RootNode.h

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// Copyright Contributors to the OpenVDB Project
// SPDX-License-Identifier: MPL-2.0
///
/// @file RootNode.h
///
/// @brief The root node of an OpenVDB tree

#ifndef OPENVDB_TREE_ROOTNODE_HAS_BEEN_INCLUDED
#define OPENVDB_TREE_ROOTNODE_HAS_BEEN_INCLUDED

#include <openvdb/Exceptions.h>
#include <openvdb/Types.h>
#include <openvdb/io/Compression.h> // for truncateRealToHalf()
#include <openvdb/math/Math.h> // for isZero(), isExactlyEqual(), etc.
#include <openvdb/math/BBox.h>
#include <openvdb/util/NodeMasks.h> // for backward compatibility only (see readTopology())
#include <openvdb/version.h>
#include <tbb/parallel_for.h>
#include <map>
#include <set>
#include <sstream>
#include <vector>


namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace tree {

// Forward declarations
template<typename HeadType, int HeadLevel> struct NodeChain;
template<typename, typename> struct SameRootConfig;
template<typename, typename, bool> struct RootNodeCopyHelper;
template<typename, typename, typename, bool> struct RootNodeCombineHelper;


template<typename ChildType>
class RootNode
{
public:
    using ChildNodeType = ChildType;
    using LeafNodeType = typename ChildType::LeafNodeType;
    using ValueType = typename ChildType::ValueType;
    using BuildType = typename ChildType::BuildType;

    static const Index LEVEL = 1 + ChildType::LEVEL; // level 0 = leaf

    /// NodeChainType is a list of this tree's node types, from LeafNodeType to RootNode.
    using NodeChainType = typename NodeChain<RootNode, LEVEL>::Type;
    static_assert(NodeChainType::Size == LEVEL + 1,
        "wrong number of entries in RootNode node chain");

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

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


    /// Construct a new tree with a background value of 0.
    RootNode();

    /// Construct a new tree with the given background value.
    explicit RootNode(const ValueType& background);

    RootNode(const RootNode& other) { *this = other; }

    /// @brief Construct a new tree that reproduces the topology and active states
    /// of a tree of a different ValueType but the same configuration (levels,
    /// node dimensions and branching factors).  Cast the other tree's values to
    /// this tree's ValueType.
    /// @throw TypeError if the other tree's configuration doesn't match this tree's
    /// or if this tree's ValueType is not constructible from the other tree's ValueType.
    template<typename OtherChildType>
    explicit RootNode(const RootNode<OtherChildType>& other) { *this = other; }

    /// @brief Construct a new tree that reproduces the topology and active states of
    /// another tree (which may have a different ValueType), but not the other tree's values.
    /// @details All tiles and voxels that are active in the other tree are set to
    /// @a foreground in the new tree, and all inactive tiles and voxels are set to @a background.
    /// @param other       the root node of a tree having (possibly) a different ValueType
    /// @param background  the value to which inactive tiles and voxels are initialized
    /// @param foreground  the value to which active tiles and voxels are initialized
    /// @throw TypeError if the other tree's configuration doesn't match this tree's.
    template<typename OtherChildType>
    RootNode(const RootNode<OtherChildType>& other,
        const ValueType& background, const ValueType& foreground, TopologyCopy);

    /// @brief Construct a new tree that reproduces the topology and active states of
    /// another tree (which may have a different ValueType), but not the other tree's values.
    /// All tiles and voxels in the new tree are set to @a background regardless of
    /// their active states in the other tree.
    /// @param other       the root node of a tree having (possibly) a different ValueType
    /// @param background  the value to which inactive tiles and voxels are initialized
    /// @note This copy constructor is generally faster than the one that takes both
    /// a foreground and a background value.  Its main application is in multithreaded
    /// operations where the topology of the output tree exactly matches the input tree.
    /// @throw TypeError if the other tree's configuration doesn't match this tree's.
    template<typename OtherChildType>
    RootNode(const RootNode<OtherChildType>& other, const ValueType& background, TopologyCopy);

    /// @brief Copy a root node of the same type as this node.
    RootNode& operator=(const RootNode& other);
    /// @brief Copy a root node of the same tree configuration as this node
    /// but a different ValueType.
    /// @throw TypeError if the other tree's configuration doesn't match this tree's.
    /// @note This node's ValueType must be constructible from the other node's ValueType.
    /// For example, a root node with values of type float can be assigned to a root node
    /// with values of type Vec3s, because a Vec3s can be constructed from a float.
    /// But a Vec3s root node cannot be assigned to a float root node.
    template<typename OtherChildType>
    RootNode& operator=(const RootNode<OtherChildType>& other);

    ~RootNode() { this->clear(); }

private:
    struct Tile {
        Tile(): value(zeroVal<ValueType>()), active(false) {}
        Tile(const ValueType& v, bool b): value(v), active(b) {}
        ValueType value;
        bool      active;
    };

    // This lightweight struct pairs child pointers and tiles.
    struct NodeStruct {
        ChildType* child;
        Tile       tile;

        NodeStruct(): child(nullptr) {}
        NodeStruct(ChildType& c): child(&c) {}
        NodeStruct(const Tile& t): child(nullptr), tile(t) {}
        NodeStruct(const NodeStruct&) = default;
        NodeStruct& operator=(const NodeStruct&) = default;
        ~NodeStruct() {} ///< @note doesn't delete child

        bool isChild() const { return child != nullptr; }
        bool isTile() const { return child == nullptr; }
        bool isTileOff() const { return isTile() && !tile.active; }
        bool isTileOn() const { return isTile() && tile.active; }

        void set(ChildType& c) { delete child; child = &c; }
        void set(const Tile& t) { delete child; child = nullptr; tile = t; }
        ChildType& steal(const Tile& t) { ChildType* c=child; child=nullptr; tile=t; return *c; }
    };

    using MapType = std::map<Coord, NodeStruct>;
    using MapIter = typename MapType::iterator;
    using MapCIter = typename MapType::const_iterator;

    using CoordSet = std::set<Coord>;
    using CoordSetIter = typename CoordSet::iterator;
    using CoordSetCIter = typename CoordSet::const_iterator;

    static void             setTile(const MapIter& i, const Tile& t) { i->second.set(t); }
    static void             setChild(const MapIter& i, ChildType& c) { i->second.set(c); }
    static Tile&            getTile(const MapIter& i) { return i->second.tile; }
    static const Tile&      getTile(const MapCIter& i) { return i->second.tile; }
    static ChildType&       getChild(const MapIter& i) { return *(i->second.child); }
    static const ChildType& getChild(const MapCIter& i) { return *(i->second.child); }
    static ChildType&       stealChild(const MapIter& i, const Tile& t) {return i->second.steal(t);}
    static const ChildType& stealChild(const MapCIter& i,const Tile& t) {return i->second.steal(t);}

    static bool isChild(const MapCIter& i)   { return i->second.isChild(); }
    static bool isChild(const MapIter& i)    { return i->second.isChild(); }
    static bool isTile(const MapCIter& i)    { return i->second.isTile(); }
    static bool isTile(const MapIter& i)     { return i->second.isTile(); }
    static bool isTileOff(const MapCIter& i) { return i->second.isTileOff(); }
    static bool isTileOff(const MapIter& i)  { return i->second.isTileOff(); }
    static bool isTileOn(const MapCIter& i)  { return i->second.isTileOn(); }
    static bool isTileOn(const MapIter& i)   { return i->second.isTileOn(); }

    struct NullPred {
        static inline bool test(const MapIter&) { return true; }
        static inline bool test(const MapCIter&) { return true; }
    };
    struct ValueOnPred {
        static inline bool test(const MapIter& i) { return isTileOn(i); }
        static inline bool test(const MapCIter& i) { return isTileOn(i); }
    };
    struct ValueOffPred {
        static inline bool test(const MapIter& i) { return isTileOff(i); }
        static inline bool test(const MapCIter& i) { return isTileOff(i); }
    };
    struct ValueAllPred {
        static inline bool test(const MapIter& i) { return isTile(i); }
        static inline bool test(const MapCIter& i) { return isTile(i); }
    };
    struct ChildOnPred {
        static inline bool test(const MapIter& i) { return isChild(i); }
        static inline bool test(const MapCIter& i) { return isChild(i); }
    };
    struct ChildOffPred {
        static inline bool test(const MapIter& i) { return isTile(i); }
        static inline bool test(const MapCIter& i) { return isTile(i); }
    };

    template<typename _RootNodeT, typename _MapIterT, typename FilterPredT>
    class BaseIter
    {
    public:
        using RootNodeT = _RootNodeT;
        using MapIterT = _MapIterT; // either MapIter or MapCIter

        bool operator==(const BaseIter& other) const
        {
            return (mParentNode == other.mParentNode) && (mIter == other.mIter);
        }
        bool operator!=(const BaseIter& other) const { return !(*this == other); }

        RootNodeT* getParentNode() const { return mParentNode; }
        /// Return a reference to the node over which this iterator iterates.
        RootNodeT& parent() const
        {
            if (!mParentNode) OPENVDB_THROW(ValueError, "iterator references a null parent node");
            return *mParentNode;
        }

        bool test() const { assert(mParentNode); return mIter != mParentNode->mTable.end(); }
        operator bool() const { return this->test(); }

        void increment() { if (this->test()) { ++mIter; } this->skip(); }
        bool next() { this->increment(); return this->test(); }
        void increment(Index n) { for (Index i = 0; i < n && this->next(); ++i) {} }

        /// @brief Return this iterator's position as an offset from
        /// the beginning of the parent node's map.
        Index pos() const
        {
            return !mParentNode ? 0U : Index(std::distance(mParentNode->mTable.begin(), mIter));
        }

        bool isValueOn() const { return RootNodeT::isTileOn(mIter); }
        bool isValueOff() const { return RootNodeT::isTileOff(mIter); }
        void setValueOn(bool on = true) const { mIter->second.tile.active = on; }
        void setValueOff() const { mIter->second.tile.active = false; }

        /// Return the coordinates of the item to which this iterator is pointing.
        Coord getCoord() const { return mIter->first; }
        /// Return in @a xyz the coordinates of the item to which this iterator is pointing.
        void getCoord(Coord& xyz) const { xyz = this->getCoord(); }

    protected:
        BaseIter(): mParentNode(nullptr) {}
        BaseIter(RootNodeT& parent, const MapIterT& iter): mParentNode(&parent), mIter(iter) {}

        void skip() { while (this->test() && !FilterPredT::test(mIter)) ++mIter; }

        RootNodeT* mParentNode;
        MapIterT mIter;
    }; // BaseIter

    template<typename RootNodeT, typename MapIterT, typename FilterPredT, typename ChildNodeT>
    class ChildIter: public BaseIter<RootNodeT, MapIterT, FilterPredT>
    {
    public:
        using BaseT = BaseIter<RootNodeT, MapIterT, FilterPredT>;
        using NodeType = RootNodeT;
        using ValueType = NodeType;
        using ChildNodeType = ChildNodeT;
        using NonConstNodeType = typename std::remove_const<NodeType>::type;
        using NonConstValueType = typename std::remove_const<ValueType>::type;
        using NonConstChildNodeType = typename std::remove_const<ChildNodeType>::type;
        using BaseT::mIter;

        ChildIter() {}
        ChildIter(RootNodeT& parent, const MapIterT& iter): BaseT(parent, iter) { BaseT::skip(); }

        ChildIter& operator++() { BaseT::increment(); return *this; }

        ChildNodeT& getValue() const { return getChild(mIter); }
        ChildNodeT& operator*() const { return this->getValue(); }
        ChildNodeT* operator->() const { return &this->getValue(); }
    }; // ChildIter

    template<typename RootNodeT, typename MapIterT, typename FilterPredT, typename ValueT>
    class ValueIter: public BaseIter<RootNodeT, MapIterT, FilterPredT>
    {
    public:
        using BaseT = BaseIter<RootNodeT, MapIterT, FilterPredT>;
        using NodeType = RootNodeT;
        using ValueType = ValueT;
        using NonConstNodeType = typename std::remove_const<NodeType>::type;
        using NonConstValueType = typename std::remove_const<ValueT>::type;
        using BaseT::mIter;

        ValueIter() {}
        ValueIter(RootNodeT& parent, const MapIterT& iter): BaseT(parent, iter) { BaseT::skip(); }

        ValueIter& operator++() { BaseT::increment(); return *this; }

        ValueT& getValue() const { return getTile(mIter).value; }
        ValueT& operator*() const { return this->getValue(); }
        ValueT* operator->() const { return &(this->getValue()); }

        void setValue(const ValueT& v) const { assert(isTile(mIter)); getTile(mIter).value = v; }

        template<typename ModifyOp>
        void modifyValue(const ModifyOp& op) const
        {
            assert(isTile(mIter));
            op(getTile(mIter).value);
        }
    }; // ValueIter

    template<typename RootNodeT, typename MapIterT, typename ChildNodeT, typename ValueT>
    class DenseIter: public BaseIter<RootNodeT, MapIterT, NullPred>
    {
    public:
        using BaseT = BaseIter<RootNodeT, MapIterT, NullPred>;
        using NodeType = RootNodeT;
        using ValueType = ValueT;
        using ChildNodeType = ChildNodeT;
        using NonConstNodeType = typename std::remove_const<NodeType>::type;
        using NonConstValueType = typename std::remove_const<ValueT>::type;
        using NonConstChildNodeType = typename std::remove_const<ChildNodeT>::type;
        using BaseT::mIter;

        DenseIter() {}
        DenseIter(RootNodeT& parent, const MapIterT& iter): BaseT(parent, iter) {}

        DenseIter& operator++() { BaseT::increment(); return *this; }

        bool isChildNode() const { return isChild(mIter); }

        ChildNodeT* probeChild(NonConstValueType& value) const
        {
            if (isChild(mIter)) return &getChild(mIter);
            value = getTile(mIter).value;
            return nullptr;
        }
        bool probeChild(ChildNodeT*& child, NonConstValueType& value) const
        {
            child = this->probeChild(value);
            return child != nullptr;
        }
        bool probeValue(NonConstValueType& value) const { return !this->probeChild(value); }

        void setChild(ChildNodeT& c) const { RootNodeT::setChild(mIter, c); }
        void setChild(ChildNodeT* c) const { assert(c != nullptr); RootNodeT::setChild(mIter, *c); }
        void setValue(const ValueT& v) const
        {
            if (isTile(mIter)) getTile(mIter).value = v;
            /// @internal For consistency with iterators for other node types
            /// (see, e.g., InternalNode::DenseIter::unsetItem()), we don't call
            /// setTile() here, because that would also delete the child.
            else stealChild(mIter, Tile(v, /*active=*/true));
        }
    }; // DenseIter

public:
    using ChildOnIter = ChildIter<RootNode, MapIter, ChildOnPred, ChildType>;
    using ChildOnCIter = ChildIter<const RootNode, MapCIter, ChildOnPred, const ChildType>;
    using ChildOffIter = ValueIter<RootNode, MapIter, ChildOffPred, const ValueType>;
    using ChildOffCIter = ValueIter<const RootNode, MapCIter, ChildOffPred, ValueType>;
    using ChildAllIter = DenseIter<RootNode, MapIter, ChildType, ValueType>;
    using ChildAllCIter = DenseIter<const RootNode, MapCIter, const ChildType, const ValueType>;

    using ValueOnIter = ValueIter<RootNode, MapIter, ValueOnPred, ValueType>;
    using ValueOnCIter = ValueIter<const RootNode, MapCIter, ValueOnPred, const ValueType>;
    using ValueOffIter = ValueIter<RootNode, MapIter, ValueOffPred, ValueType>;
    using ValueOffCIter = ValueIter<const RootNode, MapCIter, ValueOffPred, const ValueType>;
    using ValueAllIter = ValueIter<RootNode, MapIter, ValueAllPred, ValueType>;
    using ValueAllCIter = ValueIter<const RootNode, MapCIter, ValueAllPred, const ValueType>;


    ChildOnCIter  cbeginChildOn()  const { return ChildOnCIter(*this, mTable.begin()); }
    ChildOffCIter cbeginChildOff() const { return ChildOffCIter(*this, mTable.begin()); }
    ChildAllCIter cbeginChildAll() const { return ChildAllCIter(*this, mTable.begin()); }
    ChildOnCIter   beginChildOn()  const { return cbeginChildOn(); }
    ChildOffCIter  beginChildOff() const { return cbeginChildOff(); }
    ChildAllCIter  beginChildAll() const { return cbeginChildAll(); }
    ChildOnIter    beginChildOn()  { return ChildOnIter(*this, mTable.begin()); }
    ChildOffIter   beginChildOff() { return ChildOffIter(*this, mTable.begin()); }
    ChildAllIter   beginChildAll() { return ChildAllIter(*this, mTable.begin()); }

    ValueOnCIter  cbeginValueOn()  const { return ValueOnCIter(*this, mTable.begin()); }
    ValueOffCIter cbeginValueOff() const { return ValueOffCIter(*this, mTable.begin()); }
    ValueAllCIter cbeginValueAll() const { return ValueAllCIter(*this, mTable.begin()); }
    ValueOnCIter   beginValueOn()  const { return cbeginValueOn(); }
    ValueOffCIter  beginValueOff() const { return cbeginValueOff(); }
    ValueAllCIter  beginValueAll() const { return cbeginValueAll(); }
    ValueOnIter    beginValueOn()  { return ValueOnIter(*this, mTable.begin()); }
    ValueOffIter   beginValueOff() { return ValueOffIter(*this, mTable.begin()); }
    ValueAllIter   beginValueAll() { return ValueAllIter(*this, mTable.begin()); }

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

    /// @brief Expand the specified bbox so it includes the active tiles of
    /// this root 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;

    /// Return the bounding box of this RootNode, i.e., an infinite bounding box.
    static CoordBBox getNodeBoundingBox() { return CoordBBox::inf(); }

    /// @brief Change inactive tiles or voxels with a value equal to +/- the
    /// old background to the specified value (with the same sign). Active values
    /// are unchanged.
    ///
    /// @param value The new background value
    /// @param updateChildNodes If true the background values of the
    /// child nodes is also updated. Else only the background value
    /// stored in the RootNode itself is changed.
    ///
    /// @note Instead of setting @a updateChildNodes to true, consider
    /// using tools::changeBackground or
    /// tools::changeLevelSetBackground which are multi-threaded!
    void setBackground(const ValueType& value, bool updateChildNodes);

    /// Return this node's background value.
    const ValueType& background() const { return mBackground; }

    /// Return @c true if the given tile is inactive and has the background value.
    bool isBackgroundTile(const Tile&) const;
    //@{
    /// Return @c true if the given iterator points to an inactive tile with the background value.
    bool isBackgroundTile(const MapIter&) const;
    bool isBackgroundTile(const MapCIter&) const;
    //@}

    /// Return the number of background tiles.
    size_t numBackgroundTiles() const;
    /// @brief Remove all background tiles.
    /// @return the number of tiles removed.
    size_t eraseBackgroundTiles();
    inline void clear();

    /// Return @c true if this node's table is either empty or contains only background tiles.
    bool empty() const { return mTable.size() == numBackgroundTiles(); }

    /// @brief Expand this node's table so that (x, y, z) is included in the index range.
    /// @return @c true if an expansion was performed (i.e., if (x, y, z) was not already
    /// included in the index range).
    bool expand(const Coord& xyz);

    static Index getLevel() { return LEVEL; }
    static void getNodeLog2Dims(std::vector<Index>& dims);
    static Index getChildDim() { return ChildType::DIM; }

    /// Return the number of entries in this node's table.
    Index getTableSize() const { return static_cast<Index>(mTable.size()); }

    Index getWidth() const { return this->getMaxIndex()[0] - this->getMinIndex()[0]; }
    Index getHeight() const { return this->getMaxIndex()[1] - this->getMinIndex()[1]; }
    Index getDepth() const { return this->getMaxIndex()[2] - this->getMinIndex()[2]; }

    /// Return the smallest index of the current tree.
    Coord getMinIndex() const;
    /// Return the largest index of the current tree.
    Coord getMaxIndex() const;
    /// Return the current index range.  Both min and max are inclusive.
    void getIndexRange(CoordBBox& bbox) const;

    /// @brief Return @c true if the given tree has the same node and active value
    /// topology as this tree (but possibly a different @c ValueType).
    template<typename OtherChildType>
    bool hasSameTopology(const RootNode<OtherChildType>& other) const;

    /// Return @c false if the other node's dimensions don't match this node's.
    template<typename OtherChildType>
    static bool hasSameConfiguration(const RootNode<OtherChildType>& other);

    /// Return @c true if values of the other node's ValueType can be converted
    /// to values of this node's ValueType.
    template<typename OtherChildType>
    static bool hasCompatibleValueType(const RootNode<OtherChildType>& other);

    Index32 leafCount() const;
    Index32 nonLeafCount() const;
    Index32 childCount() const;
    Index64 onVoxelCount() const;
    Index64 offVoxelCount() const;
    Index64 onLeafVoxelCount() const;
    Index64 offLeafVoxelCount() const;
    Index64 onTileCount() const;
    void nodeCount(std::vector<Index32> &vec) const;

    bool isValueOn(const Coord& xyz) const;

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

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

    /// @brief Return the tree depth (0 = root) at which the value of voxel (x, y, z) resides.
    /// @details If (x, y, z) isn't explicitly represented in the tree (i.e.,
    /// it is implicitly a background voxel), return -1.
    int getValueDepth(const Coord& xyz) 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);
    /// 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);

    //@{
    /// @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);
    void sparseFill(const CoordBBox& bbox, const ValueType& value, bool active = true)
    {
        this->fill(bbox, value, active);
    }
    //@}

    /// @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).
    ///
    /// @warning This method can explode the tree's memory footprint, especially if it
    /// contains active tiles at the upper levels (in particular the root level)!
    ///
    /// @sa denseFill()
    void voxelizeActiveTiles(bool threaded = true);

    /// @brief Copy into a dense grid the values of all voxels, both active and inactive,
    /// that intersect 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)
    template<typename DenseT>
    void copyToDense(const CoordBBox& bbox, DenseT& dense) const;


    //
    // I/O
    //
    bool writeTopology(std::ostream&, bool toHalf = false) const;
    bool 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);


    //
    // Voxel access
    //
    /// 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 coordinates without changing 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&);

    /// 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;

    /// Return the tree depth (0 = root) at which the value of voxel (x, y, z) resides.
    /// If (x, y, z) isn't explicitly represented in the tree (i.e., it is implicitly
    /// a background voxel), return -1. 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>
    int getValueDepthAndCache(const Coord& xyz, AccessorT&) const;

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

    /// @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.
    ///
    /// @note Consider instead using tools::prune which is multi-threaded!
    void prune(const ValueType& tolerance = zeroVal<ValueType>());

    /// @brief Add the given leaf node to this tree, creating a new branch if necessary.
    /// If a leaf node with the same origin already exists, replace it.
    void addLeaf(LeafNodeType* leaf);

    /// @brief Same as addLeaf() but, if necessary, update the given 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 the root level.
    /// If a child node with the same origin 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 RootNode).
    /// @return @c true (for consistency with InternalNode::addChild)
    bool addChild(ChildType* child);

    /// @brief Add a tile containing voxel (x, y, z) at the root level,
    /// deleting the existing branch if necessary.
    void addTile(const Coord& xyz, const ValueType& value, bool state);

    /// @brief Add a tile containing voxel (x, y, z) at the specified tree level,
    /// creating a new branch if necessary.  Delete any existing lower-level nodes
    /// that contain (x, y, z).
    void addTile(Index level, const Coord& xyz, const ValueType& value, bool state);

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

    /// @brief Return a pointer to the leaf node that contains voxel (x, y, z).
    /// If no such node exists, create one that preserves 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() but, if necessary, update the given 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& acc);

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

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


    //
    // Aux methods
    //

    //@{
    /// @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);
    template<typename ArrayT>
    void stealNodes(ArrayT& array) { this->stealNodes(array, mBackground, false); }
    //@}

    /// @brief Efficiently merge another tree into this tree using one of several schemes.
    /// @details This operation is primarily intended to combine trees that are mostly
    /// non-overlapping (for example, intermediate trees from computations that are
    /// parallelized across disjoint regions of space).
    /// @note This operation is not guaranteed to produce an optimally sparse tree.
    /// Follow merge() with prune() for optimal sparseness.
    /// @warning This operation always empties the other tree.
    template<MergePolicy Policy> void merge(RootNode& other);

    /// @brief Union 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 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.
    ///
    /// @note This operation modifies only active states, not values.
    /// Specifically, active tiles and voxels in this tree are not changed, and
    /// tiles or voxels that were inactive in this tree but active in the other tree
    /// are marked as active in this tree but left with their original values.
    template<typename OtherChildType>
    void topologyUnion(const RootNode<OtherChildType>& other);

    /// @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 OtherChildType>
    void topologyIntersection(const RootNode<OtherChildType>& other);

    /// @brief Difference this tree's set of active values with the active values
    /// of the other tree, whose @c ValueType may be different. So a
    /// resulting voxel will be active only if the original voxel is
    /// active in this tree and inactive in the other tree.
    ///
    /// @note This operation can delete branches in this grid if they
    /// overlap with active 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 OtherChildType>
    void topologyDifference(const RootNode<OtherChildType>& other);

    template<typename CombineOp>
    void combine(RootNode& other, CombineOp&, bool prune = false);

    template<typename CombineOp, typename OtherRootNode /*= RootNode*/>
    void combine2(const RootNode& other0, const OtherRootNode& other1,
                  CombineOp& op, bool prune = false);

    /// @brief Call the templated functor BBoxOp with bounding box
    /// information for all active tiles and leaf nodes in the tree.
    /// An additional level argument is provided for each callback.
    ///
    /// @note The bounding boxes are guaranteed to be non-overlapping.
    template<typename BBoxOp> void visitActiveBBox(BBoxOp&) const;

    template<typename VisitorOp> void visit(VisitorOp&);
    template<typename VisitorOp> void visit(VisitorOp&) const;

    template<typename OtherRootNodeType, typename VisitorOp>
    void visit2(OtherRootNodeType& other, VisitorOp&);
    template<typename OtherRootNodeType, typename VisitorOp>
    void visit2(OtherRootNodeType& other, VisitorOp&) const;

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

    template<typename, typename, bool> friend struct RootNodeCopyHelper;
    template<typename, typename, typename, bool> friend struct RootNodeCombineHelper;

    /// Currently no-op, but can be used to define empty and delete keys for mTable
    void initTable() {}
    //@{
    /// @internal Used by doVisit2().
    void resetTable(MapType& table) { mTable.swap(table); table.clear(); }
    void resetTable(const MapType&) const {}
    //@}

    Index getChildCount() const;
    Index getTileCount() const;
    Index getActiveTileCount() const;
    Index getInactiveTileCount() const;

    /// Return a MapType key for the given coordinates.
    static Coord coordToKey(const Coord& xyz) { return xyz & ~(ChildType::DIM - 1); }

    /// Insert this node's mTable keys into the given set.
    void insertKeys(CoordSet&) const;

    /// Return @c true if this node's mTable contains the given key.
    bool hasKey(const Coord& key) const { return mTable.find(key) != mTable.end(); }
    //@{
    /// @brief Look up the given key in this node's mTable.
    /// @return an iterator pointing to the matching mTable entry or to mTable.end().
    MapIter findKey(const Coord& key) { return mTable.find(key); }
    MapCIter findKey(const Coord& key) const { return mTable.find(key); }
    //@}
    //@{
    /// @brief Convert the given coordinates to a key and look the key up in this node's mTable.
    /// @return an iterator pointing to the matching mTable entry or to mTable.end().
    MapIter findCoord(const Coord& xyz) { return mTable.find(coordToKey(xyz)); }
    MapCIter findCoord(const Coord& xyz) const { return mTable.find(coordToKey(xyz)); }
    //@}
    /// @brief Convert the given coordinates to a key and look the key up in this node's mTable.
    /// @details If the key is not found, insert a background tile with that key.
    /// @return an iterator pointing to the matching mTable entry.
    MapIter findOrAddCoord(const Coord& xyz);

    /// @brief Verify that the tree rooted at @a other has the same configuration
    /// (levels, branching factors and node dimensions) as this tree, but allow
    /// their ValueTypes to differ.
    /// @throw TypeError if the other tree's configuration doesn't match this tree's.
    template<typename OtherChildType>
    static void enforceSameConfiguration(const RootNode<OtherChildType>& other);

    /// @brief Verify that @a other has values of a type that can be converted
    /// to this node's ValueType.
    /// @details For example, values of type float are compatible with values of type Vec3s,
    /// because a Vec3s can be constructed from a float.  But the reverse is not true.
    /// @throw TypeError if the other node's ValueType is not convertible into this node's.
    template<typename OtherChildType>
    static void enforceCompatibleValueTypes(const RootNode<OtherChildType>& other);

    template<typename CombineOp, typename OtherRootNode /*= RootNode*/>
    void doCombine2(const RootNode&, const OtherRootNode&, CombineOp&, bool prune);

    template<typename RootNodeT, typename VisitorOp, typename ChildAllIterT>
    static inline void doVisit(RootNodeT&, VisitorOp&);

    template<typename RootNodeT, typename OtherRootNodeT, typename VisitorOp,
        typename ChildAllIterT, typename OtherChildAllIterT>
    static inline void doVisit2(RootNodeT&, OtherRootNodeT&, VisitorOp&);


    MapType mTable;
    ValueType mBackground;
}; // end of RootNode class


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


/// @brief NodeChain<RootNodeType, RootNodeType::LEVEL>::Type is a openvdb::TypeList
/// that lists the types of the nodes of the tree rooted at RootNodeType in reverse order,
/// from LeafNode to RootNode.
/// @details For example, if RootNodeType is
/// @code
/// RootNode<InternalNode<InternalNode<LeafNode> > >
/// @endcode
/// then NodeChain::Type is
/// @code
/// openvdb::TypeList<
///     LeafNode,
///     InternalNode<LeafNode>,
///     InternalNode<InternalNode<LeafNode> >,
///     RootNode<InternalNode<InternalNode<LeafNode> > > >
/// @endcode
///
/// @note Use the following to get the Nth node type, where N=0 is the LeafNodeType:
/// @code
/// NodeChainType::Get<N>;
/// @endcode
template<typename HeadT, int HeadLevel>
struct NodeChain {
    using SubtreeT = typename NodeChain<typename HeadT::ChildNodeType, HeadLevel-1>::Type;
    using Type = typename SubtreeT::template Append<HeadT>;
};

/// Specialization to terminate NodeChain
template<typename HeadT>
struct NodeChain<HeadT, /*HeadLevel=*/1> {
    using Type = TypeList<typename HeadT::ChildNodeType, HeadT>;
};


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


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

template<typename ChildT1, typename ChildT2>
struct SameRootConfig<ChildT1, RootNode<ChildT2> > {
    static const bool value = ChildT1::template SameConfiguration<ChildT2>::value;
};
//@}


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


template<typename ChildT>
inline
RootNode<ChildT>::RootNode(): mBackground(zeroVal<ValueType>())
{
    this->initTable();
}


template<typename ChildT>
inline
RootNode<ChildT>::RootNode(const ValueType& background): mBackground(background)
{
    this->initTable();
}


template<typename ChildT>
template<typename OtherChildType>
inline
RootNode<ChildT>::RootNode(const RootNode<OtherChildType>& other,
    const ValueType& backgd, const ValueType& foregd, TopologyCopy):
    mBackground(backgd)
{
    using OtherRootT = RootNode<OtherChildType>;

    enforceSameConfiguration(other);

    const Tile bgTile(backgd, /*active=*/false), fgTile(foregd, true);
    this->initTable();

    for (typename OtherRootT::MapCIter i=other.mTable.begin(), e=other.mTable.end(); i != e; ++i) {
        mTable[i->first] = OtherRootT::isTile(i)
            ? NodeStruct(OtherRootT::isTileOn(i) ? fgTile : bgTile)
            : NodeStruct(*(new ChildT(OtherRootT::getChild(i), backgd, foregd, TopologyCopy())));
    }
}


template<typename ChildT>
template<typename OtherChildType>
inline
RootNode<ChildT>::RootNode(const RootNode<OtherChildType>& other,
    const ValueType& backgd, TopologyCopy):
    mBackground(backgd)
{
    using OtherRootT = RootNode<OtherChildType>;

    enforceSameConfiguration(other);

    const Tile bgTile(backgd, /*active=*/false), fgTile(backgd, true);
    this->initTable();
    for (typename OtherRootT::MapCIter i=other.mTable.begin(), e=other.mTable.end(); i != e; ++i) {
        mTable[i->first] = OtherRootT::isTile(i)
            ? NodeStruct(OtherRootT::isTileOn(i) ? fgTile : bgTile)
            : NodeStruct(*(new ChildT(OtherRootT::getChild(i), backgd, TopologyCopy())));
    }
}


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


// This helper class is a friend of RootNode and is needed so that assignment
// with value conversion can be specialized for compatible and incompatible
// pairs of RootNode types.
template<typename RootT, typename OtherRootT, bool Compatible = false>
struct RootNodeCopyHelper
{
    static inline void copyWithValueConversion(RootT& self, const OtherRootT& other)
    {
        // If the two root nodes have different configurations or incompatible ValueTypes,
        // throw an exception.
        self.enforceSameConfiguration(other);
        self.enforceCompatibleValueTypes(other);
        // One of the above two tests should throw, so we should never get here:
        std::ostringstream ostr;
        ostr << "cannot convert a " << typeid(OtherRootT).name()
            << " to a " << typeid(RootT).name();
        OPENVDB_THROW(TypeError, ostr.str());
    }
};

// Specialization for root nodes of compatible types
template<typename RootT, typename OtherRootT>
struct RootNodeCopyHelper<RootT, OtherRootT, /*Compatible=*/true>
{
    static inline void copyWithValueConversion(RootT& self, const OtherRootT& other)
    {
        using ValueT = typename RootT::ValueType;
        using ChildT = typename RootT::ChildNodeType;
        using NodeStruct = typename RootT::NodeStruct;
        using Tile = typename RootT::Tile;
        using OtherValueT = typename OtherRootT::ValueType;
        using OtherMapCIter = typename OtherRootT::MapCIter;
        using OtherTile = typename OtherRootT::Tile;

        struct Local {
            /// @todo Consider using a value conversion functor passed as an argument instead.
            static inline ValueT convertValue(const OtherValueT& val) { return ValueT(val); }
        };

        self.mBackground = Local::convertValue(other.mBackground);

        self.clear();
        self.initTable();

        for (OtherMapCIter i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
            if (other.isTile(i)) {
                // Copy the other node's tile, but convert its value to this node's ValueType.
                const OtherTile& otherTile = other.getTile(i);
                self.mTable[i->first] = NodeStruct(
                    Tile(Local::convertValue(otherTile.value), otherTile.active));
            } else {
                // Copy the other node's child, but convert its values to this node's ValueType.
                self.mTable[i->first] = NodeStruct(*(new ChildT(other.getChild(i))));
            }
        }
    }
};


// Overload for root nodes of the same type as this node
template<typename ChildT>
inline RootNode<ChildT>&
RootNode<ChildT>::operator=(const RootNode& other)
{
    if (&other != this) {
        mBackground = other.mBackground;

        this->clear();
        this->initTable();

        for (MapCIter i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
            mTable[i->first] =
                isTile(i) ? NodeStruct(getTile(i)) : NodeStruct(*(new ChildT(getChild(i))));
        }
    }
    return *this;
}

// Overload for root nodes of different types
template<typename ChildT>
template<typename OtherChildType>
inline RootNode<ChildT>&
RootNode<ChildT>::operator=(const RootNode<OtherChildType>& other)
{
    using OtherRootT = RootNode<OtherChildType>;
    using OtherValueT = typename OtherRootT::ValueType;
    static const bool compatible = (SameConfiguration<OtherRootT>::value
        && CanConvertType</*from=*/OtherValueT, /*to=*/ValueType>::value);
    RootNodeCopyHelper<RootNode, OtherRootT, compatible>::copyWithValueConversion(*this, other);
    return *this;
}


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

template<typename ChildT>
inline void
RootNode<ChildT>::setBackground(const ValueType& background, bool updateChildNodes)
{
    if (math::isExactlyEqual(background, mBackground)) return;

    if (updateChildNodes) {
        // Traverse the tree, replacing occurrences of mBackground with background
        // and -mBackground with -background.
        for (MapIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
            ChildT *child = iter->second.child;
            if (child) {
                child->resetBackground(/*old=*/mBackground, /*new=*/background);
            } else {
                Tile& tile = getTile(iter);
                if (tile.active) continue;//only change inactive tiles
                if (math::isApproxEqual(tile.value, mBackground)) {
                    tile.value = background;
                } else if (math::isApproxEqual(tile.value, math::negative(mBackground))) {
                    tile.value = math::negative(background);
                }
            }
        }
    }
    mBackground = background;
}

template<typename ChildT>
inline bool
RootNode<ChildT>::isBackgroundTile(const Tile& tile) const
{
    return !tile.active && math::isApproxEqual(tile.value, mBackground);
}

template<typename ChildT>
inline bool
RootNode<ChildT>::isBackgroundTile(const MapIter& iter) const
{
    return isTileOff(iter) && math::isApproxEqual(getTile(iter).value, mBackground);
}

template<typename ChildT>
inline bool
RootNode<ChildT>::isBackgroundTile(const MapCIter& iter) const
{
    return isTileOff(iter) && math::isApproxEqual(getTile(iter).value, mBackground);
}


template<typename ChildT>
inline size_t
RootNode<ChildT>::numBackgroundTiles() const
{
    size_t count = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (this->isBackgroundTile(i)) ++count;
    }
    return count;
}


template<typename ChildT>
inline size_t
RootNode<ChildT>::eraseBackgroundTiles()
{
    std::set<Coord> keysToErase;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (this->isBackgroundTile(i)) keysToErase.insert(i->first);
    }
    for (std::set<Coord>::iterator i = keysToErase.begin(), e = keysToErase.end(); i != e; ++i) {
        mTable.erase(*i);
    }
    return keysToErase.size();
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::insertKeys(CoordSet& keys) const
{
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        keys.insert(i->first);
    }
}


template<typename ChildT>
inline typename RootNode<ChildT>::MapIter
RootNode<ChildT>::findOrAddCoord(const Coord& xyz)
{
    const Coord key = coordToKey(xyz);
    std::pair<MapIter, bool> result = mTable.insert(
        typename MapType::value_type(key, NodeStruct(Tile(mBackground, /*active=*/false))));
    return result.first;
}


template<typename ChildT>
inline bool
RootNode<ChildT>::expand(const Coord& xyz)
{
    const Coord key = coordToKey(xyz);
    std::pair<MapIter, bool> result = mTable.insert(
        typename MapType::value_type(key, NodeStruct(Tile(mBackground, /*active=*/false))));
    return result.second; // return true if the key did not already exist
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::getNodeLog2Dims(std::vector<Index>& dims)
{
    dims.push_back(0); // magic number; RootNode has no Log2Dim
    ChildT::getNodeLog2Dims(dims);
}


template<typename ChildT>
inline Coord
RootNode<ChildT>::getMinIndex() const
{
    return mTable.empty() ? Coord(0) : mTable.begin()->first;
}

template<typename ChildT>
inline Coord
RootNode<ChildT>::getMaxIndex() const
{
    return mTable.empty() ? Coord(0) : mTable.rbegin()->first + Coord(ChildT::DIM - 1);
}


template<typename ChildT>
inline void
RootNode<ChildT>::getIndexRange(CoordBBox& bbox) const
{
    bbox.min() = this->getMinIndex();
    bbox.max() = this->getMaxIndex();
}


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


template<typename ChildT>
template<typename OtherChildType>
inline bool
RootNode<ChildT>::hasSameTopology(const RootNode<OtherChildType>& other) const
{
    using OtherRootT = RootNode<OtherChildType>;
    using OtherMapT = typename OtherRootT::MapType;
    using OtherIterT = typename OtherRootT::MapIter;
    using OtherCIterT = typename OtherRootT::MapCIter;

    if (!hasSameConfiguration(other)) return false;

    // Create a local copy of the other node's table.
    OtherMapT copyOfOtherTable = other.mTable;

    // For each entry in this node's table...
    for (MapCIter thisIter = mTable.begin(); thisIter != mTable.end(); ++thisIter) {
        if (this->isBackgroundTile(thisIter)) continue; // ignore background tiles

        // Fail if there is no corresponding entry in the other node's table.
        OtherCIterT otherIter = other.findKey(thisIter->first);
        if (otherIter == other.mTable.end()) return false;

        // Fail if this entry is a tile and the other is a child or vice-versa.
        if (isChild(thisIter)) {//thisIter points to a child
            if (OtherRootT::isTile(otherIter)) return false;
            // Fail if both entries are children, but the children have different topology.
            if (!getChild(thisIter).hasSameTopology(&OtherRootT::getChild(otherIter))) return false;
        } else {//thisIter points to a tile
            if (OtherRootT::isChild(otherIter)) return false;
            if (getTile(thisIter).active != OtherRootT::getTile(otherIter).active) return false;
        }

        // Remove tiles and child nodes with matching topology from
        // the copy of the other node's table. This is required since
        // the two root tables can include an arbitrary number of
        // background tiles and still have the same topology!
        copyOfOtherTable.erase(otherIter->first);
    }
    // Fail if the remaining entries in copyOfOtherTable are not all background tiles.
    for (OtherIterT i = copyOfOtherTable.begin(), e = copyOfOtherTable.end(); i != e; ++i) {
        if (!other.isBackgroundTile(i)) return false;
    }
    return true;
}


template<typename ChildT>
template<typename OtherChildType>
inline bool
RootNode<ChildT>::hasSameConfiguration(const RootNode<OtherChildType>&)
{
    std::vector<Index> thisDims, otherDims;
    RootNode::getNodeLog2Dims(thisDims);
    RootNode<OtherChildType>::getNodeLog2Dims(otherDims);
    return (thisDims == otherDims);
}


template<typename ChildT>
template<typename OtherChildType>
inline void
RootNode<ChildT>::enforceSameConfiguration(const RootNode<OtherChildType>&)
{
    std::vector<Index> thisDims, otherDims;
    RootNode::getNodeLog2Dims(thisDims);
    RootNode<OtherChildType>::getNodeLog2Dims(otherDims);
    if (thisDims != otherDims) {
        std::ostringstream ostr;
        ostr << "grids have incompatible configurations (" << thisDims[0];
        for (size_t i = 1, N = thisDims.size(); i < N; ++i) ostr << " x " << thisDims[i];
        ostr << " vs. " << otherDims[0];
        for (size_t i = 1, N = otherDims.size(); i < N; ++i) ostr << " x " << otherDims[i];
        ostr << ")";
        OPENVDB_THROW(TypeError, ostr.str());
    }
}


template<typename ChildT>
template<typename OtherChildType>
inline bool
RootNode<ChildT>::hasCompatibleValueType(const RootNode<OtherChildType>&)
{
    using OtherValueType = typename OtherChildType::ValueType;
    return CanConvertType</*from=*/OtherValueType, /*to=*/ValueType>::value;
}


template<typename ChildT>
template<typename OtherChildType>
inline void
RootNode<ChildT>::enforceCompatibleValueTypes(const RootNode<OtherChildType>&)
{
    using OtherValueType = typename OtherChildType::ValueType;
    if (!CanConvertType</*from=*/OtherValueType, /*to=*/ValueType>::value) {
        std::ostringstream ostr;
        ostr << "values of type " << typeNameAsString<OtherValueType>()
            << " cannot be converted to type " << typeNameAsString<ValueType>();
        OPENVDB_THROW(TypeError, ostr.str());
    }
}


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


template<typename ChildT>
inline Index64
RootNode<ChildT>::memUsage() const
{
    Index64 sum = sizeof(*this);
    for (MapCIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
        if (const ChildT *child = iter->second.child) {
            sum += child->memUsage();
        }
    }
    return sum;
}


template<typename ChildT>
inline void
RootNode<ChildT>::clear()
{
    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        delete i->second.child;
    }
    mTable.clear();
}


template<typename ChildT>
inline void
RootNode<ChildT>::evalActiveBoundingBox(CoordBBox& bbox, bool visitVoxels) const
{
    for (MapCIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
        if (const ChildT *child = iter->second.child) {
            child->evalActiveBoundingBox(bbox, visitVoxels);
        } else if (isTileOn(iter)) {
            bbox.expand(iter->first, ChildT::DIM);
        }
    }
}


template<typename ChildT>
inline Index
RootNode<ChildT>::getChildCount() const {
    Index sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) ++sum;
    }
    return sum;
}


template<typename ChildT>
inline Index
RootNode<ChildT>::getTileCount() const
{
    Index sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isTile(i)) ++sum;
    }
    return sum;
}


template<typename ChildT>
inline Index
RootNode<ChildT>::getActiveTileCount() const
{
    Index sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isTileOn(i)) ++sum;
    }
    return sum;
}


template<typename ChildT>
inline Index
RootNode<ChildT>::getInactiveTileCount() const
{
    Index sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isTileOff(i)) ++sum;
    }
    return sum;
}


template<typename ChildT>
inline Index32
RootNode<ChildT>::leafCount() const
{
    Index32 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) sum += getChild(i).leafCount();
    }
    return sum;
}


template<typename ChildT>
inline Index32
RootNode<ChildT>::nonLeafCount() const
{
    Index32 sum = 1;
    if (ChildT::LEVEL != 0) {
        for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
            if (isChild(i)) sum += getChild(i).nonLeafCount();
        }
    }
    return sum;
}


template<typename ChildT>
inline Index32
RootNode<ChildT>::childCount() const
{
    return this->getChildCount();
}


template<typename ChildT>
inline Index64
RootNode<ChildT>::onVoxelCount() const
{
    Index64 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) {
            sum += getChild(i).onVoxelCount();
        } else if (isTileOn(i)) {
            sum += ChildT::NUM_VOXELS;
        }
    }
    return sum;
}


template<typename ChildT>
inline Index64
RootNode<ChildT>::offVoxelCount() const
{
    Index64 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) {
            sum += getChild(i).offVoxelCount();
        } else if (isTileOff(i) && !this->isBackgroundTile(i)) {
            sum += ChildT::NUM_VOXELS;
        }
    }
    return sum;
}


template<typename ChildT>
inline Index64
RootNode<ChildT>::onLeafVoxelCount() const
{
    Index64 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) sum += getChild(i).onLeafVoxelCount();
    }
    return sum;
}


template<typename ChildT>
inline Index64
RootNode<ChildT>::offLeafVoxelCount() const
{
    Index64 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) sum += getChild(i).offLeafVoxelCount();
    }
    return sum;
}

template<typename ChildT>
inline Index64
RootNode<ChildT>::onTileCount() const
{
    Index64 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) {
            sum += getChild(i).onTileCount();
        } else if (isTileOn(i)) {
            sum += 1;
        }
    }
    return sum;
}

template<typename ChildT>
inline void
RootNode<ChildT>::nodeCount(std::vector<Index32> &vec) const
{
    assert(vec.size() > LEVEL);
    Index32 sum = 0;
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) {
            ++sum;
            getChild(i).nodeCount(vec);
        }
    }
    vec[LEVEL] = 1;// one root node
    vec[ChildNodeType::LEVEL] = sum;
}

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


template<typename ChildT>
inline bool
RootNode<ChildT>::isValueOn(const Coord& xyz) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTileOff(iter)) return false;
    return isTileOn(iter) ? true : getChild(iter).isValueOn(xyz);
}

template<typename ChildT>
inline bool
RootNode<ChildT>::hasActiveTiles() const
{
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i) ? getChild(i).hasActiveTiles() : getTile(i).active) return true;
    }
    return false;
}

template<typename ChildT>
template<typename AccessorT>
inline bool
RootNode<ChildT>::isValueOnAndCache(const Coord& xyz, AccessorT& acc) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTileOff(iter)) return false;
    if (isTileOn(iter)) return true;
    acc.insert(xyz, &getChild(iter));
    return getChild(iter).isValueOnAndCache(xyz, acc);
}


template<typename ChildT>
inline const typename ChildT::ValueType&
RootNode<ChildT>::getValue(const Coord& xyz) const
{
    MapCIter iter = this->findCoord(xyz);
    return iter == mTable.end() ? mBackground
        : (isTile(iter) ? getTile(iter).value : getChild(iter).getValue(xyz));
}

template<typename ChildT>
template<typename AccessorT>
inline const typename ChildT::ValueType&
RootNode<ChildT>::getValueAndCache(const Coord& xyz, AccessorT& acc) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) return mBackground;
    if (isChild(iter)) {
        acc.insert(xyz, &getChild(iter));
        return getChild(iter).getValueAndCache(xyz, acc);
    }
    return getTile(iter).value;
}


template<typename ChildT>
inline int
RootNode<ChildT>::getValueDepth(const Coord& xyz) const
{
    MapCIter iter = this->findCoord(xyz);
    return iter == mTable.end() ? -1
        : (isTile(iter) ? 0 : int(LEVEL) - int(getChild(iter).getValueLevel(xyz)));
}

template<typename ChildT>
template<typename AccessorT>
inline int
RootNode<ChildT>::getValueDepthAndCache(const Coord& xyz, AccessorT& acc) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) return -1;
    if (isTile(iter)) return 0;
    acc.insert(xyz, &getChild(iter));
    return int(LEVEL) - int(getChild(iter).getValueLevelAndCache(xyz, acc));
}


template<typename ChildT>
inline void
RootNode<ChildT>::setValueOff(const Coord& xyz)
{
    MapIter iter = this->findCoord(xyz);
    if (iter != mTable.end() && !isTileOff(iter)) {
        if (isTileOn(iter)) {
            setChild(iter, *new ChildT(xyz, getTile(iter).value, /*active=*/true));
        }
        getChild(iter).setValueOff(xyz);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::setActiveState(const Coord& xyz, bool on)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (on) {
            child = new ChildT(xyz, mBackground);
            mTable[this->coordToKey(xyz)] = NodeStruct(*child);
        } else {
            // Nothing to do; (x, y, z) is background and therefore already inactive.
        }
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (on != getTile(iter).active) {
        child = new ChildT(xyz, getTile(iter).value, !on);
        setChild(iter, *child);
    }
    if (child) child->setActiveState(xyz, on);
}

template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::setActiveStateAndCache(const Coord& xyz, bool on, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (on) {
            child = new ChildT(xyz, mBackground);
            mTable[this->coordToKey(xyz)] = NodeStruct(*child);
        } else {
            // Nothing to do; (x, y, z) is background and therefore already inactive.
        }
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (on != getTile(iter).active) {
        child = new ChildT(xyz, getTile(iter).value, !on);
        setChild(iter, *child);
    }
    if (child) {
        acc.insert(xyz, child);
        child->setActiveStateAndCache(xyz, on, acc);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::setValueOff(const Coord& xyz, const ValueType& value)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (!math::isExactlyEqual(mBackground, value)) {
            child = new ChildT(xyz, mBackground);
            mTable[this->coordToKey(xyz)] = NodeStruct(*child);
        }
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (isTileOn(iter) || !math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) child->setValueOff(xyz, value);
}

template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::setValueOffAndCache(const Coord& xyz, const ValueType& value, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (!math::isExactlyEqual(mBackground, value)) {
            child = new ChildT(xyz, mBackground);
            mTable[this->coordToKey(xyz)] = NodeStruct(*child);
        }
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (isTileOn(iter) || !math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) {
        acc.insert(xyz, child);
        child->setValueOffAndCache(xyz, value, acc);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::setValueOn(const Coord& xyz, const ValueType& value)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (isTileOff(iter) || !math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) child->setValueOn(xyz, value);
}

template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::setValueAndCache(const Coord& xyz, const ValueType& value, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (isTileOff(iter) || !math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) {
        acc.insert(xyz, child);
        child->setValueAndCache(xyz, value, acc);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::setValueOnly(const Coord& xyz, const ValueType& value)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (!math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) child->setValueOnly(xyz, value);
}

template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::setValueOnlyAndCache(const Coord& xyz, const ValueType& value, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else if (!math::isExactlyEqual(getTile(iter).value, value)) {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    if (child) {
        acc.insert(xyz, child);
        child->setValueOnlyAndCache(xyz, value, acc);
    }
}


template<typename ChildT>
template<typename ModifyOp>
inline void
RootNode<ChildT>::modifyValue(const Coord& xyz, const ModifyOp& op)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        // Need to create a child if the tile is inactive,
        // in order to activate voxel (x, y, z).
        bool createChild = isTileOff(iter);
        if (!createChild) {
            // Need to create a child if applying the functor
            // to the tile value produces a different value.
            const ValueType& tileVal = getTile(iter).value;
            ValueType modifiedVal = tileVal;
            op(modifiedVal);
            createChild = !math::isExactlyEqual(tileVal, modifiedVal);
        }
        if (createChild) {
            child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
            setChild(iter, *child);
        }
    }
    if (child) child->modifyValue(xyz, op);
}

template<typename ChildT>
template<typename ModifyOp, typename AccessorT>
inline void
RootNode<ChildT>::modifyValueAndCache(const Coord& xyz, const ModifyOp& op, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        // Need to create a child if the tile is inactive,
        // in order to activate voxel (x, y, z).
        bool createChild = isTileOff(iter);
        if (!createChild) {
            // Need to create a child if applying the functor
            // to the tile value produces a different value.
            const ValueType& tileVal = getTile(iter).value;
            ValueType modifiedVal = tileVal;
            op(modifiedVal);
            createChild = !math::isExactlyEqual(tileVal, modifiedVal);
        }
        if (createChild) {
            child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
            setChild(iter, *child);
        }
    }
    if (child) {
        acc.insert(xyz, child);
        child->modifyValueAndCache(xyz, op, acc);
    }
}


template<typename ChildT>
template<typename ModifyOp>
inline void
RootNode<ChildT>::modifyValueAndActiveState(const Coord& xyz, const ModifyOp& op)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        const Tile& tile = getTile(iter);
        bool modifiedState = tile.active;
        ValueType modifiedVal = tile.value;
        op(modifiedVal, modifiedState);
        // Need to create a child if applying the functor to the tile
        // produces a different value or active state.
        if (modifiedState != tile.active || !math::isExactlyEqual(modifiedVal, tile.value)) {
            child = new ChildT(xyz, tile.value, tile.active);
            setChild(iter, *child);
        }
    }
    if (child) child->modifyValueAndActiveState(xyz, op);
}

template<typename ChildT>
template<typename ModifyOp, typename AccessorT>
inline void
RootNode<ChildT>::modifyValueAndActiveStateAndCache(
    const Coord& xyz, const ModifyOp& op, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        const Tile& tile = getTile(iter);
        bool modifiedState = tile.active;
        ValueType modifiedVal = tile.value;
        op(modifiedVal, modifiedState);
        // Need to create a child if applying the functor to the tile
        // produces a different value or active state.
        if (modifiedState != tile.active || !math::isExactlyEqual(modifiedVal, tile.value)) {
            child = new ChildT(xyz, tile.value, tile.active);
            setChild(iter, *child);
        }
    }
    if (child) {
        acc.insert(xyz, child);
        child->modifyValueAndActiveStateAndCache(xyz, op, acc);
    }
}


template<typename ChildT>
inline bool
RootNode<ChildT>::probeValue(const Coord& xyz, ValueType& value) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        value = mBackground;
        return false;
    } else if (isChild(iter)) {
        return getChild(iter).probeValue(xyz, value);
    }
    value = getTile(iter).value;
    return isTileOn(iter);
}

template<typename ChildT>
template<typename AccessorT>
inline bool
RootNode<ChildT>::probeValueAndCache(const Coord& xyz, ValueType& value, AccessorT& acc) const
{
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        value = mBackground;
        return false;
    } else if (isChild(iter)) {
        acc.insert(xyz, &getChild(iter));
        return getChild(iter).probeValueAndCache(xyz, value, acc);
    }
    value = getTile(iter).value;
    return isTileOn(iter);
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::fill(const CoordBBox& bbox, const ValueType& value, bool active)
{
    if (bbox.empty()) 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, tileMax;
    for (int x = bbox.min().x(); x <= bbox.max().x(); x = tileMax.x() + 1) {
        xyz.setX(x);
        for (int y = bbox.min().y(); y <= bbox.max().y(); y = tileMax.y() + 1) {
            xyz.setY(y);
            for (int z = bbox.min().z(); z <= bbox.max().z(); z = tileMax.z() + 1) {
                xyz.setZ(z);

                // Get the bounds of the tile that contains voxel (x, y, z).
                Coord tileMin = coordToKey(xyz);
                tileMax = tileMin.offsetBy(ChildT::DIM - 1);

                if (xyz != tileMin || Coord::lessThan(bbox.max(), tileMax)) {
                    // If the box defined by (xyz, bbox.max()) doesn't completely enclose
                    // the tile to which xyz belongs, create a child node (or retrieve
                    // the existing one).
                    ChildT* child = nullptr;
                    MapIter iter = this->findKey(tileMin);
                    if (iter == mTable.end()) {
                        // No child or tile exists.  Create a child and initialize it
                        // with the background value.
                        child = new ChildT(xyz, mBackground);
                        mTable[tileMin] = NodeStruct(*child);
                    } else if (isTile(iter)) {
                        // Replace the tile with a newly-created child that is filled
                        // with the tile's value and active state.
                        const Tile& tile = getTile(iter);
                        child = new ChildT(xyz, tile.value, tile.active);
                        mTable[tileMin] = NodeStruct(*child);
                    } else if (isChild(iter)) {
                        child = &getChild(iter);
                    }
                    // Forward the fill request to the child.
                    if (child) {
                        const Coord tmp = Coord::minComponent(bbox.max(), tileMax);
                        child->fill(CoordBBox(xyz, tmp), value, active);
                    }
                } else {
                    // If the box given by (xyz, bbox.max()) completely encloses
                    // the tile to which xyz belongs, create the tile (if it
                    // doesn't already exist) and give it the fill value.
                    MapIter iter = this->findOrAddCoord(tileMin);
                    setTile(iter, Tile(value, active));
                }
            }
        }
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::denseFill(const CoordBBox& bbox, const ValueType& value, bool active)
{
    if (bbox.empty()) return;

    if (active && mTable.empty()) {
        // If this tree is empty, then a sparse fill followed by (threaded)
        // densification of active tiles is the more efficient approach.
        sparseFill(bbox, value, active);
        voxelizeActiveTiles(/*threaded=*/true);
        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 = bbox.min().x(); x <= bbox.max().x(); x = tileMax.x() + 1) {
        xyz.setX(x);
        for (int y = bbox.min().y(); y <= bbox.max().y(); y = tileMax.y() + 1) {
            xyz.setY(y);
            for (int z = bbox.min().z(); z <= bbox.max().z(); z = tileMax.z() + 1) {
                xyz.setZ(z);

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

                // Retrieve the table entry for the tile that contains xyz,
                // or, if there is no table entry, add a background tile.
                const auto iter = findOrAddCoord(tileMin);

                if (isTile(iter)) {
                    // If the table entry is a tile, replace it with a child node
                    // that is filled with the tile's value and active state.
                    const auto& tile = getTile(iter);
                    auto* child = new ChildT{tileMin, tile.value, tile.active};
                    setChild(iter, *child);
                }
                // Forward the fill request to the child.
                getChild(iter).denseFill(bbox, value, active);
            }
        }
    }
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::voxelizeActiveTiles(bool threaded)
{
    // There is little point in threading over the root table since each tile
    // spans a huge index space (by default 4096^3) and hence we expect few
    // active tiles if any at all.  In fact, you're very likely to run out of
    // memory if this method is called on a tree with root-level active tiles!
    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (this->isTileOff(i)) continue;
        ChildT* child = i->second.child;
        if (child == nullptr) {
            // If this table entry is an active tile (i.e., not off and not a child node),
            // replace it with a child node filled with active tiles of the same value.
            child = new ChildT{i->first, this->getTile(i).value, true};
            i->second.child = child;
        }
        child->voxelizeActiveTiles(threaded);
    }
}


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


template<typename ChildT>
template<typename DenseT>
inline void
RootNode<ChildT>::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();
    CoordBBox nodeBBox;
    for (Coord xyz = bbox.min(); xyz[0] <= bbox.max()[0]; xyz[0] = nodeBBox.max()[0] + 1) {
        for (xyz[1] = bbox.min()[1]; xyz[1] <= bbox.max()[1]; xyz[1] = nodeBBox.max()[1] + 1) {
            for (xyz[2] = bbox.min()[2]; xyz[2] <= bbox.max()[2]; xyz[2] = nodeBBox.max()[2] + 1) {

                // Get the coordinate bbox of the child node that contains voxel xyz.
                nodeBBox = CoordBBox::createCube(coordToKey(xyz), ChildT::DIM);

                // Get the coordinate bbox of the interection of inBBox and nodeBBox
                CoordBBox sub(xyz, Coord::minComponent(bbox.max(), nodeBBox.max()));

                MapCIter iter = this->findKey(nodeBBox.min());
                if (iter != mTable.end() && isChild(iter)) {//is a child
                    getChild(iter).copyToDense(sub, dense);
                } else {//is background or a tile value
                    const ValueType value = iter==mTable.end() ? mBackground : getTile(iter).value;
                    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>
inline bool
RootNode<ChildT>::writeTopology(std::ostream& os, bool toHalf) const
{
    if (!toHalf) {
        os.write(reinterpret_cast<const char*>(&mBackground), sizeof(ValueType));
    } else {
        ValueType truncatedVal = io::truncateRealToHalf(mBackground);
        os.write(reinterpret_cast<const char*>(&truncatedVal), sizeof(ValueType));
    }
    io::setGridBackgroundValuePtr(os, &mBackground);

    const Index numTiles = this->getTileCount(), numChildren = this->getChildCount();
    os.write(reinterpret_cast<const char*>(&numTiles), sizeof(Index));
    os.write(reinterpret_cast<const char*>(&numChildren), sizeof(Index));

    if (numTiles == 0 && numChildren == 0) return false;

    // Write tiles.
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) continue;
        os.write(reinterpret_cast<const char*>(i->first.asPointer()), 3 * sizeof(Int32));
        os.write(reinterpret_cast<const char*>(&getTile(i).value), sizeof(ValueType));
        os.write(reinterpret_cast<const char*>(&getTile(i).active), sizeof(bool));
    }
    // Write child nodes.
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isTile(i)) continue;
        os.write(reinterpret_cast<const char*>(i->first.asPointer()), 3 * sizeof(Int32));
        getChild(i).writeTopology(os, toHalf);
    }

    return true; // not empty
}


template<typename ChildT>
inline bool
RootNode<ChildT>::readTopology(std::istream& is, bool fromHalf)
{
    // Delete the existing tree.
    this->clear();

    if (io::getFormatVersion(is) < OPENVDB_FILE_VERSION_ROOTNODE_MAP) {
        // Read and convert an older-format RootNode.

        // For backward compatibility with older file formats, read both
        // outside and inside background values.
        is.read(reinterpret_cast<char*>(&mBackground), sizeof(ValueType));
        ValueType inside;
        is.read(reinterpret_cast<char*>(&inside), sizeof(ValueType));

        io::setGridBackgroundValuePtr(is, &mBackground);

        // Read the index range.
        Coord rangeMin, rangeMax;
        is.read(reinterpret_cast<char*>(rangeMin.asPointer()), 3 * sizeof(Int32));
        is.read(reinterpret_cast<char*>(rangeMax.asPointer()), 3 * sizeof(Int32));

        this->initTable();
        Index tableSize = 0, log2Dim[4] = { 0, 0, 0, 0 };
        Int32 offset[3];
        for (int i = 0; i < 3; ++i) {
            offset[i] = rangeMin[i] >> ChildT::TOTAL;
            rangeMin[i] = offset[i] << ChildT::TOTAL;
            log2Dim[i] = 1 + util::FindHighestOn((rangeMax[i] >> ChildT::TOTAL) - offset[i]);
            tableSize += log2Dim[i];
            rangeMax[i] = (((1 << log2Dim[i]) + offset[i]) << ChildT::TOTAL) - 1;
        }
        log2Dim[3] = log2Dim[1] + log2Dim[2];
        tableSize = 1U << tableSize;

        // Read masks.
        util::RootNodeMask childMask(tableSize), valueMask(tableSize);
        childMask.load(is);
        valueMask.load(is);

        // Read child nodes/values.
        for (Index i = 0; i < tableSize; ++i) {
            // Compute origin = offset2coord(i).
            Index n = i;
            Coord origin;
            origin[0] = (n >> log2Dim[3]) + offset[0];
            n &= (1U << log2Dim[3]) - 1;
            origin[1] = (n >> log2Dim[2]) + offset[1];
            origin[2] = (n & ((1U << log2Dim[2]) - 1)) + offset[1];
            origin <<= ChildT::TOTAL;

            if (childMask.isOn(i)) {
                // Read in and insert a child node.
                ChildT* child = new ChildT(PartialCreate(), origin, mBackground);
                child->readTopology(is);
                mTable[origin] = NodeStruct(*child);
            } else {
                // Read in a tile value and insert a tile, but only if the value
                // is either active or non-background.
                ValueType value;
                is.read(reinterpret_cast<char*>(&value), sizeof(ValueType));
                if (valueMask.isOn(i) || (!math::isApproxEqual(value, mBackground))) {
                    mTable[origin] = NodeStruct(Tile(value, valueMask.isOn(i)));
                }
            }
        }
        return true;
    }

    // Read a RootNode that was stored in the current format.

    is.read(reinterpret_cast<char*>(&mBackground), sizeof(ValueType));
    io::setGridBackgroundValuePtr(is, &mBackground);

    Index numTiles = 0, numChildren = 0;
    is.read(reinterpret_cast<char*>(&numTiles), sizeof(Index));
    is.read(reinterpret_cast<char*>(&numChildren), sizeof(Index));

    if (numTiles == 0 && numChildren == 0) return false;

    Int32 vec[3];
    ValueType value;
    bool active;

    // Read tiles.
    for (Index n = 0; n < numTiles; ++n) {
        is.read(reinterpret_cast<char*>(vec), 3 * sizeof(Int32));
        is.read(reinterpret_cast<char*>(&value), sizeof(ValueType));
        is.read(reinterpret_cast<char*>(&active), sizeof(bool));
        mTable[Coord(vec)] = NodeStruct(Tile(value, active));
    }

    // Read child nodes.
    for (Index n = 0; n < numChildren; ++n) {
        is.read(reinterpret_cast<char*>(vec), 3 * sizeof(Int32));
        Coord origin(vec);
        ChildT* child = new ChildT(PartialCreate(), origin, mBackground);
        child->readTopology(is, fromHalf);
        mTable[Coord(vec)] = NodeStruct(*child);
    }

    return true; // not empty
}


template<typename ChildT>
inline void
RootNode<ChildT>::writeBuffers(std::ostream& os, bool toHalf) const
{
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) getChild(i).writeBuffers(os, toHalf);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::readBuffers(std::istream& is, bool fromHalf)
{
    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) getChild(i).readBuffers(is, fromHalf);
    }
}


template<typename ChildT>
inline void
RootNode<ChildT>::readBuffers(std::istream& is, const CoordBBox& clipBBox, bool fromHalf)
{
    const Tile bgTile(mBackground, /*active=*/false);

    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (isChild(i)) {
            // Stream in and clip 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.)
            ChildT& child = getChild(i);
            child.readBuffers(is, clipBBox, fromHalf);
        }
    }
    // Clip root-level tiles and prune children that were clipped.
    this->clip(clipBBox);
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::clip(const CoordBBox& clipBBox)
{
    const Tile bgTile(mBackground, /*active=*/false);

    // Iterate over a copy of this node's table so that we can modify the original.
    // (Copying the table copies child node pointers, not the nodes themselves.)
    MapType copyOfTable(mTable);
    for (MapIter i = copyOfTable.begin(), e = copyOfTable.end(); i != e; ++i) {
        const Coord& xyz = i->first; // 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.  Delete it.
            setTile(this->findCoord(xyz), bgTile); // delete any existing child node first
            mTable.erase(xyz);
        } else if (!clipBBox.isInside(tileBBox)) {
            // This table entry does not lie completely inside the clipping region
            // and must be clipped.
            if (isChild(i)) {
                getChild(i).clip(clipBBox, mBackground);
            } 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 Tile& origTile = getTile(i);
                setTile(this->findCoord(xyz), bgTile);
                this->sparseFill(tileBBox, origTile.value, origTile.active);
            }
        } else {
            // This table entry lies completely inside the clipping region.  Leave it intact.
        }
    }
    this->prune(); // also erases root-level background tiles
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::prune(const ValueType& tolerance)
{
    bool state = false;
    ValueType value = zeroVal<ValueType>();
    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (this->isTile(i)) continue;
        this->getChild(i).prune(tolerance);
        if (this->getChild(i).isConstant(value, state, tolerance)) {
            this->setTile(i, Tile(value, state));
        }
    }
    this->eraseBackgroundTiles();
}


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


template<typename ChildT>
template<typename NodeT>
inline NodeT*
RootNode<ChildT>::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
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTile(iter)) return nullptr;
    return (std::is_same<NodeT, ChildT>::value)
        ? reinterpret_cast<NodeT*>(&stealChild(iter, Tile(value, state)))
        : getChild(iter).template stealNode<NodeT>(xyz, value, state);
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT>
inline void
RootNode<ChildT>::addLeaf(LeafNodeType* leaf)
{
    if (leaf == nullptr) return;
    ChildT* child = nullptr;
    const Coord& xyz = leaf->origin();
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, mBackground, false);
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        if (ChildT::LEVEL>0) {
            child = &getChild(iter);
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
            setChild(iter, *child);//this also deletes the existing child node
        }
    } else {//tile
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        setChild(iter, *child);
    }
    child->addLeaf(leaf);
}


template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::addLeafAndCache(LeafNodeType* leaf, AccessorT& acc)
{
    if (leaf == nullptr) return;
    ChildT* child = nullptr;
    const Coord& xyz = leaf->origin();
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, mBackground, false);
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        if (ChildT::LEVEL>0) {
            child = &getChild(iter);
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
            setChild(iter, *child);//this also deletes the existing child node
        }
    } else {//tile
        if (ChildT::LEVEL>0) {
            child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        } else {
            child = reinterpret_cast<ChildT*>(leaf);
        }
        setChild(iter, *child);
    }
    acc.insert(xyz, child);
    child->addLeafAndCache(leaf, acc);
}

template<typename ChildT>
inline bool
RootNode<ChildT>::addChild(ChildT* child)
{
    if (!child) return false;
    const Coord& xyz = child->origin();
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {//background
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else {//child or tile
        setChild(iter, *child);//this also deletes the existing child node
    }
    return true;
}

template<typename ChildT>
inline void
RootNode<ChildT>::addTile(const Coord& xyz, const ValueType& value, bool state)
{
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {//background
        mTable[this->coordToKey(xyz)] = NodeStruct(Tile(value, state));
    } else {//child or tile
        setTile(iter, Tile(value, state));//this also deletes the existing child node
    }
}

template<typename ChildT>
inline void
RootNode<ChildT>::addTile(Index level, const Coord& xyz,
                          const ValueType& value, bool state)
{
    if (LEVEL >= level) {
        MapIter iter = this->findCoord(xyz);
        if (iter == mTable.end()) {//background
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, mBackground, false);
                mTable[this->coordToKey(xyz)] = NodeStruct(*child);
                child->addTile(level, xyz, value, state);
            } else {
                mTable[this->coordToKey(xyz)] = NodeStruct(Tile(value, state));
            }
        } else if (isChild(iter)) {//child
            if (LEVEL > level) {
                getChild(iter).addTile(level, xyz, value, state);
            } else {
                setTile(iter, Tile(value, state));//this also deletes the existing child node
            }
        } else {//tile
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
                setChild(iter, *child);
                child->addTile(level, xyz, value, state);
            } else {
                setTile(iter, Tile(value, state));
            }
        }
    }
}


template<typename ChildT>
template<typename AccessorT>
inline void
RootNode<ChildT>::addTileAndCache(Index level, const Coord& xyz, const ValueType& value,
                                  bool state, AccessorT& acc)
{
    if (LEVEL >= level) {
        MapIter iter = this->findCoord(xyz);
        if (iter == mTable.end()) {//background
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, mBackground, false);
                acc.insert(xyz, child);
                mTable[this->coordToKey(xyz)] = NodeStruct(*child);
                child->addTileAndCache(level, xyz, value, state, acc);
            } else {
                mTable[this->coordToKey(xyz)] = NodeStruct(Tile(value, state));
            }
        } else if (isChild(iter)) {//child
            if (LEVEL > level) {
                ChildT* child = &getChild(iter);
                acc.insert(xyz, child);
                child->addTileAndCache(level, xyz, value, state, acc);
            } else {
                setTile(iter, Tile(value, state));//this also deletes the existing child node
            }
        } else {//tile
            if (LEVEL > level) {
                ChildT* child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
                acc.insert(xyz, child);
                setChild(iter, *child);
                child->addTileAndCache(level, xyz, value, state, acc);
            } else {
                setTile(iter, Tile(value, state));
            }
        }
    }
}


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


template<typename ChildT>
inline typename ChildT::LeafNodeType*
RootNode<ChildT>::touchLeaf(const Coord& xyz)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground, false);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    return child->touchLeaf(xyz);
}


template<typename ChildT>
template<typename AccessorT>
inline typename ChildT::LeafNodeType*
RootNode<ChildT>::touchLeafAndCache(const Coord& xyz, AccessorT& acc)
{
    ChildT* child = nullptr;
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end()) {
        child = new ChildT(xyz, mBackground, false);
        mTable[this->coordToKey(xyz)] = NodeStruct(*child);
    } else if (isChild(iter)) {
        child = &getChild(iter);
    } else {
        child = new ChildT(xyz, getTile(iter).value, isTileOn(iter));
        setChild(iter, *child);
    }
    acc.insert(xyz, child);
    return child->touchLeafAndCache(xyz, acc);
}


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


template<typename ChildT>
template<typename NodeT>
inline NodeT*
RootNode<ChildT>::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
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTile(iter)) return nullptr;
    ChildT* child = &getChild(iter);
    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>
template<typename NodeT>
inline const NodeT*
RootNode<ChildT>::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
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTile(iter)) return nullptr;
    const ChildT* child = &getChild(iter);
    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>
inline typename ChildT::LeafNodeType*
RootNode<ChildT>::probeLeaf(const Coord& xyz)
{
    return this->template probeNode<LeafNodeType>(xyz);
}


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


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


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


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


template<typename ChildT>
template<typename NodeT, typename AccessorT>
inline NodeT*
RootNode<ChildT>::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
    MapIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTile(iter)) return nullptr;
    ChildT* child = &getChild(iter);
    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>
template<typename NodeT,typename AccessorT>
inline const NodeT*
RootNode<ChildT>::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
    MapCIter iter = this->findCoord(xyz);
    if (iter == mTable.end() || isTile(iter)) return nullptr;
    const ChildT* child = &getChild(iter);
    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>
template<typename ArrayT>
inline void
RootNode<ChildT>::getNodes(ArrayT& array)
{
    using NodePtr = typename ArrayT::value_type;
    static_assert(std::is_pointer<NodePtr>::value,
        "argument to getNodes() must be a pointer array");
    using NodeType = typename std::remove_pointer<NodePtr>::type;
    using NonConstNodeType = typename std::remove_const<NodeType>::type;
    static_assert(NodeChainType::template Contains<NonConstNodeType>,
        "can't extract non-const nodes from a const tree");
    using ArrayChildT = typename std::conditional<
        std::is_const<NodeType>::value, const ChildT, ChildT>::type;

    for (MapIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
        if (ChildT* child = iter->second.child) {
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
            if (std::is_same<NodePtr, ArrayChildT*>::value) {
                array.push_back(reinterpret_cast<NodePtr>(iter->second.child));
            } else {
                child->getNodes(array);//descent
            }
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
        }
    }
}

template<typename ChildT>
template<typename ArrayT>
inline void
RootNode<ChildT>::getNodes(ArrayT& array) const
{
    using NodePtr = typename ArrayT::value_type;
    static_assert(std::is_pointer<NodePtr>::value,
        "argument to getNodes() must be a pointer array");
    using NodeType = typename std::remove_pointer<NodePtr>::type;
    static_assert(std::is_const<NodeType>::value,
        "argument to getNodes() must be an array of const node pointers");
    using NonConstNodeType = typename std::remove_const<NodeType>::type;
    static_assert(NodeChainType::template Contains<NonConstNodeType>,
        "can't extract non-const nodes from a const tree");

    for (MapCIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
        if (const ChildNodeType *child = iter->second.child) {
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
            if (std::is_same<NodePtr, const ChildT*>::value) {
                array.push_back(reinterpret_cast<NodePtr>(iter->second.child));
            } else {
                child->getNodes(array);//descent
            }
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
        }
    }
}

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

template<typename ChildT>
template<typename ArrayT>
inline void
RootNode<ChildT>::stealNodes(ArrayT& array, const ValueType& value, bool state)
{
    using NodePtr = typename ArrayT::value_type;
    static_assert(std::is_pointer<NodePtr>::value,
        "argument to stealNodes() must be a pointer array");
    using NodeType = typename std::remove_pointer<NodePtr>::type;
    using NonConstNodeType = typename std::remove_const<NodeType>::type;
    static_assert(NodeChainType::template Contains<NonConstNodeType>,
        "can't extract non-const nodes from a const tree");
    using ArrayChildT = typename std::conditional<
        std::is_const<NodeType>::value, const ChildT, ChildT>::type;

    for (MapIter iter=mTable.begin(); iter!=mTable.end(); ++iter) {
        if (ChildT* child = iter->second.child) {
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN
            if (std::is_same<NodePtr, ArrayChildT*>::value) {
                array.push_back(reinterpret_cast<NodePtr>(&stealChild(iter, Tile(value, state))));
            } else {
                child->stealNodes(array, value, state);//descent
            }
            OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
        }
    }
}


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


template<typename ChildT>
template<MergePolicy Policy>
inline void
RootNode<ChildT>::merge(RootNode& other)
{
    OPENVDB_NO_UNREACHABLE_CODE_WARNING_BEGIN

    switch (Policy) {

    default:
    case MERGE_ACTIVE_STATES:
        for (MapIter i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
            MapIter j = mTable.find(i->first);
            if (other.isChild(i)) {
                if (j == mTable.end()) { // insert other node's child
                    ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                    child.resetBackground(other.mBackground, mBackground);
                    mTable[i->first] = NodeStruct(child);
                } else if (isTile(j)) {
                    if (isTileOff(j)) { // replace inactive tile with other node's child
                        ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                        child.resetBackground(other.mBackground, mBackground);
                        setChild(j, child);
                    }
                } else { // merge both child nodes
                    getChild(j).template merge<MERGE_ACTIVE_STATES>(getChild(i),
                        other.mBackground, mBackground);
                }
            } else if (other.isTileOn(i)) {
                if (j == mTable.end()) { // insert other node's active tile
                    mTable[i->first] = i->second;
                } else if (!isTileOn(j)) {
                    // Replace anything except an active tile with the other node's active tile.
                    setTile(j, Tile(other.getTile(i).value, true));
                }
            }
        }
        break;

    case MERGE_NODES:
        for (MapIter i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
            MapIter j = mTable.find(i->first);
            if (other.isChild(i)) {
                if (j == mTable.end()) { // insert other node's child
                    ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                    child.resetBackground(other.mBackground, mBackground);
                    mTable[i->first] = NodeStruct(child);
                } else if (isTile(j)) { // replace tile with other node's child
                    ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                    child.resetBackground(other.mBackground, mBackground);
                    setChild(j, child);
                } else { // merge both child nodes
                    getChild(j).template merge<MERGE_NODES>(
                        getChild(i), other.mBackground, mBackground);
                }
            }
        }
        break;

    case MERGE_ACTIVE_STATES_AND_NODES:
        for (MapIter i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
            MapIter j = mTable.find(i->first);
            if (other.isChild(i)) {
                if (j == mTable.end()) {
                    // Steal and insert the other node's child.
                    ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                    child.resetBackground(other.mBackground, mBackground);
                    mTable[i->first] = NodeStruct(child);
                } else if (isTile(j)) {
                    // Replace this node's tile with the other node's child.
                    ChildNodeType& child = stealChild(i, Tile(other.mBackground, /*on=*/false));
                    child.resetBackground(other.mBackground, mBackground);
                    const Tile tile = getTile(j);
                    setChild(j, child);
                    if (tile.active) {
                        // Merge the other node's child with this node's active tile.
                        child.template merge<MERGE_ACTIVE_STATES_AND_NODES>(
                            tile.value, tile.active);
                    }
                } else /*if (isChild(j))*/ {
                    // Merge the other node's child into this node's child.
                    getChild(j).template merge<MERGE_ACTIVE_STATES_AND_NODES>(getChild(i),
                        other.mBackground, mBackground);
                }
            } else if (other.isTileOn(i)) {
                if (j == mTable.end()) {
                    // Insert a copy of the other node's active tile.
                    mTable[i->first] = i->second;
                } else if (isTileOff(j)) {
                    // Replace this node's inactive tile with a copy of the other's active tile.
                    setTile(j, Tile(other.getTile(i).value, true));
                } else if (isChild(j)) {
                    // Merge the other node's active tile into this node's child.
                    const Tile& tile = getTile(i);
                    getChild(j).template merge<MERGE_ACTIVE_STATES_AND_NODES>(
                        tile.value, tile.active);
                }
            } // else if (other.isTileOff(i)) {} // ignore the other node's inactive tiles
        }
        break;
    }

    // Empty the other tree so as not to leave it in a partially cannibalized state.
    other.clear();

    OPENVDB_NO_UNREACHABLE_CODE_WARNING_END
}


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


template<typename ChildT>
template<typename OtherChildType>
inline void
RootNode<ChildT>::topologyUnion(const RootNode<OtherChildType>& other)
{
    using OtherRootT = RootNode<OtherChildType>;
    using OtherCIterT = typename OtherRootT::MapCIter;

    enforceSameConfiguration(other);

    for (OtherCIterT i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
        MapIter j = mTable.find(i->first);
        if (other.isChild(i)) {
            if (j == mTable.end()) { // create child branch with identical topology
                mTable[i->first] = NodeStruct(
                    *(new ChildT(other.getChild(i), mBackground, TopologyCopy())));
            } else if (this->isChild(j)) { // union with child branch
                this->getChild(j).topologyUnion(other.getChild(i));
            } else {// this is a tile so replace it with a child branch with identical topology
                ChildT* child = new ChildT(
                    other.getChild(i), this->getTile(j).value, TopologyCopy());
                if (this->isTileOn(j)) child->setValuesOn();//this is an active tile
                this->setChild(j, *child);
            }
        } else if (other.isTileOn(i)) { // other is an active tile
            if (j == mTable.end()) { // insert an active tile
                mTable[i->first] = NodeStruct(Tile(mBackground, true));
            } else if (this->isChild(j)) {
                this->getChild(j).setValuesOn();
            } else if (this->isTileOff(j)) {
                this->setTile(j, Tile(this->getTile(j).value, true));
            }
        }
    }
}

template<typename ChildT>
template<typename OtherChildType>
inline void
RootNode<ChildT>::topologyIntersection(const RootNode<OtherChildType>& other)
{
    using OtherRootT = RootNode<OtherChildType>;
    using OtherCIterT = typename OtherRootT::MapCIter;

    enforceSameConfiguration(other);

    std::set<Coord> tmp;//keys to erase
    for (MapIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        OtherCIterT j = other.mTable.find(i->first);
        if (this->isChild(i)) {
            if (j == other.mTable.end() || other.isTileOff(j)) {
                tmp.insert(i->first);//delete child branch
            } else if (other.isChild(j)) { // intersect with child branch
                this->getChild(i).topologyIntersection(other.getChild(j), mBackground);
            }
        } else if (this->isTileOn(i)) {
            if (j == other.mTable.end() || other.isTileOff(j)) {
                this->setTile(i, Tile(this->getTile(i).value, false));//turn inactive
            } else if (other.isChild(j)) { //replace with a child branch with identical topology
                ChildT* child =
                    new ChildT(other.getChild(j), this->getTile(i).value, TopologyCopy());
                this->setChild(i, *child);
            }
        }
    }
    for (std::set<Coord>::iterator i = tmp.begin(), e = tmp.end(); i != e; ++i) {
        MapIter it = this->findCoord(*i);
        setTile(it, Tile()); // delete any existing child node first
        mTable.erase(it);
    }
}

template<typename ChildT>
template<typename OtherChildType>
inline void
RootNode<ChildT>::topologyDifference(const RootNode<OtherChildType>& other)
{
    using OtherRootT = RootNode<OtherChildType>;
    using OtherCIterT = typename OtherRootT::MapCIter;

    enforceSameConfiguration(other);

    for (OtherCIterT i = other.mTable.begin(), e = other.mTable.end(); i != e; ++i) {
        MapIter j = mTable.find(i->first);
        if (other.isChild(i)) {
            if (j == mTable.end() || this->isTileOff(j)) {
                //do nothing
            } else if (this->isChild(j)) { // difference with child branch
                this->getChild(j).topologyDifference(other.getChild(i), mBackground);
            } else if (this->isTileOn(j)) {
                // this is an active tile so create a child node and descent
                ChildT* child = new ChildT(j->first, this->getTile(j).value, true);
                child->topologyDifference(other.getChild(i), mBackground);
                this->setChild(j, *child);
            }
        } else if (other.isTileOn(i)) { // other is an active tile
            if (j == mTable.end() || this->isTileOff(j)) {
                // do nothing
            } else if (this->isChild(j)) {
                setTile(j, Tile()); // delete any existing child node first
                mTable.erase(j);
            } else if (this->isTileOn(j)) {
                this->setTile(j, Tile(this->getTile(j).value, false));
            }
        }
    }
}

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


template<typename ChildT>
template<typename CombineOp>
inline void
RootNode<ChildT>::combine(RootNode& other, CombineOp& op, bool prune)
{
    CombineArgs<ValueType> args;

    CoordSet keys;
    this->insertKeys(keys);
    other.insertKeys(keys);

    for (CoordSetCIter i = keys.begin(), e = keys.end(); i != e; ++i) {
        MapIter iter = findOrAddCoord(*i), otherIter = other.findOrAddCoord(*i);
        if (isTile(iter) && isTile(otherIter)) {
            // 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(getTile(iter).value)
                .setAIsActive(isTileOn(iter))
                .setBRef(getTile(otherIter).value)
                .setBIsActive(isTileOn(otherIter)));
            setTile(iter, Tile(args.result(), args.resultIsActive()));

        } else if (isChild(iter) && isTile(otherIter)) {
            // Combine this node's child with the other node's constant value.
            ChildT& child = getChild(iter);
            child.combine(getTile(otherIter).value, isTileOn(otherIter), op);

        } else if (isTile(iter) && isChild(otherIter)) {
            // 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);
            ChildT& child = getChild(otherIter);
            child.combine(getTile(iter).value, isTileOn(iter), swappedOp);

            // Steal the other node's child.
            setChild(iter, stealChild(otherIter, Tile()));

        } else /*if (isChild(iter) && isChild(otherIter))*/ {
            // Combine this node's child with the other node's child.
            ChildT &child = getChild(iter), &otherChild = getChild(otherIter);
            child.combine(otherChild, op);
        }
        if (prune && isChild(iter)) getChild(iter).prune();
    }

    // Combine background values.
    op(args.setARef(mBackground).setBRef(other.mBackground));
    mBackground = args.result();

    // Empty the other tree so as not to leave it in a partially cannibalized state.
    other.clear();
}


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


// This helper class is a friend of RootNode and is needed so that combine2
// can be specialized for compatible and incompatible pairs of RootNode types.
template<typename CombineOp, typename RootT, typename OtherRootT, bool Compatible = false>
struct RootNodeCombineHelper
{
    static inline void combine2(RootT& self, const RootT&, const OtherRootT& other1,
        CombineOp&, bool)
    {
        // If the two root nodes have different configurations or incompatible ValueTypes,
        // throw an exception.
        self.enforceSameConfiguration(other1);
        self.enforceCompatibleValueTypes(other1);
        // One of the above two tests should throw, so we should never get here:
        std::ostringstream ostr;
        ostr << "cannot combine a " << typeid(OtherRootT).name()
            << " into a " << typeid(RootT).name();
        OPENVDB_THROW(TypeError, ostr.str());
    }
};

// Specialization for root nodes of compatible types
template<typename CombineOp, typename RootT, typename OtherRootT>
struct RootNodeCombineHelper<CombineOp, RootT, OtherRootT, /*Compatible=*/true>
{
    static inline void combine2(RootT& self, const RootT& other0, const OtherRootT& other1,
        CombineOp& op, bool prune)
    {
        self.doCombine2(other0, other1, op, prune);
    }
};


template<typename ChildT>
template<typename CombineOp, typename OtherRootNode>
inline void
RootNode<ChildT>::combine2(const RootNode& other0, const OtherRootNode& other1,
    CombineOp& op, bool prune)
{
    using OtherValueType = typename OtherRootNode::ValueType;
    static const bool compatible = (SameConfiguration<OtherRootNode>::value
        && CanConvertType</*from=*/OtherValueType, /*to=*/ValueType>::value);
    RootNodeCombineHelper<CombineOp, RootNode, OtherRootNode, compatible>::combine2(
        *this, other0, other1, op, prune);
}


template<typename ChildT>
template<typename CombineOp, typename OtherRootNode>
inline void
RootNode<ChildT>::doCombine2(const RootNode& other0, const OtherRootNode& other1,
    CombineOp& op, bool prune)
{
    enforceSameConfiguration(other1);

    using OtherValueT = typename OtherRootNode::ValueType;
    using OtherTileT = typename OtherRootNode::Tile;
    using OtherNodeStructT = typename OtherRootNode::NodeStruct;
    using OtherMapCIterT = typename OtherRootNode::MapCIter;

    CombineArgs<ValueType, OtherValueT> args;

    CoordSet keys;
    other0.insertKeys(keys);
    other1.insertKeys(keys);

    const NodeStruct bg0(Tile(other0.mBackground, /*active=*/false));
    const OtherNodeStructT bg1(OtherTileT(other1.mBackground, /*active=*/false));

    for (CoordSetCIter i = keys.begin(), e = keys.end(); i != e; ++i) {
        MapIter thisIter = this->findOrAddCoord(*i);
        MapCIter iter0 = other0.findKey(*i);
        OtherMapCIterT iter1 = other1.findKey(*i);
        const NodeStruct& ns0 = (iter0 != other0.mTable.end()) ? iter0->second : bg0;
        const OtherNodeStructT& ns1 = (iter1 != other1.mTable.end()) ? iter1->second : bg1;
        if (ns0.isTile() && ns1.isTile()) {
            // Both input nodes have constant values (tiles).
            // Combine the two values and add a new tile to this node with the result.
            op(args.setARef(ns0.tile.value)
                .setAIsActive(ns0.isTileOn())
                .setBRef(ns1.tile.value)
                .setBIsActive(ns1.isTileOn()));
            setTile(thisIter, Tile(args.result(), args.resultIsActive()));
        } else {
            if (!isChild(thisIter)) {
                // Add a new child with the same coordinates, etc. as the other node's child.
                const Coord& childOrigin =
                    ns0.isChild() ? ns0.child->origin() : ns1.child->origin();
                setChild(thisIter, *(new ChildT(childOrigin, getTile(thisIter).value)));
            }
            ChildT& child = getChild(thisIter);

            if (ns0.isTile()) {
                // Combine node1's child with node0's constant value
                // and write the result into this node's child.
                child.combine2(ns0.tile.value, *ns1.child, ns0.isTileOn(), op);
            } else if (ns1.isTile()) {
                // Combine node0's child with node1's constant value
                // and write the result into this node's child.
                child.combine2(*ns0.child, ns1.tile.value, ns1.isTileOn(), op);
            } else {
                // Combine node0's child with node1's child
                // and write the result into this node's child.
                child.combine2(*ns0.child, *ns1.child, op);
            }
        }
        if (prune && isChild(thisIter)) getChild(thisIter).prune();
    }

    // Combine background values.
    op(args.setARef(other0.mBackground).setBRef(other1.mBackground));
    mBackground = args.result();
}


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


template<typename ChildT>
template<typename BBoxOp>
inline void
RootNode<ChildT>::visitActiveBBox(BBoxOp& op) const
{
    const bool descent = op.template descent<LEVEL>();
    for (MapCIter i = mTable.begin(), e = mTable.end(); i != e; ++i) {
        if (this->isTileOff(i)) continue;
        if (this->isChild(i) && descent) {
            this->getChild(i).visitActiveBBox(op);
        } else {
            op.template operator()<LEVEL>(CoordBBox::createCube(i->first, ChildT::DIM));
        }
    }
}


template<typename ChildT>
template<typename VisitorOp>
inline void
RootNode<ChildT>::visit(VisitorOp& op)
{
    doVisit<RootNode, VisitorOp, ChildAllIter>(*this, op);
}


template<typename ChildT>
template<typename VisitorOp>
inline void
RootNode<ChildT>::visit(VisitorOp& op) const
{
    doVisit<const RootNode, VisitorOp, ChildAllCIter>(*this, op);
}


template<typename ChildT>
template<typename RootNodeT, typename VisitorOp, typename ChildAllIterT>
inline void
RootNode<ChildT>::doVisit(RootNodeT& self, VisitorOp& op)
{
    typename RootNodeT::ValueType val;
    for (ChildAllIterT iter = self.beginChildAll(); iter; ++iter) {
        if (op(iter)) continue;
        if (typename ChildAllIterT::ChildNodeType* child = iter.probeChild(val)) {
            child->visit(op);
        }
    }
}


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


template<typename ChildT>
template<typename OtherRootNodeType, typename VisitorOp>
inline void
RootNode<ChildT>::visit2(OtherRootNodeType& other, VisitorOp& op)
{
    doVisit2<RootNode, OtherRootNodeType, VisitorOp, ChildAllIter,
        typename OtherRootNodeType::ChildAllIter>(*this, other, op);
}


template<typename ChildT>
template<typename OtherRootNodeType, typename VisitorOp>
inline void
RootNode<ChildT>::visit2(OtherRootNodeType& other, VisitorOp& op) const
{
    doVisit2<const RootNode, OtherRootNodeType, VisitorOp, ChildAllCIter,
        typename OtherRootNodeType::ChildAllCIter>(*this, other, op);
}


template<typename ChildT>
template<
    typename RootNodeT,
    typename OtherRootNodeT,
    typename VisitorOp,
    typename ChildAllIterT,
    typename OtherChildAllIterT>
inline void
RootNode<ChildT>::doVisit2(RootNodeT& self, OtherRootNodeT& other, VisitorOp& op)
{
    enforceSameConfiguration(other);

    typename RootNodeT::ValueType val;
    typename OtherRootNodeT::ValueType otherVal;

    // The two nodes are required to have corresponding table entries,
    // but since that might require background tiles to be added to one or both,
    // and the nodes might be const, we operate on shallow copies of the nodes instead.
    RootNodeT copyOfSelf(self.mBackground);
    copyOfSelf.mTable = self.mTable;
    OtherRootNodeT copyOfOther(other.mBackground);
    copyOfOther.mTable = other.mTable;

    // Add background tiles to both nodes as needed.
    CoordSet keys;
    self.insertKeys(keys);
    other.insertKeys(keys);
    for (CoordSetCIter i = keys.begin(), e = keys.end(); i != e; ++i) {
        copyOfSelf.findOrAddCoord(*i);
        copyOfOther.findOrAddCoord(*i);
    }

    ChildAllIterT iter = copyOfSelf.beginChildAll();
    OtherChildAllIterT otherIter = copyOfOther.beginChildAll();

    for ( ; iter && otherIter; ++iter, ++otherIter)
    {
        const size_t skipBranch = static_cast<size_t>(op(iter, otherIter));

        typename ChildAllIterT::ChildNodeType* child =
            (skipBranch & 1U) ? nullptr : iter.probeChild(val);
        typename OtherChildAllIterT::ChildNodeType* otherChild =
            (skipBranch & 2U) ? nullptr : otherIter.probeChild(otherVal);

        if (child != nullptr && otherChild != nullptr) {
            child->visit2Node(*otherChild, op);
        } else if (child != nullptr) {
            child->visit2(otherIter, op);
        } else if (otherChild != nullptr) {
            otherChild->visit2(iter, op, /*otherIsLHS=*/true);
        }
    }
    // Remove any background tiles that were added above,
    // as well as any that were created by the visitors.
    copyOfSelf.eraseBackgroundTiles();
    copyOfOther.eraseBackgroundTiles();

    // If either input node is non-const, replace its table with
    // the (possibly modified) copy.
    self.resetTable(copyOfSelf.mTable);
    other.resetTable(copyOfOther.mTable);
}

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

#endif // OPENVDB_TREE_ROOTNODE_HAS_BEEN_INCLUDED