iter.pos(),
                new ChildNodeType(iter.getCoord(), iter.getValue(), true));
        }
        for (ChildOnIter iter = this->beginChildOn(); iter; ++iter)
            iter->voxelizeActiveTiles(false);
    }
}


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


template<typename ChildT, Index Log2Dim>
template<MergePolicy Policy>
inline void
InternalNode<ChildT, Log2Dim>::merge(InternalNode& other,
    const ValueType& background, const ValueType& otherBackground)
{
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN

    switch (Policy) {

    case MERGE_ACTIVE_STATES:
    default:
    {
        for (ChildOnIter iter = other.beginChildOn(); iter; ++iter) {
            const Index n = iter.pos();
            if (mChildMask.isOn(n)) {
                // Merge this node's child with the other node's child.
                mNodes[n].getChild()->template merge<MERGE_ACTIVE_STATES>(*iter,
                    background, otherBackground);
            } else if (mValueMask.isOff(n)) {
                // Replace this node's inactive tile with the other node's child
                // and replace the other node's child with a tile of undefined value
                // (which is okay since the other tree is assumed to be cannibalized
                // in the process of merging).
                ChildNodeType* child = other.mNodes[n].getChild();
                other.mChildMask.setOff(n);
                child->resetBackground(otherBackground, background);
                this->setChildNode(n, child);
            }
        }

        // Copy active tile values.
        for (ValueOnCIter iter = other.cbeginValueOn(); iter; ++iter) {
            const Index n = iter.pos();
            if (mValueMask.isOff(n)) {
                // Replace this node's child or inactive tile with the other node's active tile.
                this->makeChildNodeEmpty(n, iter.getValue());
                mValueMask.setOn(n);
            }
        }
        break;
    }

    case MERGE_NODES:
    {
        for (ChildOnIter iter = other.beginChildOn(); iter; ++iter) {
            const Index n = iter.pos();
            if (mChildMask.isOn(n)) {
                // Merge this node's child with the other node's child.
                mNodes[n].getChild()->template merge<Policy>(*iter, background, otherBackground);
            } else {
                // Replace this node's tile (regardless of its active state) with
                // the other node's child and replace the other node's child with
                // a tile of undefined value (which is okay since the other tree
                // is assumed to be cannibalized in the process of merging).
                ChildNodeType* child = other.mNodes[n].getChild();
                other.mChildMask.setOff(n);
                child->resetBackground(otherBackground, background);
                this->setChildNode(n, child);
            }
        }
        break;
    }

    case MERGE_ACTIVE_STATES_AND_NODES:
    {
        // Transfer children from the other tree to this tree.
        for (ChildOnIter iter = other.beginChildOn(); iter; ++iter) {
            const Index n = iter.pos();
            if (mChildMask.isOn(n)) {
                // Merge this node's child with the other node's child.
                mNodes[n].getChild()->template merge<Policy>(*iter, background, otherBackground);
            } else {
                // Replace this node's tile with the other node's child, leaving the other
                // node with an inactive tile of undefined value (which is okay since
                // the other tree is assumed to be cannibalized in the process of merging).
                ChildNodeType* child = other.mNodes[n].getChild();
                other.mChildMask.setOff(n);
                child->resetBackground(otherBackground, background);
                if (mValueMask.isOn(n)) {
                    // Merge the child with this node's active tile.
                    child->template merge<Policy>(mNodes[n].getValue(), /*on=*/true);
                    mValueMask.setOff(n);
                }
                mChildMask.setOn(n);
                mNodes[n].setChild(child);
            }
        }

        // Merge active tiles into this tree.
        for (ValueOnCIter iter = other.cbeginValueOn(); iter; ++iter) {
            const Index n = iter.pos();
            if (mChildMask.isOn(n)) {
                // Merge the other node's active tile into this node's child.
                mNodes[n].getChild()->template merge<Policy>(iter.getValue(), /*on=*/true);
            } else if (mValueMask.isOff(n)) {
                // Replace this node's inactive tile with the other node's active tile.
                mNodes[n].setValue(iter.getValue());
                mValueMask.setOn(n);
            }
        }
        break;
    }

    }
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


template<typename ChildT, Index Log2Dim>
template<MergePolicy Policy>
inline void
InternalNode<ChildT, Log2Dim>::merge(const ValueType& tileValue, bool tileActive)
{
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN

    if (Policy != MERGE_ACTIVE_STATES_AND_NODES) return;

    // For MERGE_ACTIVE_STATES_AND_NODES, inactive tiles in the other tree are ignored.
    if (!tileActive) return;

    // Iterate over this node's children and inactive tiles.
    for (ValueOffIter iter = this->beginValueOff(); iter; ++iter) {
        const Index n = iter.pos();
        if (mChildMask.isOn(n)) {
            // Merge the other node's active tile into this node's child.
            mNodes[n].getChild()->template merge<Policy>(tileValue, /*on=*/true);
        } else {
            // Replace this node's inactive tile with the other node's active tile.
            iter.setValue(tileValue);
            mValueMask.setOn(n);
        }
    }
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::TopologyUnion
{
    using W = typename NodeMaskType::Word;
    struct A { inline void operator()(W &tV, const W& sV, const W& tC) const
        { tV = (tV | sV) & ~tC; }
    };
    TopologyUnion(const OtherInternalNode* source, InternalNode* target, const bool preserveTiles)
        : s(source), t(target), mPreserveTiles(preserveTiles) {
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//single thread for debugging
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);

        // Bit processing is done in a single thread!
        if (!mPreserveTiles) t->mChildMask |= s->mChildMask;//serial but very fast bitwise post-process
        else                 t->mChildMask |= (s->mChildMask & !t->mValueMask);

        A op;
        t->mValueMask.foreach(s->mValueMask, t->mChildMask, op);
        OPENVDB_ASSERT((t->mValueMask & t->mChildMask).isOff());//no overlapping active tiles or child nodes
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (s->mChildMask.isOn(i)) {// Loop over other node's child nodes
                const typename OtherInternalNode::ChildNodeType& other = *(s->mNodes[i].getChild());
                if (t->mChildMask.isOn(i)) {//this has a child node
                    t->mNodes[i].getChild()->topologyUnion(other, mPreserveTiles);
                } else {// this is a tile so replace it with a child branch with identical topology
                    if (!mPreserveTiles || t->mValueMask.isOff(i)) { // force child topology
                        ChildT* child = new ChildT(other, t->mNodes[i].getValue(), TopologyCopy());
                        if (t->mValueMask.isOn(i)) child->setValuesOn();//activate all values
                        t->mNodes[i].setChild(child);
                    }
                }
            } else if (s->mValueMask.isOn(i) && t->mChildMask.isOn(i)) {
                t->mNodes[i].getChild()->setValuesOn();
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
    const bool mPreserveTiles;
};// TopologyUnion

template<typename ChildT, Index Log2Dim>
template<typename OtherChildT>
inline void
InternalNode<ChildT, Log2Dim>::topologyUnion(const InternalNode<OtherChildT, Log2Dim>& other, const bool preserveTiles)
{
    TopologyUnion<InternalNode<OtherChildT, Log2Dim> > tmp(&other, this, preserveTiles);
}

template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::TopologyIntersection
{
    using W = typename NodeMaskType::Word;
    struct A { inline void operator()(W &tC, const W& sC, const W& sV, const W& tV) const
        { tC = (tC & (sC | sV)) | (tV & sC); }
    };
    TopologyIntersection(const OtherInternalNode* source, InternalNode* target,
                         const ValueType& background) : s(source), t(target), b(background) {
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//single thread for debugging
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);

        // Bit processing is done in a single thread!
        A op;
        t->mChildMask.foreach(s->mChildMask, s->mValueMask, t->mValueMask, op);

        t->mValueMask &= s->mValueMask;
        OPENVDB_ASSERT((t->mValueMask & t->mChildMask).isOff());//no overlapping active tiles or child nodes
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (t->mChildMask.isOn(i)) {// Loop over this node's child nodes
                ChildT* child = t->mNodes[i].getChild();
                if (s->mChildMask.isOn(i)) {//other also has a child node
                    child->topologyIntersection(*(s->mNodes[i].getChild()), b);
                } else if (s->mValueMask.isOff(i)) {//other is an inactive tile
                    delete child;//convert child to an inactive tile
                    t->mNodes[i].setValue(b);
                }
            } else if (t->mValueMask.isOn(i) && s->mChildMask.isOn(i)) {//active tile -> a branch
                t->mNodes[i].setChild(new ChildT(*(s->mNodes[i].getChild()),
                                                 t->mNodes[i].getValue(), TopologyCopy()));
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
    const ValueType& b;
};// TopologyIntersection

template<typename ChildT, Index Log2Dim>
template<typename OtherChildT>
inline void
InternalNode<ChildT, Log2Dim>::topologyIntersection(
    const InternalNode<OtherChildT, Log2Dim>& other, const ValueType& background)
{
    TopologyIntersection<InternalNode<OtherChildT, Log2Dim> > tmp(&other, this, background);
}

template<typename ChildT, Index Log2Dim>
template<typename OtherInternalNode>
struct InternalNode<ChildT, Log2Dim>::TopologyDifference
{
    using W = typename NodeMaskType::Word;
    struct A {inline void operator()(W &tC, const W& sC, const W& sV, const W& tV) const
        { tC = (tC & (sC | ~sV)) | (tV & sC); }
    };
    struct B {inline void operator()(W &tV, const W& sC, const W& sV, const W& tC) const
        { tV &= ~((tC & sV) | (sC | sV)); }
    };
    TopologyDifference(const OtherInternalNode* source, InternalNode* target,
                       const ValueType& background) : s(source), t(target), b(background) {
        //(*this)(tbb::blocked_range<Index>(0, NUM_VALUES));//single thread for debugging
        tbb::parallel_for(tbb::blocked_range<Index>(0, NUM_VALUES), *this);

        // Bit processing is done in a single thread!
        const NodeMaskType oldChildMask(t->mChildMask);//important to avoid cross pollution
        A op1;
        t->mChildMask.foreach(s->mChildMask, s->mValueMask, t->mValueMask, op1);

        B op2;
        t->mValueMask.foreach(t->mChildMask, s->mValueMask, oldChildMask, op2);
        OPENVDB_ASSERT((t->mValueMask & t->mChildMask).isOff());//no overlapping active tiles or child nodes
    }
    void operator()(const tbb::blocked_range<Index> &r) const {
        for (Index i = r.begin(), end=r.end(); i!=end; ++i) {
            if (t->mChildMask.isOn(i)) {// Loop over this node's child nodes
                ChildT* child = t->mNodes[i].getChild();
                if (s->mChildMask.isOn(i)) {
                    child->topologyDifference(*(s->mNodes[i].getChild()), b);
                } else if (s->mValueMask.isOn(i)) {
                    delete child;//convert child to an inactive tile
                    t->mNodes[i].setValue(b);
                }
            } else if (t->mValueMask.isOn(i)) {//this is an active tile
                if (s->mChildMask.isOn(i)) {
                    const typename OtherInternalNode::ChildNodeType& other =
                        *(s->mNodes[i].getChild());
                    ChildT* child = new ChildT(other.origin(), t->mNodes[i].getValue(), true);
                    child->topologyDifference(other, b);
                    t->mNodes[i].setChild(child);//replace the active tile with a child branch
                }
            }
        }
    }
    const OtherInternalNode* s;
    InternalNode* t;
    const ValueType& b;
};// TopologyDifference

template<typename ChildT, Index Log2Dim>
template<typename OtherChildT>
inline void
InternalNode<ChildT, Log2Dim>::topologyDifference(const InternalNode<OtherChildT, Log2Dim>& other,
                                                  const ValueType& background)
{
    TopologyDifference<InternalNode<OtherChildT, Log2Dim> > tmp(&other, this, background);
}


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


template<typename ChildT, Index Log2Dim>
template<typename CombineOp>
inline void
InternalNode<ChildT, Log2Dim>::combine(InternalNode& other, CombineOp& op)
{
    const ValueType zero = zeroVal<ValueType>();

    CombineArgs<ValueType> args;

    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (this->isChildMaskOff(i) && other.isChildMaskOff(i)) {
            // Both this node and the other node have constant values (tiles).
            // Combine the two values and store the result as this node's new tile value.
            op(args.setARef(mNodes[i].getValue())
                .setAIsActive(isValueMaskOn(i))
                .setBRef(other.mNodes[i].getValue())
               .setBIsActive(other.isValueMaskOn(i)));
            mNodes[i].setValue(args.result());
            mValueMask.set(i, args.resultIsActive());
        } else if (this->isChildMaskOn(i) && other.isChildMaskOff(i)) {
            // Combine this node's child with the other node's constant value.
            ChildNodeType* child = mNodes[i].getChild();
            OPENVDB_ASSERT(child);
            if (child) {
                child->combine(other.mNodes[i].getValue(), other.isValueMaskOn(i), op);
            }
        } else if (this->isChildMaskOff(i) && other.isChildMaskOn(i)) {
            // Combine this node's constant value with the other node's child.
            ChildNodeType* child = other.mNodes[i].getChild();
            OPENVDB_ASSERT(child);
            if (child) {
                // Combine this node's constant value with the other node's child,
                // but use a new functor in which the A and B values are swapped,
                // since the constant value is the A value, not the B value.
                SwappedCombineOp<ValueType, CombineOp> swappedOp(op);
                child->combine(mNodes[i].getValue(), isValueMaskOn(i), swappedOp);

                // Steal the other node's child.
                other.mChildMask.setOff(i);
                other.mNodes[i].setValue(zero);
                this->setChildNode(i, child);
            }

        } else /*if (isChildMaskOn(i) && other.isChildMaskOn(i))*/ {
            // Combine this node's child with the other node's child.
            ChildNodeType
                *child = mNodes[i].getChild(),
                *otherChild = other.mNodes[i].getChild();
            OPENVDB_ASSERT(child);
            OPENVDB_ASSERT(otherChild);
            if (child && otherChild) {
                child->combine(*otherChild, op);
            }
        }
    }
}


template<typename ChildT, Index Log2Dim>
template<typename CombineOp>
inline void
InternalNode<ChildT, Log2Dim>::combine(const ValueType& value, bool valueIsActive, CombineOp& op)
{
    CombineArgs<ValueType> args;

    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (this->isChildMaskOff(i)) {
            // Combine this node's constant value with the given constant value.
            op(args.setARef(mNodes[i].getValue())
               .setAIsActive(isValueMaskOn(i))
               .setBRef(value)
               .setBIsActive(valueIsActive));
            mNodes[i].setValue(args.result());
            mValueMask.set(i, args.resultIsActive());
        } else /*if (isChildMaskOn(i))*/ {
            // Combine this node's child with the given constant value.
            ChildNodeType* child = mNodes[i].getChild();
            OPENVDB_ASSERT(child);
            if (child) child->combine(value, valueIsActive, op);
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
template<typename CombineOp, typename OtherNodeType>
inline void
InternalNode<ChildT, Log2Dim>::combine2(const InternalNode& other0, const OtherNodeType& other1,
    CombineOp& op)
{
    CombineArgs<ValueType, typename OtherNodeType::ValueType> args;

    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (other0.isChildMaskOff(i) && other1.isChildMaskOff(i)) {
            op(args.setARef(other0.mNodes[i].getValue())
                .setAIsActive(other0.isValueMaskOn(i))
                .setBRef(other1.mNodes[i].getValue())
                .setBIsActive(other1.isValueMaskOn(i)));
            // Replace child i with a constant value.
            this->makeChildNodeEmpty(i, args.result());
            mValueMask.set(i, args.resultIsActive());
        } else {
            if (this->isChildMaskOff(i)) {
                // Add a new child with the same coordinates, etc. as the other node's child.
                const Coord& childOrigin = other0.isChildMaskOn(i)
                    ? other0.mNodes[i].getChild()->origin()
                    : other1.mNodes[i].getChild()->origin();
                this->setChildNode(i, new ChildNodeType(childOrigin, mNodes[i].getValue()));
            }

            if (other0.isChildMaskOff(i)) {
                // Combine node1's child with node0's constant value
                // and write the result into child i.
                mNodes[i].getChild()->combine2(other0.mNodes[i].getValue(),
                    *other1.mNodes[i].getChild(), other0.isValueMaskOn(i), op);
            } else if (other1.isChildMaskOff(i)) {
                // Combine node0's child with node1's constant value
                // and write the result into child i.
                mNodes[i].getChild()->combine2(*other0.mNodes[i].getChild(),
                    other1.mNodes[i].getValue(), other1.isValueMaskOn(i), op);
            } else {
                // Combine node0's child with node1's child
                // and write the result into child i.
                mNodes[i].getChild()->combine2(*other0.mNodes[i].getChild(),
                    *other1.mNodes[i].getChild(), op);
            }
        }
    }
}


template<typename ChildT, Index Log2Dim>
template<typename CombineOp, typename OtherNodeType>
inline void
InternalNode<ChildT, Log2Dim>::combine2(const ValueType& value, const OtherNodeType& other,
    bool valueIsActive, CombineOp& op)
{
    CombineArgs<ValueType, typename OtherNodeType::ValueType> args;

    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (other.isChildMaskOff(i)) {
            op(args.setARef(value)
                .setAIsActive(valueIsActive)
                .setBRef(other.mNodes[i].getValue())
                .setBIsActive(other.isValueMaskOn(i)));
            // Replace child i with a constant value.
            this->makeChildNodeEmpty(i, args.result());
            mValueMask.set(i, args.resultIsActive());
        } else {
            typename OtherNodeType::ChildNodeType* otherChild = other.mNodes[i].getChild();
            OPENVDB_ASSERT(otherChild);
            if (this->isChildMaskOff(i)) {
                // Add a new child with the same coordinates, etc.
                // as the other node's child.
                this->setChildNode(i, new ChildNodeType(*otherChild));
            }
            // Combine the other node's child with a constant value
            // and write the result into child i.
            mNodes[i].getChild()->combine2(value, *otherChild, valueIsActive, op);
        }
    }
}


template<typename ChildT, Index Log2Dim>
template<typename CombineOp, typename OtherValueType>
inline void
InternalNode<ChildT, Log2Dim>::combine2(const InternalNode& other, const OtherValueType& value,
    bool valueIsActive, CombineOp& op)
{
    CombineArgs<ValueType, OtherValueType> args;

    for (Index i = 0; i < NUM_VALUES; ++i) {
        if (other.isChildMaskOff(i)) {
            op(args.setARef(other.mNodes[i].getValue())
                .setAIsActive(other.isValueMaskOn(i))
                .setBRef(value)
                .setBIsActive(valueIsActive));
            // Replace child i with a constant value.
            this->makeChildNodeEmpty(i, args.result());
            mValueMask.set(i, args.resultIsActive());
        } else {
            ChildNodeType* otherChild = other.mNodes[i].getChild();
            OPENVDB_ASSERT(otherChild);
            if (this->isChildMaskOff(i)) {
                // Add a new child with the same coordinates, etc. as the other node's child.
                this->setChildNode(i,
                    new ChildNodeType(otherChild->origin(), mNodes[i].getValue()));
            }
            // Combine the other node's child with a constant value
            // and write the result into child i.
            mNodes[i].getChild()->combine2(*otherChild, value, valueIsActive, op);
        }
    }
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::writeBuffers(std::ostream& os, bool toHalf) const
{
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        iter->writeBuffers(os, toHalf);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::readBuffers(std::istream& is, bool fromHalf)
{
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        iter->readBuffers(is, fromHalf);
    }
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::readBuffers(std::istream& is,
    const CoordBBox& clipBBox, bool fromHalf)
{
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        // Stream in the branch rooted at this child.
        // (We can't skip over children that lie outside the clipping region,
        // because buffers are serialized in depth-first order and need to be
        // unserialized in the same order.)
        iter->readBuffers(is, clipBBox, fromHalf);
    }

    // Get this tree's background value.
    ValueType background = zeroVal<ValueType>();
    if (const void* bgPtr = io::getGridBackgroundValuePtr(is)) {
        background = *static_cast<const ValueType*>(bgPtr);
    }
    this->clip(clipBBox, background);
}


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


template<typename ChildT, Index Log2Dim>
void
InternalNode<ChildT, Log2Dim>::getNodeLog2Dims(std::vector<Index>& dims)
{
    dims.push_back(Log2Dim);
    ChildNodeType::getNodeLog2Dims(dims);
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::offsetToLocalCoord(Index n, Coord &xyz)
{
    OPENVDB_ASSERT(n<(1<<3*Log2Dim));
    xyz.setX(n >> 2*Log2Dim);
    n &= ((1<<2*Log2Dim)-1);
    xyz.setY(n >> Log2Dim);
    xyz.setZ(n & ((1<<Log2Dim)-1));
}


template<typename ChildT, Index Log2Dim>
inline Index
InternalNode<ChildT, Log2Dim>::coordToOffset(const Coord& xyz)
{
    return (((xyz[0] & (DIM-1u)) >> ChildNodeType::TOTAL) << 2*Log2Dim)
        +  (((xyz[1] & (DIM-1u)) >> ChildNodeType::TOTAL) <<   Log2Dim)
        +   ((xyz[2] & (DIM-1u)) >> ChildNodeType::TOTAL);
}


template<typename ChildT, Index Log2Dim>
inline Coord
InternalNode<ChildT, Log2Dim>::offsetToGlobalCoord(Index n) const
{
    Coord local;
    this->offsetToLocalCoord(n, local);
    local <<= ChildT::TOTAL;
    return local + this->origin();
}


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


template<typename ChildT, Index Log2Dim>
template<typename ArrayT>
inline void
InternalNode<ChildT, Log2Dim>::getNodes(ArrayT& array)
{
    using T = typename ArrayT::value_type;
    static_assert(std::is_pointer<T>::value, "argument to getNodes() must be a pointer array");
    using ArrayChildT = typename std::conditional<
        std::is_const<typename std::remove_pointer<T>::type>::value, const ChildT, ChildT>::type;
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
        if (std::is_same<T, ArrayChildT*>::value) {
            array.push_back(reinterpret_cast<T>(mNodes[iter.pos()].getChild()));
        } else {
            iter->getNodes(array);//descent
        }
        OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
    }
}

template<typename ChildT, Index Log2Dim>
template<typename ArrayT>
inline void
InternalNode<ChildT, Log2Dim>::getNodes(ArrayT& array) const
{
    using T = typename ArrayT::value_type;
    static_assert(std::is_pointer<T>::value, "argument to getNodes() must be a pointer array");
    static_assert(std::is_const<typename std::remove_pointer<T>::type>::value,
        "argument to getNodes() must be an array of const node pointers");
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
        if (std::is_same<T, const ChildT*>::value) {
            array.push_back(reinterpret_cast<T>(mNodes[iter.pos()].getChild()));
        } else {
            iter->getNodes(array);//descent
        }
        OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
    }
}


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


template<typename ChildT, Index Log2Dim>
template<typename ArrayT>
inline void
InternalNode<ChildT, Log2Dim>::stealNodes(ArrayT& array, const ValueType& value, bool state)
{
    using T = typename ArrayT::value_type;
    static_assert(std::is_pointer<T>::value, "argument to stealNodes() must be a pointer array");
    using ArrayChildT = typename std::conditional<
        std::is_const<typename std::remove_pointer<T>::type>::value, const ChildT, ChildT>::type;
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
    for (ChildOnIter iter = this->beginChildOn(); iter; ++iter) {
        const Index n = iter.pos();
        if (std::is_same<T, ArrayChildT*>::value) {
            array.push_back(reinterpret_cast<T>(mNodes[n].getChild()));
            mValueMask.set(n, state);
            mNodes[n].setValue(value);
        } else {
            iter->stealNodes(array, value, state);//descent
        }
    }
    if (std::is_same<T, ArrayChildT*>::value) mChildMask.setOff();
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::resetBackground(const ValueType& oldBackground,
                                               const ValueType& newBackground)
{
    if (math::isExactlyEqual(oldBackground, newBackground)) return;
    for (Index i = 0; i < NUM_VALUES; ++i) {
       if (this->isChildMaskOn(i)) {
           mNodes[i].getChild()->resetBackground(oldBackground, newBackground);
       } else if (this->isValueMaskOff(i)) {
           if (math::isApproxEqual(mNodes[i].getValue(), oldBackground)) {
               mNodes[i].setValue(newBackground);
           } else if (math::isApproxEqual(mNodes[i].getValue(), math::negative(oldBackground))) {
               mNodes[i].setValue(math::negative(newBackground));
           }
       }
    }
}

template<typename ChildT, Index Log2Dim>
template<typename OtherChildNodeType, Index OtherLog2Dim>
inline bool
InternalNode<ChildT, Log2Dim>::hasSameTopology(
    const InternalNode<OtherChildNodeType, OtherLog2Dim>* other) const
{
    if (Log2Dim != OtherLog2Dim || mChildMask != other->mChildMask ||
        mValueMask != other->mValueMask) return false;
    for (ChildOnCIter iter = this->cbeginChildOn(); iter; ++iter) {
        if (!iter->hasSameTopology(other->mNodes[iter.pos()].getChild())) return false;
    }
    return true;
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::resetChildNode(Index i, ChildNodeType* child)
{
    OPENVDB_ASSERT(child);
    if (this->isChildMaskOn(i)) {
        delete mNodes[i].getChild();
    } else {
        mChildMask.setOn(i);
        mValueMask.setOff(i);
    }
    mNodes[i].setChild(child);
}

template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::setChildNode(Index i, ChildNodeType* child)
{
    OPENVDB_ASSERT(child);
    OPENVDB_ASSERT(mChildMask.isOff(i));
    mChildMask.setOn(i);
    mValueMask.setOff(i);
    mNodes[i].setChild(child);
}


template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::unsetChildNode(Index i, const ValueType& value)
{
    if (this->isChildMaskOff(i)) {
        mNodes[i].setValue(value);
        return nullptr;
    }
    ChildNodeType* child = mNodes[i].getChild();
    mChildMask.setOff(i);
    mNodes[i].setValue(value);
    return child;
}


template<typename ChildT, Index Log2Dim>
inline void
InternalNode<ChildT, Log2Dim>::makeChildNodeEmpty(Index n, const ValueType& value)
{
    delete this->unsetChildNode(n, value);
}

template<typename ChildT, Index Log2Dim>
inline ChildT*
InternalNode<ChildT, Log2Dim>::getChildNode(Index n)
{
    OPENVDB_ASSERT(this->isChildMaskOn(n));
    return mNodes[n].getChild();
}


template<typename ChildT, Index Log2Dim>
inline const ChildT*
InternalNode<ChildT, Log2Dim>::getChildNode(Index n) const
{
    OPENVDB_ASSERT(this->isChildMaskOn(n));
    return mNodes[n].getChild();
}

} // namespace tree
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb

#endif // OPENVDB_TREE_INTERNALNODE_HAS_BEEN_INCLUDED