data/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.C

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Copyright (C) 2011-2025 OpenFOAM Foundation
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.

    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.

\*---------------------------------------------------------------------------*/

#include "indexedOctree.H"
#include "linePointRef.H"
#include "OFstream.H"
#include "ListOps.H"
#include "memInfo.H"

// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //

template<class Type>
Foam::scalar Foam::indexedOctree<Type>::perturbTol_ = 10*small;


// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //

template<class Type>
bool Foam::indexedOctree<Type>::overlaps
(
    const point& p0,
    const point& p1,
    const scalar nearestDistSqr,
    const point& sample
)
{
    boundBox bb(p0, p1);

    return bb.overlaps(sample, nearestDistSqr);
}


template<class Type>
bool Foam::indexedOctree<Type>::overlaps
(
    const treeBoundBox& parentBb,
    const direction octant,
    const scalar nearestDistSqr,
    const point& sample
)
{
    //- Accelerated version of
    //     treeBoundBox subBb(parentBb.subBbox(mid, octant))
    //     overlaps
    //     (
    //          subBb.min(),
    //          subBb.max(),
    //          nearestDistSqr,
    //          sample
    //     )

    const point& min = parentBb.min();
    const point& max = parentBb.max();

    point other;

    if (octant & treeBoundBox::octantBit::rightHalf)
    {
        other.x() = max.x();
    }
    else
    {
        other.x() = min.x();
    }

    if (octant & treeBoundBox::octantBit::topHalf)
    {
        other.y() = max.y();
    }
    else
    {
        other.y() = min.y();
    }

    if (octant & treeBoundBox::octantBit::frontHalf)
    {
        other.z() = max.z();
    }
    else
    {
        other.z() = min.z();
    }

    const point mid(0.5*(min+max));

    return overlaps(mid, other, nearestDistSqr, sample);
}


template<class Type>
void Foam::indexedOctree<Type>::divide
(
    const labelList& indices,
    const treeBoundBox& bb,
    labelListList& result
) const
{
    List<DynamicList<label>> subIndices(8);
    for (direction octant = 0; octant < subIndices.size(); octant++)
    {
        subIndices[octant].setCapacity(indices.size()/8);
    }

    // Precalculate bounding boxes.
    FixedList<treeBoundBox, 8> subBbs;
    for (direction octant = 0; octant < subBbs.size(); octant++)
    {
        subBbs[octant] = bb.subBbox(octant);
    }

    forAll(indices, i)
    {
        label shapeI = indices[i];

        for (direction octant = 0; octant < 8; octant++)
        {
            if (shapes_.overlaps(shapeI, subBbs[octant]))
            {
                subIndices[octant].append(shapeI);
            }
        }
    }

    result.setSize(8);
    for (direction octant = 0; octant < subIndices.size(); octant++)
    {
        result[octant].transfer(subIndices[octant]);
    }
}


template<class Type>
typename Foam::indexedOctree<Type>::node
Foam::indexedOctree<Type>::divide
(
    const treeBoundBox& bb,
    DynamicList<labelList>& contents,
    const label contentI
) const
{
    const labelList& indices = contents[contentI];

    node nod;

    if
    (
        bb.min()[0] >= bb.max()[0]
     || bb.min()[1] >= bb.max()[1]
     || bb.min()[2] >= bb.max()[2]
    )
    {
        FatalErrorInFunction
            << "Badly formed bounding box:" << bb
            << abort(FatalError);
    }

    nod.bb_ = bb;
    nod.parent_ = -1;

    labelListList dividedIndices(8);
    divide(indices, bb, dividedIndices);

    // Have now divided the indices into 8 (possibly empty) subsets.
    // Replace current contentI with the first (non-empty) subset.
    // Append the rest.
    bool replaced = false;

    for (direction octant = 0; octant < dividedIndices.size(); octant++)
    {
        labelList& subIndices = dividedIndices[octant];

        if (subIndices.size())
        {
            if (!replaced)
            {
                contents[contentI].transfer(subIndices);
                nod.subNodes_[octant] = contentPlusOctant(contentI, octant);
                replaced = true;
            }
            else
            {
                // Store at end of contents.
                // note dummy append + transfer trick
                label sz = contents.size();
                contents.append(labelList(0));
                contents[sz].transfer(subIndices);
                nod.subNodes_[octant] = contentPlusOctant(sz, octant);
            }
        }
        else
        {
            // Mark node as empty
            nod.subNodes_[octant] = emptyPlusOctant(octant);
        }
    }

    return nod;
}


template<class Type>
void Foam::indexedOctree<Type>::splitNodes
(
    const label minSize,
    DynamicList<indexedOctree<Type>::node>& nodes,
    DynamicList<labelList>& contents
) const
{
    label currentSize = nodes.size();

    // Take care to loop only over old nodes.
    // Also we loop over the same DynamicList which gets modified and
    // moved so make sure not to keep any references!
    for (label nodeI = 0; nodeI < currentSize; nodeI++)
    {
        for
        (
            direction octant = 0;
            octant < nodes[nodeI].subNodes_.size();
            octant++
        )
        {
            labelBits index = nodes[nodeI].subNodes_[octant];

            if (isNode(index))
            {
                // tree node. Leave intact.
            }
            else if (isContent(index))
            {
                label contentI = getContent(index);

                if (contents[contentI].size() > minSize)
                {
                    // Create node for content.

                    // Find the bounding box for the subnode
                    const node& nod = nodes[nodeI];
                    const treeBoundBox bb(nod.bb_.subBbox(octant));

                    node subNode(divide(bb, contents, contentI));
                    subNode.parent_ = nodeI;
                    label sz = nodes.size();
                    nodes.append(subNode);
                    nodes[nodeI].subNodes_[octant] = nodePlusOctant(sz, octant);
                }
            }
        }
    }
}


template<class Type>
Foam::label Foam::indexedOctree<Type>::compactContents
(
    DynamicList<node>& nodes,
    DynamicList<labelList>& contents,
    const label compactLevel,
    const label nodeI,
    const label level,

    List<labelList>& compactedContents,
    label& compactI
)
{
    const node& nod = nodes[nodeI];

    label nNodes = 0;

    if (level < compactLevel)
    {
        for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
        {
            labelBits index = nod.subNodes_[octant];

            if (isNode(index))
            {
                nNodes += compactContents
                (
                    nodes,
                    contents,
                    compactLevel,
                    getNode(index),
                    level+1,
                    compactedContents,
                    compactI
                );
            }
        }
    }
    else if (level == compactLevel)
    {
        // Compact all content on this level
        for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
        {
            labelBits index = nod.subNodes_[octant];

            if (isContent(index))
            {
                label contentI = getContent(index);

                compactedContents[compactI].transfer(contents[contentI]);

                // Subnode is at compactI. Adapt nodeI to point to it
                nodes[nodeI].subNodes_[octant] =
                    contentPlusOctant(compactI, octant);

                compactI++;
            }
            else if (isNode(index))
            {
                nNodes++;
            }
        }
    }
    return nNodes;
}


template<class Type>
Foam::volumeType Foam::indexedOctree<Type>::calcVolumeType
(
    const label nodeI
) const
{
    // Pre-calculates wherever possible the volume status per node/subnode.
    // Recurses to determine status of lowest level boxes. Level above is
    // combination of octants below.

    const node& nod = nodes_[nodeI];

    volumeType myType = volumeType::unknown;

    for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
    {
        volumeType subType;

        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            // tree node. Recurse.
            subType = calcVolumeType(getNode(index));
        }
        else if (isContent(index))
        {
            // Contents. Depending on position in box might be on either
            // side.
            subType = volumeType::mixed;
        }
        else
        {
            // No data in this octant. Set type for octant acc. to the mid
            // of its bounding box.
            const treeBoundBox subBb = nod.bb_.subBbox(octant);

            subType = shapes_.getVolumeType(*this, subBb.midpoint());
        }

        // Store octant type
        nodeTypes_.set((nodeI<<3)+octant, subType);

        // Combine sub node types into type for treeNode. Result is 'mixed' if
        // types differ among subnodes.
        if (myType == volumeType::unknown)
        {
            myType = subType;
        }
        else if (subType != myType)
        {
            myType = volumeType::mixed;
        }
    }
    return myType;
}


template<class Type>
Foam::volumeType Foam::indexedOctree<Type>::getVolumeType
(
    const label nodeI,
    const point& sample
) const
{
    const node& nod = nodes_[nodeI];

    direction octant = nod.bb_.subOctant(sample);

    volumeType octantType = volumeType::type(nodeTypes_.get((nodeI<<3)+octant));

    if (octantType == volumeType::inside)
    {
        return octantType;
    }
    else if (octantType == volumeType::outside)
    {
        return octantType;
    }
    else if (octantType == volumeType::unknown)
    {
        // Can happen for e.g. non-manifold surfaces.
        return octantType;
    }
    else if (octantType == volumeType::mixed)
    {
        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            // Recurse
            volumeType subType = getVolumeType(getNode(index), sample);

            return subType;
        }
        else if (isContent(index))
        {
            // Content. Defer to shapes.
            return volumeType(shapes_.getVolumeType(*this, sample));
        }
        else
        {
            // Empty node. Cannot have 'mixed' as its type since not divided
            // up and has no items inside it.
            FatalErrorInFunction
                << "Sample:" << sample << " node:" << nodeI
                << " with bb:" << nodes_[nodeI].bb_ << nl
                << "Empty subnode has invalid volume type mixed."
                << abort(FatalError);

            return volumeType::unknown;
        }
    }
    else
    {
        FatalErrorInFunction
            << "Sample:" << sample << " at node:" << nodeI
            << " octant:" << octant
            << " with bb:" << nod.bb_.subBbox(octant) << nl
            << "Node has invalid volume type " << octantType
            << abort(FatalError);

        return volumeType::unknown;
    }
}


template<class Type>
Foam::volumeType Foam::indexedOctree<Type>::getSide
(
    const vector& outsideNormal,
    const vector& vec
)
{
    if ((outsideNormal&vec) >= 0)
    {
        return volumeType::outside;
    }
    else
    {
        return volumeType::inside;
    }
}


template<class Type>
template<class FindNearestOp>
void Foam::indexedOctree<Type>::findNearest
(
    const label nodeI,
    const point& sample,

    scalar& nearestDistSqr,
    label& nearestShapeI,
    point& nearestPoint,

    const FindNearestOp& fnOp
) const
{
    const node& nod = nodes_[nodeI];

    // Determine order to walk through octants
    FixedList<direction, 8> octantOrder;
    nod.bb_.searchOrder(sample, octantOrder);

    // Go into all suboctants (one containing sample first) and update nearest.
    for (direction i = 0; i < 8; i++)
    {
        direction octant = octantOrder[i];

        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            label subNodeI = getNode(index);

            const treeBoundBox& subBb = nodes_[subNodeI].bb_;

            if (overlaps(subBb.min(), subBb.max(), nearestDistSqr, sample))
            {
                findNearest
                (
                    subNodeI,
                    sample,

                    nearestDistSqr,
                    nearestShapeI,
                    nearestPoint,

                    fnOp
                );
            }
        }
        else if (isContent(index))
        {
            if
            (
                overlaps
                (
                    nod.bb_,
                    octant,
                    nearestDistSqr,
                    sample
                )
            )
            {
                fnOp
                (
                    contents_[getContent(index)],
                    sample,

                    nearestDistSqr,
                    nearestShapeI,
                    nearestPoint
                );
            }
        }
    }
}


template<class Type>
template<class FindNearestOp>
void Foam::indexedOctree<Type>::findNearest
(
    const label nodeI,
    const linePointRef& ln,

    treeBoundBox& tightest,
    label& nearestShapeI,
    point& linePoint,
    point& nearestPoint,

    const FindNearestOp& fnOp
) const
{
    const node& nod = nodes_[nodeI];
    const treeBoundBox& nodeBb = nod.bb_;

    // Determine order to walk through octants
    FixedList<direction, 8> octantOrder;
    nod.bb_.searchOrder(ln.centre(), octantOrder);

    // Go into all suboctants (one containing sample first) and update nearest.
    for (direction i = 0; i < 8; i++)
    {
        direction octant = octantOrder[i];

        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            const treeBoundBox& subBb = nodes_[getNode(index)].bb_;

            if (subBb.overlaps(tightest))
            {
                findNearest
                (
                    getNode(index),
                    ln,

                    tightest,
                    nearestShapeI,
                    linePoint,
                    nearestPoint,

                    fnOp
                );
            }
        }
        else if (isContent(index))
        {
            const treeBoundBox subBb(nodeBb.subBbox(octant));

            if (subBb.overlaps(tightest))
            {
                fnOp
                (
                    contents_[getContent(index)],
                    ln,

                    tightest,
                    nearestShapeI,
                    linePoint,
                    nearestPoint
                );
            }
        }
    }
}


template<class Type>
Foam::treeBoundBox Foam::indexedOctree<Type>::subBbox
(
    const label parentNodeI,
    const direction octant
) const
{
    // Get type of node at octant
    const node& nod = nodes_[parentNodeI];
    labelBits index = nod.subNodes_[octant];

    if (isNode(index))
    {
        // Use stored bb
        return nodes_[getNode(index)].bb_;
    }
    else
    {
        // Calculate subBb
        return nod.bb_.subBbox(octant);
    }
}


template<class Type>
Foam::point Foam::indexedOctree<Type>::pushPoint
(
    const treeBoundBox& bb,
    const point& pt,
    const bool pushInside
)
{
    // Get local length scale.
    const vector perturbVec = perturbTol_*bb.span();

    point perturbedPt(pt);

    // Modify all components which are close to any face of the bb to be
    // well inside/outside them.

    if (pushInside)
    {
        for (direction dir = 0; dir < vector::nComponents; dir++)
        {
            if (mag(pt[dir]-bb.min()[dir]) < mag(perturbVec[dir]))
            {
                // Close to 'left' side. Push well beyond left side.
                scalar perturbDist = perturbVec[dir] + rootVSmall;
                perturbedPt[dir] = bb.min()[dir] + perturbDist;
            }
            else if (mag(pt[dir]-bb.max()[dir]) < mag(perturbVec[dir]))
            {
                // Close to 'right' side. Push well beyond right side.
                scalar perturbDist = perturbVec[dir] + rootVSmall;
                perturbedPt[dir] = bb.max()[dir] - perturbDist;
            }
        }
    }
    else
    {
        for (direction dir = 0; dir < vector::nComponents; dir++)
        {
            if (mag(pt[dir]-bb.min()[dir]) < mag(perturbVec[dir]))
            {
                scalar perturbDist = perturbVec[dir] + rootVSmall;
                perturbedPt[dir] = bb.min()[dir] - perturbDist;
            }
            else if (mag(pt[dir]-bb.max()[dir]) < mag(perturbVec[dir]))
            {
                scalar perturbDist = perturbVec[dir] + rootVSmall;
                perturbedPt[dir] = bb.max()[dir] + perturbDist;
            }
        }
    }

    if (debug)
    {
        if (pushInside != bb.contains(perturbedPt))
        {
            FatalErrorInFunction
                << "pushed point:" << pt
                << " to:" << perturbedPt
                << " wanted side:" << pushInside
                << " obtained side:" << bb.contains(perturbedPt)
                << " of bb:" << bb
                << abort(FatalError);
        }
    }

    return perturbedPt;
}


template<class Type>
Foam::point Foam::indexedOctree<Type>::pushPoint
(
    const treeBoundBox& bb,
    const direction faceID,
    const point& pt,
    const bool pushInside
)
{
    // Get local length scale.
    const vector perturbVec = perturbTol_*bb.span();

    point perturbedPt(pt);

    // Modify all components which are close to any face of the bb to be
    // well outside them.

    if (faceID == 0)
    {
        FatalErrorInFunction
            << abort(FatalError);
    }

    if (faceID & treeBoundBox::faceBit::left)
    {
        if (pushInside)
        {
            perturbedPt[0] = bb.min()[0] + (perturbVec[0] + rootVSmall);
        }
        else
        {
            perturbedPt[0] = bb.min()[0] - (perturbVec[0] + rootVSmall);
        }
    }
    else if (faceID & treeBoundBox::faceBit::right)
    {
        if (pushInside)
        {
            perturbedPt[0] = bb.max()[0] - (perturbVec[0] + rootVSmall);
        }
        else
        {
            perturbedPt[0] = bb.max()[0] + (perturbVec[0] + rootVSmall);
        }
    }

    if (faceID & treeBoundBox::faceBit::bottom)
    {
        if (pushInside)
        {
            perturbedPt[1] = bb.min()[1] + (perturbVec[1] + rootVSmall);
        }
        else
        {
            perturbedPt[1] = bb.min()[1] - (perturbVec[1] + rootVSmall);
        }
    }
    else if (faceID & treeBoundBox::faceBit::top)
    {
        if (pushInside)
        {
            perturbedPt[1] = bb.max()[1] - (perturbVec[1] + rootVSmall);
        }
        else
        {
            perturbedPt[1] = bb.max()[1] + (perturbVec[1] + rootVSmall);
        }
    }

    if (faceID & treeBoundBox::faceBit::back)
    {
        if (pushInside)
        {
            perturbedPt[2] = bb.min()[2] + (perturbVec[2] + rootVSmall);
        }
        else
        {
            perturbedPt[2] = bb.min()[2] - (perturbVec[2] + rootVSmall);
        }
    }
    else if (faceID & treeBoundBox::faceBit::front)
    {
        if (pushInside)
        {
            perturbedPt[2] = bb.max()[2] - (perturbVec[2] + rootVSmall);
        }
        else
        {
            perturbedPt[2] = bb.max()[2] + (perturbVec[2] + rootVSmall);
        }
    }

    if (debug)
    {
        if (pushInside != bb.contains(perturbedPt))
        {
            FatalErrorInFunction
                << "pushed point:" << pt << " on face:" << faceString(faceID)
                << " to:" << perturbedPt
                << " wanted side:" << pushInside
                << " obtained side:" << bb.contains(perturbedPt)
                << " of bb:" << bb
                << abort(FatalError);
        }
    }

    return perturbedPt;
}


template<class Type>
Foam::point Foam::indexedOctree<Type>::pushPointIntoFace
(
    const treeBoundBox& bb,
    const vector& dir,          // end-start
    const point& pt
)
{
    if (debug)
    {
        if (bb.posBits(pt) != 0)
        {
            FatalErrorInFunction
                << " bb:" << bb << endl
                << "does not contain point " << pt << abort(FatalError);
        }
    }


    // Handle two cases:
    // - point exactly on multiple faces. Push away from all but one.
    // - point on a single face. Push away from edges of face.

    direction ptFaceID = bb.faceBits(pt);

    direction nFaces = 0;
    FixedList<direction, 3> faceIndices;

    if (ptFaceID & treeBoundBox::faceBit::left)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::left;
    }
    else if (ptFaceID & treeBoundBox::faceBit::right)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::right;
    }

    if (ptFaceID & treeBoundBox::faceBit::bottom)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::bottom;
    }
    else if (ptFaceID & treeBoundBox::faceBit::top)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::top;
    }

    if (ptFaceID & treeBoundBox::faceBit::back)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::back;
    }
    else if (ptFaceID & treeBoundBox::faceBit::front)
    {
        faceIndices[nFaces++] = treeBoundBox::faceId::front;
    }


    // Determine the face we want to keep the point on

    direction keepFaceID;

    if (nFaces == 0)
    {
        // Return original point
        return pt;
    }
    else if (nFaces == 1)
    {
        // Point is on a single face
        keepFaceID = faceIndices[0];
    }
    else
    {
        // Determine best face out of faceIndices[0 .. nFaces-1].
        // The best face is the one most perpendicular to the ray direction.

        keepFaceID = faceIndices[0];
        scalar maxInproduct = mag(treeBoundBox::faceNormals[keepFaceID] & dir);

        for (direction i = 1; i < nFaces; i++)
        {
            direction face = faceIndices[i];
            scalar s = mag(treeBoundBox::faceNormals[face] & dir);
            if (s > maxInproduct)
            {
                maxInproduct = s;
                keepFaceID = face;
            }
        }
    }


    // 1. Push point into bb, away from all corners

    point facePoint(pushPoint(bb, pt, true));
    direction faceID = 0;

    // 2. Snap it back onto the preferred face

    if (keepFaceID == treeBoundBox::faceId::left)
    {
        facePoint.x() = bb.min().x();
        faceID = treeBoundBox::faceBit::left;
    }
    else if (keepFaceID == treeBoundBox::faceId::right)
    {
        facePoint.x() = bb.max().x();
        faceID = treeBoundBox::faceBit::right;
    }
    else if (keepFaceID == treeBoundBox::faceId::bottom)
    {
        facePoint.y() = bb.min().y();
        faceID = treeBoundBox::faceBit::bottom;
    }
    else if (keepFaceID == treeBoundBox::faceId::top)
    {
        facePoint.y() = bb.max().y();
        faceID = treeBoundBox::faceBit::top;
    }
    else if (keepFaceID == treeBoundBox::faceId::back)
    {
        facePoint.z() = bb.min().z();
        faceID = treeBoundBox::faceBit::back;
    }
    else if (keepFaceID == treeBoundBox::faceId::front)
    {
        facePoint.z() = bb.max().z();
        faceID = treeBoundBox::faceBit::front;
    }


    if (debug)
    {
        if (faceID != bb.faceBits(facePoint))
        {
            FatalErrorInFunction
                << "Pushed point from " << pt
                << " on face:" << ptFaceID << " of bb:" << bb << endl
                << "onto " << facePoint
                << " on face:" << faceID
                << " which is not consistent with geometric face "
                << bb.faceBits(facePoint)
                << abort(FatalError);
        }
        if (bb.posBits(facePoint) != 0)
        {
            FatalErrorInFunction
                << " bb:" << bb << endl
                << "does not contain perturbed point "
                << facePoint << abort(FatalError);
        }
    }


    return facePoint;
}


template<class Type>
bool Foam::indexedOctree<Type>::walkToParent
(
    const label nodeI,
    const direction octant,

    label& parentNodeI,
    label& parentOctant
) const
{
    parentNodeI = nodes_[nodeI].parent_;

    if (parentNodeI == -1)
    {
        // Reached edge of tree
        return false;
    }

    const node& parentNode = nodes_[parentNodeI];

    // Find octant nodeI is in.
    parentOctant = 255;

    for (direction i = 0; i < parentNode.subNodes_.size(); i++)
    {
        labelBits index = parentNode.subNodes_[i];

        if (isNode(index) && getNode(index) == nodeI)
        {
            parentOctant = i;
            break;
        }
    }

    if (parentOctant == 255)
    {
        FatalErrorInFunction
            << "Problem: no parent found for octant:" << octant
            << " node:" << nodeI
            << abort(FatalError);
    }

    return true;
}


template<class Type>
bool Foam::indexedOctree<Type>::walkToNeighbour
(
    const point& facePoint,
    const direction faceID,  // face(s) that facePoint is on
    label& nodeI,
    direction& octant
) const
{
    // Gets current position as node and octant in this node and walks in the
    // direction given by the facePointBits (combination of
    // treeBoundBox::left, top etc.)  Returns false if edge of tree hit.

    label oldNodeI = nodeI;
    direction oldOctant = octant;

    // Find out how to test for octant. Say if we want to go left we need
    // to traverse up the tree until we hit a node where our octant is
    // on the right.

    // Coordinate direction to test
    const direction X = treeBoundBox::octantBit::rightHalf;
    const direction Y = treeBoundBox::octantBit::topHalf;
    const direction Z = treeBoundBox::octantBit::frontHalf;

    direction octantMask = 0;
    direction wantedValue = 0;

    if ((faceID & treeBoundBox::faceBit::left) != 0)
    {
        // We want to go left so check if in right octant (i.e. x-bit is set)
        octantMask |= X;
        wantedValue |= X;
    }
    else if ((faceID & treeBoundBox::faceBit::right) != 0)
    {
        octantMask |= X;  // wantedValue already 0
    }

    if ((faceID & treeBoundBox::faceBit::bottom) != 0)
    {
        // Want to go down so check for y-bit set.
        octantMask |= Y;
        wantedValue |= Y;
    }
    else if ((faceID & treeBoundBox::faceBit::top) != 0)
    {
        // Want to go up so check for y-bit not set.
        octantMask |= Y;
    }

    if ((faceID & treeBoundBox::faceBit::back) != 0)
    {
        octantMask |= Z;
        wantedValue |= Z;
    }
    else if ((faceID & treeBoundBox::faceBit::front) != 0)
    {
        octantMask |= Z;
    }

    // So now we have the coordinate directions in the octant we need to check
    // and the resulting value.

    /*
    // +---+---+
    // |   |   |
    // |   |   |
    // |   |   |
    // +---+-+-+
    // |   | | |
    // |  a+-+-+
    // |   |\| |
    // +---+-+-+
    //        \
    //
    // e.g. ray is at (a) in octant 0(or 4) with faceIDs : left+top.
    // If we would be in octant 1(or 5) we could go to the correct octant
    // in the same node by just flipping the x and y bits (exoring).
    // But if we are not in octant 1/5 we have to go up until we are.
    // In general for leftbit+topbit:
    // - we have to check for x and y : octantMask  = 011
    // - the checked bits have to be  : wantedValue = ?01
    */

    // Pout<< "For point " << facePoint << endl;

    // Go up until we have chance to cross to the wanted direction
    while (wantedValue != (octant & octantMask))
    {
        // Go up to the parent.

        // Remove the directions that are not on the boundary of the parent.
        // See diagram above
        if (wantedValue & X)    // && octantMask&X
        {
            // Looking for right octant.
            if (octant & X)
            {
                // My octant is one of the left ones so punch out the x check
                octantMask &= ~X;
                wantedValue &= ~X;
            }
        }
        else
        {
            if (!(octant & X))
            {
                // My octant is right but I want to go left.
                octantMask &= ~X;
                wantedValue &= ~X;
            }
        }

        if (wantedValue & Y)
        {
            if (octant & Y)
            {
                octantMask &= ~Y;
                wantedValue &= ~Y;
            }
        }
        else
        {
            if (!(octant & Y))
            {
                octantMask &= ~Y;
                wantedValue &= ~Y;
            }
        }

        if (wantedValue & Z)
        {
            if (octant & Z)
            {
                octantMask &= ~Z;
                wantedValue &= ~Z;
            }
        }
        else
        {
            if (!(octant & Z))
            {
                octantMask &= ~Z;
                wantedValue &= ~Z;
            }
        }


        label parentNodeI;
        label parentOctant;
        walkToParent(nodeI, octant, parentNodeI, parentOctant);

        if (parentNodeI == -1)
        {
            // Reached edge of tree
            return false;
        }

        // Pout<< "    walked from node:" << nodeI << " octant:" << octant
        //    << " bb:" << nodes_[nodeI].bb_.subBbox(octant) << endl
        //    << "    to:" << parentNodeI << " octant:" << parentOctant
        //    << " bb:" << nodes_[parentNodeI].bb_.subBbox(parentOctant)
        //    << endl;
        //
        // Pout<< "    octantMask:" << octantMask
        //    << " wantedValue:" << wantedValue << endl;

        nodeI = parentNodeI;
        octant = parentOctant;
    }

    // So now we hit the correct parent node. Switch to the correct octant.
    // Is done by jumping to the 'other half' so if e.g. in x direction in
    // right half we now jump to the left half.
    octant ^= octantMask;

    // Pout<< "    to node:" << nodeI << " octant:" << octant
    //    << " subBb:" <<subBbox(nodeI, octant) << endl;


    if (debug)
    {
        const treeBoundBox subBb(subBbox(nodeI, octant));

        if (!subBb.contains(facePoint))
        {
            FatalErrorInFunction
                << "When searching for " << facePoint
                << " ended up in node:" << nodeI
                << " octant:" << octant
                << " with bb:" << subBb
                << abort(FatalError);
        }
    }


    // See if we need to travel down. Note that we already go into the
    // the first level ourselves (instead of having findNode decide)
    labelBits index = nodes_[nodeI].subNodes_[octant];

    if (isNode(index))
    {
        labelBits node = findNode(getNode(index), facePoint);

        nodeI = getNode(node);
        octant = getOctant(node);
    }


    if (debug)
    {
        const treeBoundBox subBb(subBbox(nodeI, octant));

        if (nodeI == oldNodeI && octant == oldOctant)
        {
            FatalErrorInFunction
                << "Did not go to neighbour when searching for " << facePoint
                << endl
                << "    starting from face:" << faceString(faceID)
                << " node:" << nodeI
                << " octant:" << octant
                << " bb:" << subBb
                << abort(FatalError);
        }

        if (!subBb.contains(facePoint))
        {
            FatalErrorInFunction
                << "When searching for " << facePoint
                << " ended up in node:" << nodeI
                << " octant:" << octant
                << " bb:" << subBb
                << abort(FatalError);
        }
    }


    return true;
}


template<class Type>
Foam::word Foam::indexedOctree<Type>::faceString
(
    const direction faceID
)
{
    word desc;

    if (faceID == 0)
    {
        desc = "noFace";
    }
    if (faceID & treeBoundBox::faceBit::left)
    {
        if (!desc.empty()) desc += "+";
        desc += "left";
    }
    if (faceID & treeBoundBox::faceBit::right)
    {
        if (!desc.empty()) desc += "+";
        desc += "right";
    }
    if (faceID & treeBoundBox::faceBit::bottom)
    {
        if (!desc.empty()) desc += "+";
        desc += "bottom";
    }
    if (faceID & treeBoundBox::faceBit::top)
    {
        if (!desc.empty()) desc += "+";
        desc += "top";
    }
    if (faceID & treeBoundBox::faceBit::back)
    {
        if (!desc.empty()) desc += "+";
        desc += "back";
    }
    if (faceID & treeBoundBox::faceBit::front)
    {
        if (!desc.empty()) desc += "+";
        desc += "front";
    }
    return desc;
}


template<class Type>
template<class FindIntersectOp>
void Foam::indexedOctree<Type>::traverseNode
(
    const bool findAny,
    const point& treeStart,
    const vector& treeVec,

    const point& start,
    const point& end,
    const label nodeI,
    const direction octant,

    pointIndexHit& hitInfo,
    direction& hitBits,

    const FindIntersectOp& fiOp
) const
{
    // Traverse a node. If intersects a triangle return first intersection
    // point:
    //  hitInfo.index = index of shape
    //  hitInfo.point = point on shape
    // Else return a miss and the bounding box face hit:
    //  hitInfo.point = coordinate of intersection of ray with bounding box
    //  hitBits  = posbits of point on bounding box

    if (debug)
    {
        const treeBoundBox octantBb(subBbox(nodeI, octant));

        if (octantBb.posBits(start) != 0)
        {
            FatalErrorInFunction
                << "Node:" << nodeI << " octant:" << octant
                << " bb:" << octantBb << endl
                << "does not contain point " << start << abort(FatalError);
        }
    }

    const node& nod = nodes_[nodeI];

    labelBits index = nod.subNodes_[octant];

    if (isContent(index))
    {
        const labelList& indices = contents_[getContent(index)];

        if (indices.size())
        {
            if (findAny)
            {
                // Find any intersection

                forAll(indices, elemI)
                {
                    label shapeI = indices[elemI];

                    point pt;
                    bool hit = fiOp(shapeI, start, end, pt);

                    // Note that intersection of shape might actually be
                    // in a neighbouring box. For findAny this is not important.
                    if (hit)
                    {
                        // Hit so pt is nearer than nearestPoint.
                        // Update hit info
                        hitInfo.setHit();
                        hitInfo.setIndex(shapeI);
                        hitInfo.setPoint(pt);
                        return;
                    }
                }
            }
            else
            {
                // Find nearest intersection

                const treeBoundBox octantBb(subBbox(nodeI, octant));

                point nearestPoint(end);

                forAll(indices, elemI)
                {
                    label shapeI = indices[elemI];

                    point pt;
                    bool hit = fiOp(shapeI, start, nearestPoint, pt);

                    // Note that intersection of shape might actually be
                    // in a neighbouring box. Since we need to maintain strict
                    // (findAny=false) ordering skip such an intersection. It
                    // will be found when we are doing the next box.

                    if (hit && octantBb.contains(pt))
                    {
                        // Hit so pt is nearer than nearestPoint.
                        nearestPoint = pt;
                        // Update hit info
                        hitInfo.setHit();
                        hitInfo.setIndex(shapeI);
                        hitInfo.setPoint(pt);
                    }
                }

                if (hitInfo.hit())
                {
                    // Found intersected shape.
                    return;
                }
            }
        }
    }

    // Nothing intersected in this node
    // Traverse to end of node. Do by ray tracing back from end and finding
    // intersection with bounding box of node.
    // start point is now considered to be inside bounding box.

    const treeBoundBox octantBb(subBbox(nodeI, octant));

    point pt;
    bool intersected = octantBb.intersects
    (
        end,            // treeStart,
        (start-end),    // treeVec,

        end,
        start,

        pt,
        hitBits
    );


    if (intersected)
    {
        // Return miss. Set misspoint to face.
        hitInfo.setPoint(pt);
    }
    else
    {
        // Rare case: did not find intersection of ray with octantBb. Can
        // happen if end is on face/edge of octantBb. Do like
        // lagrangian and re-track with perturbed vector (slightly pushed out
        // of bounding box)

        point perturbedEnd(pushPoint(octantBb, end, false));

        traverseNode
        (
            findAny,
            treeStart,
            treeVec,
            start,
            perturbedEnd,
            nodeI,
            octant,

            hitInfo,
            hitBits,

            fiOp
        );
    }
}


template<class Type>
template<class FindIntersectOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLine
(
    const bool findAny,
    const point& treeStart,
    const point& treeEnd,
    const label startNodeI,
    const direction startOctant,
    const FindIntersectOp& fiOp,
    const bool verbose
) const
{
    const vector treeVec(treeEnd - treeStart);

    // Current node as parent+octant
    label nodeI = startNodeI;
    direction octant = startOctant;

    if (verbose)
    {
        Pout<< "findLine : treeStart:" << treeStart
            << " treeEnd:" << treeEnd << endl
            << "node:" << nodeI
            << " octant:" << octant
            << " bb:" << subBbox(nodeI, octant) << endl;
    }

    // Current position. Initialise to miss
    pointIndexHit hitInfo(false, treeStart, -1);

    // while (true)
    label i = 0;
    for (; i < 100000; i++)
    {
        // Ray-trace to end of current node. Updates point (either on triangle
        // in case of hit or on node bounding box in case of miss)

        const treeBoundBox octantBb(subBbox(nodeI, octant));

        // Make sure point is away from any edges/corners
        point startPoint
        (
            pushPointIntoFace
            (
                octantBb,
                treeVec,
                hitInfo.rawPoint()
            )
        );

        if (verbose)
        {
            Pout<< "iter:" << i
                << " at current:" << hitInfo.rawPoint()
                << " (perturbed:" << startPoint << ")" << endl
                << "    node:" << nodeI
                << " octant:" << octant
                << " bb:" << subBbox(nodeI, octant) << endl;
        }




        // Faces of current bounding box current point is on
        direction hitFaceID = 0;

        traverseNode
        (
            findAny,
            treeStart,
            treeVec,

            startPoint,     // Note: pass in copy since hitInfo
                            // also used in return value.
            treeEnd,        // pass in overall end so is nicely outside bb
            nodeI,
            octant,

            hitInfo,
            hitFaceID,

            fiOp
        );

        // Did we hit a triangle?
        if (hitInfo.hit())
        {
            break;
        }

        if (hitFaceID == 0 || hitInfo.rawPoint() == treeEnd)
        {
            // endpoint inside the tree. Return miss.
            break;
        }

        // Create a point on other side of face.
        point perturbedPoint
        (
            pushPoint
            (
                octantBb,
                hitFaceID,
                hitInfo.rawPoint(),
                false                   // push outside of octantBb
            )
        );

        if (verbose)
        {
            Pout<< "    iter:" << i
                << " hit face:" << faceString(hitFaceID)
                << " at:" << hitInfo.rawPoint() << nl
                << "    node:" << nodeI
                << " octant:" << octant
                << " bb:" << subBbox(nodeI, octant) << nl
                << "    walking to neighbour containing:" << perturbedPoint
                << endl;
        }


        // Nothing hit so we are on face of bounding box (given as node+octant+
        // position bits). Traverse to neighbouring node. Use slightly perturbed
        // point.

        bool ok = walkToNeighbour
        (
            perturbedPoint,
            hitFaceID,  // face(s) that hitInfo is on

            nodeI,
            octant
        );

        if (!ok)
        {
            // Hit the edge of the tree. Return miss.
            break;
        }

        if (verbose)
        {
            const treeBoundBox octantBb(subBbox(nodeI, octant));
            Pout<< "    walked for point:" << hitInfo.rawPoint() << endl
                << "    to neighbour node:" << nodeI
                << " octant:" << octant
                << " face:" << faceString(octantBb.faceBits(hitInfo.rawPoint()))
                << " of octantBb:" << octantBb << endl
                << endl;
        }
    }

    if (i == 100000)
    {
        // Probably in loop.
        if (!verbose)
        {
            // Redo intersection but now with verbose flag switched on.
            return findLine
            (
                findAny,
                treeStart,
                treeEnd,
                startNodeI,
                startOctant,
                fiOp,
                true            // verbose,
            );
        }
        if (debug)
        {
            FatalErrorInFunction
                << "Got stuck in loop raytracing from:" << treeStart
                << " to:" << treeEnd << endl
                << "inside top box:" << subBbox(startNodeI, startOctant)
                << abort(FatalError);
        }
        else
        {
            WarningInFunction
                << "Got stuck in loop raytracing from:" << treeStart
                << " to:" << treeEnd << endl
                << "inside top box:" << subBbox(startNodeI, startOctant)
                << endl;
        }
    }

    return hitInfo;
}


template<class Type>
template<class FindIntersectOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLine
(
    const bool findAny,
    const point& start,
    const point& end,
    const FindIntersectOp& fiOp
) const
{
    pointIndexHit hitInfo;

    if (nodes_.size())
    {
        const treeBoundBox& treeBb = nodes_[0].bb_;

        // No effort is made to deal with points which are on edge of tree
        // bounding box for now.

        direction startBit = treeBb.posBits(start);
        direction endBit = treeBb.posBits(end);

        if ((startBit & endBit) != 0)
        {
            // Both start and end outside domain and in same block.
            return pointIndexHit(false, Zero, -1);
        }


        // Trim segment to treeBb

        point trackStart(start);
        point trackEnd(end);

        if (startBit != 0)
        {
            // Track start to inside domain.
            if (!treeBb.intersects(start, end, trackStart))
            {
                return pointIndexHit(false, Zero, -1);
            }
        }

        if (endBit != 0)
        {
            // Track end to inside domain.
            if (!treeBb.intersects(end, trackStart, trackEnd))
            {
                return pointIndexHit(false, Zero, -1);
            }
        }


        // Find lowest level tree node that start is in.
        labelBits index = findNode(0, trackStart);

        label parentNodeI = getNode(index);
        direction octant = getOctant(index);

        hitInfo = findLine
        (
            findAny,
            trackStart,
            trackEnd,
            parentNodeI,
            octant,
            fiOp
        );
    }

    return hitInfo;
}


template<class Type>
void Foam::indexedOctree<Type>::findBox
(
    const label nodeI,
    const treeBoundBox& searchBox,
    labelHashSet& elements
) const
{
    const node& nod = nodes_[nodeI];
    const treeBoundBox& nodeBb = nod.bb_;

    for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
    {
        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            const treeBoundBox& subBb = nodes_[getNode(index)].bb_;

            if (subBb.overlaps(searchBox))
            {
                findBox(getNode(index), searchBox, elements);
            }
        }
        else if (isContent(index))
        {
            const treeBoundBox subBb(nodeBb.subBbox(octant));

            if (subBb.overlaps(searchBox))
            {
                const labelList& indices = contents_[getContent(index)];

                forAll(indices, i)
                {
                    label shapeI = indices[i];

                    if (shapes_.overlaps(shapeI, searchBox))
                    {
                        elements.insert(shapeI);
                    }
                }
            }
        }
    }
}


template<class Type>
void Foam::indexedOctree<Type>::findSphere
(
    const label nodeI,
    const point& centre,
    const scalar radiusSqr,
    labelHashSet& elements
) const
{
    const node& nod = nodes_[nodeI];
    const treeBoundBox& nodeBb = nod.bb_;

    for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
    {
        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            const treeBoundBox& subBb = nodes_[getNode(index)].bb_;

            if (subBb.overlaps(centre, radiusSqr))
            {
                findSphere(getNode(index), centre, radiusSqr, elements);
            }
        }
        else if (isContent(index))
        {
            const treeBoundBox subBb(nodeBb.subBbox(octant));

            if (subBb.overlaps(centre, radiusSqr))
            {
                const labelList& indices = contents_[getContent(index)];

                forAll(indices, i)
                {
                    label shapeI = indices[i];

                    if (shapes_.overlaps(shapeI, centre, radiusSqr))
                    {
                        elements.insert(shapeI);
                    }
                }
            }
        }
    }
}


template<class Type>
template<class CompareOp>
void Foam::indexedOctree<Type>::findNear
(
    const scalar nearDist,
    const bool okOrder,
    const indexedOctree<Type>& tree1,
    const labelBits index1,
    const treeBoundBox& bb1,
    const indexedOctree<Type>& tree2,
    const labelBits index2,
    const treeBoundBox& bb2,
    CompareOp& cop
)
{
    const vector nearSpan(nearDist, nearDist, nearDist);

    if (tree1.isNode(index1))
    {
        const node& nod1 = tree1.nodes()[tree1.getNode(index1)];
        const treeBoundBox searchBox
        (
            bb1.min()-nearSpan,
            bb1.max()+nearSpan
        );

        if (tree2.isNode(index2))
        {
            if (bb2.overlaps(searchBox))
            {
                const node& nod2 = tree2.nodes()[tree2.getNode(index2)];

                for (direction i2 = 0; i2 < nod2.subNodes_.size(); i2++)
                {
                    labelBits subIndex2 = nod2.subNodes_[i2];
                    const treeBoundBox subBb2
                    (
                        tree2.isNode(subIndex2)
                      ? tree2.nodes()[tree2.getNode(subIndex2)].bb_
                      : bb2.subBbox(i2)
                    );

                    findNear
                    (
                        nearDist,
                        !okOrder,
                        tree2,
                        subIndex2,
                        subBb2,
                        tree1,
                        index1,
                        bb1,
                        cop
                    );
                }
            }
        }
        else if (tree2.isContent(index2))
        {
            // index2 is leaf, index1 not yet.
            for (direction i1 = 0; i1 < nod1.subNodes_.size(); i1++)
            {
                labelBits subIndex1 = nod1.subNodes_[i1];
                const treeBoundBox subBb1
                (
                    tree1.isNode(subIndex1)
                  ? tree1.nodes()[tree1.getNode(subIndex1)].bb_
                  : bb1.subBbox(i1)
                );

                findNear
                (
                    nearDist,
                    !okOrder,
                    tree2,
                    index2,
                    bb2,
                    tree1,
                    subIndex1,
                    subBb1,
                    cop
                );
            }
        }
    }
    else if (tree1.isContent(index1))
    {
        const treeBoundBox searchBox
        (
            bb1.min()-nearSpan,
            bb1.max()+nearSpan
        );

        if (tree2.isNode(index2))
        {
            const node& nod2 =
                tree2.nodes()[tree2.getNode(index2)];

            if (bb2.overlaps(searchBox))
            {
                for (direction i2 = 0; i2 < nod2.subNodes_.size(); i2++)
                {
                    labelBits subIndex2 = nod2.subNodes_[i2];
                    const treeBoundBox subBb2
                    (
                        tree2.isNode(subIndex2)
                      ? tree2.nodes()[tree2.getNode(subIndex2)].bb_
                      : bb2.subBbox(i2)
                    );

                    findNear
                    (
                        nearDist,
                        !okOrder,
                        tree2,
                        subIndex2,
                        subBb2,
                        tree1,
                        index1,
                        bb1,
                        cop
                    );
                }
            }
        }
        else if (tree2.isContent(index2))
        {
            // Both are leaves. Check n^2.

            const labelList& indices1 =
                tree1.contents()[tree1.getContent(index1)];
            const labelList& indices2 =
                tree2.contents()[tree2.getContent(index2)];

            forAll(indices1, i)
            {
                label shape1 = indices1[i];

                forAll(indices2, j)
                {
                    label shape2 = indices2[j];

                    if ((&tree1 != &tree2) || (shape1 != shape2))
                    {
                        if (okOrder)
                        {
                            cop
                            (
                                nearDist,
                                tree1.shapes(),
                                shape1,
                                tree2.shapes(),
                                shape2
                            );
                        }
                        else
                        {
                            cop
                            (
                                nearDist,
                                tree2.shapes(),
                                shape2,
                                tree1.shapes(),
                                shape1
                            );
                        }
                    }
                }
            }
        }
    }
}


template<class Type>
Foam::label Foam::indexedOctree<Type>::countElements
(
    const labelBits index
) const
{
    label nElems = 0;

    if (isNode(index))
    {
        // tree node.
        label nodeI = getNode(index);

        const node& nod = nodes_[nodeI];

        for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
        {
            nElems += countElements(nod.subNodes_[octant]);
        }
    }
    else if (isContent(index))
    {
        nElems += contents_[getContent(index)].size();
    }
    else
    {
        // empty node
    }

    return nElems;
}


template<class Type>
void Foam::indexedOctree<Type>::writeOBJ
(
    const label nodeI,
    const direction octant
) const
{
    OFstream str
    (
        "node" + Foam::name(nodeI) + "_octant" + Foam::name(octant) + ".obj"
    );

    labelBits index = nodes_[nodeI].subNodes_[octant];

    treeBoundBox subBb;

    if (isNode(index))
    {
        subBb = nodes_[getNode(index)].bb_;
    }
    else if (isContent(index) || isEmpty(index))
    {
        subBb = nodes_[nodeI].bb_.subBbox(octant);
    }

    Pout<< "dumpContentNode : writing node:" << nodeI << " octant:" << octant
        << " to " << str.name() << endl;

    // Dump bounding box
    pointField bbPoints(subBb.points());

    forAll(bbPoints, i)
    {
        const point& pt = bbPoints[i];

        str<< "v " << pt.x() << ' ' << pt.y() << ' ' << pt.z() << endl;
    }

    forAll(treeBoundBox::edges, i)
    {
        const edge& e = treeBoundBox::edges[i];

        str<< "l " << e[0] + 1 << ' ' << e[1] + 1 << nl;
    }
}


// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

template<class Type>
Foam::indexedOctree<Type>::indexedOctree(const Type& shapes)
:
    shapes_(shapes),
    nodes_(0),
    contents_(0),
    nodeTypes_(0)
{}


template<class Type>
Foam::indexedOctree<Type>::indexedOctree
(
    const Type& shapes,
    const List<node>& nodes,
    const labelListList& contents
)
:
    shapes_(shapes),
    nodes_(nodes),
    contents_(contents),
    nodeTypes_(0)
{}


template<class Type>
Foam::indexedOctree<Type>::indexedOctree
(
    const Type& shapes,
    const treeBoundBox& bb,
    const label maxLevels,          // maximum number of levels
    const scalar maxLeafRatio,
    const scalar maxDuplicity
)
:
    shapes_(shapes),
    nodes_(0),
    contents_(0),
    nodeTypes_(0)
{
    int oldMemSize = 0;
    if (debug)
    {
        Pout<< "indexedOctree<Type>::indexedOctree:" << nl
            << "    shapes:" << shapes.size() << nl
            << "    bb:" << bb << nl
            << endl;
        oldMemSize = memInfo().size();
    }

    if (shapes.size() == 0)
    {
        return;
    }

    // Start off with one node with all shapes in it.
    DynamicList<node> nodes(label(shapes.size() / maxLeafRatio));
    DynamicList<labelList> contents(label(shapes.size() / maxLeafRatio));
    contents.append(identityMap(shapes.size()));

    // Create topnode.
    node topNode(divide(bb, contents, 0));
    nodes.append(topNode);


    // Now have all contents at level 1. Create levels by splitting levels
    // above.

    label nLevels = 1;

    for (; nLevels < maxLevels; nLevels++)
    {
        // Count number of references into shapes (i.e. contents)
        label nEntries = 0;
        forAll(contents, i)
        {
            nEntries += contents[i].size();
        }

        if (debug)
        {
            Pout<< "indexedOctree<Type>::indexedOctree:" << nl
                << "    nLevels:" << nLevels << nl
                << "    nEntries per treeLeaf:" << nEntries/contents.size()
                << nl
                << "    nEntries per shape (duplicity):"
                << nEntries/shapes.size()
                << nl
                << endl;
        }

        if
        (
            // nEntries < maxLeafRatio*contents.size()
         // ||
            nEntries > maxDuplicity*shapes.size()
        )
        {
            break;
        }


        // Split nodes with more than maxLeafRatio elements
        label nOldNodes = nodes.size();
        splitNodes
        (
            label(maxLeafRatio),
            nodes,
            contents
        );

        if (nOldNodes == nodes.size())
        {
            break;
        }
    }

    // Shrink
    nodes.shrink();
    contents.shrink();


    // Compact such that deeper level contents are always after the
    // ones for a shallower level. This way we can slice a coarser level
    // off the tree.
    contents_.setSize(contents.size());
    label compactI = 0;

    label level = 0;

    while (true)
    {
        label nNodes = compactContents
        (
            nodes,
            contents,
            level,
            0,
            0,
            contents_,
            compactI
        );

        if (compactI == 0 && nNodes == 0)
        {
            // Did not put contents anywhere - are outside bb!
            break;
        }

        if (compactI == contents_.size())
        {
            // Transferred all contents to contents_ (in order breadth first)
            break;
        }

        level++;
    }
    nodes_.transfer(nodes);
    nodes.clear();

    if (debug)
    {
        label nEntries = 0;
        forAll(contents_, i)
        {
            nEntries += contents_[i].size();
        }

        label memSize = memInfo().size();


        Pout<< "indexedOctree<Type>::indexedOctree"
            << " : finished construction of tree of:" << shapes.typeName
            << nl
            << "    bb:" << this->bb() << nl
            << "    shapes:" << shapes.size() << nl
            << "    nLevels:" << nLevels << nl
            << "    treeNodes:" << nodes_.size() << nl
            << "    nEntries:" << nEntries << nl
            << "        per treeLeaf:"
            << scalar(nEntries)/contents.size() << nl
            << "        per shape (duplicity):"
            << scalar(nEntries)/shapes.size() << nl
            << "    total memory:" << memSize-oldMemSize
            << endl;
    }
}


template<class Type>
Foam::indexedOctree<Type>::indexedOctree
(
    const Type& shapes,
    Istream& is
)
:
    shapes_(shapes),
    nodes_(is),
    contents_(is),
    nodeTypes_(0)
{}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

template<class Type>
Foam::scalar& Foam::indexedOctree<Type>::perturbTol()
{
    return perturbTol_;
}


template<class Type>
Foam::pointIndexHit Foam::indexedOctree<Type>::findNearest
(
    const point& sample,
    const scalar startDistSqr
) const
{
    return findNearest
    (
        sample,
        startDistSqr,
        typename Type::findNearestOp(*this)
    );
}


template<class Type>
template<class FindNearestOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findNearest
(
    const point& sample,
    const scalar startDistSqr,

    const FindNearestOp& fnOp
) const
{
    scalar nearestDistSqr = startDistSqr;
    label nearestShapeI = -1;
    point nearestPoint = Zero;

    if (nodes_.size())
    {
        findNearest
        (
            0,
            sample,

            nearestDistSqr,
            nearestShapeI,
            nearestPoint,

            fnOp
        );
    }

    return pointIndexHit(nearestShapeI != -1, nearestPoint, nearestShapeI);
}


template<class Type>
Foam::pointIndexHit Foam::indexedOctree<Type>::findNearest
(
    const linePointRef& ln,
    treeBoundBox& tightest,
    point& linePoint
) const
{
    return findNearest
    (
        ln,
        tightest,
        linePoint,
        typename Type::findNearestOp(*this)
    );
}


template<class Type>
template<class FindNearestOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findNearest
(
    const linePointRef& ln,
    treeBoundBox& tightest,
    point& linePoint,

    const FindNearestOp& fnOp
) const
{
    label nearestShapeI = -1;
    point nearestPoint = Zero;

    if (nodes_.size())
    {
        findNearest
        (
            0,
            ln,

            tightest,
            nearestShapeI,
            linePoint,
            nearestPoint,

            fnOp
        );
    }

    return pointIndexHit(nearestShapeI != -1, nearestPoint, nearestShapeI);
}


template<class Type>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLine
(
    const point& start,
    const point& end
) const
{
    return findLine
    (
        false,
        start,
        end,
        typename Type::findIntersectOp(*this)
    );
}


template<class Type>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLineAny
(
    const point& start,
    const point& end
) const
{
    return findLine
    (
        true,
        start,
        end,
        typename Type::findIntersectOp(*this)
    );
}


template<class Type>
template<class FindIntersectOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLine
(
    const point& start,
    const point& end,
    const FindIntersectOp& fiOp
) const
{
    return findLine(false, start, end, fiOp);
}


template<class Type>
template<class FindIntersectOp>
Foam::pointIndexHit Foam::indexedOctree<Type>::findLineAny
(
    const point& start,
    const point& end,
    const FindIntersectOp& fiOp
) const
{
    return findLine(true, start, end, fiOp);
}


template<class Type>
Foam::labelList Foam::indexedOctree<Type>::findBox
(
    const treeBoundBox& searchBox
) const
{
    // Storage for labels of shapes inside bb. Size estimate.
    labelHashSet elements(shapes_.size() / 100);

    if (nodes_.size())
    {
        findBox(0, searchBox, elements);
    }

    return elements.toc();
}


template<class Type>
Foam::labelList Foam::indexedOctree<Type>::findSphere
(
    const point& centre,
    const scalar radiusSqr
) const
{
    // Storage for labels of shapes inside bb. Size estimate.
    labelHashSet elements(shapes_.size() / 100);

    if (nodes_.size())
    {
        findSphere(0, centre, radiusSqr, elements);
    }

    return elements.toc();
}


template<class Type>
Foam::labelBits Foam::indexedOctree<Type>::findNode
(
    const label nodeI,
    const point& sample
) const
{
    if (nodes_.empty())
    {
        // Empty tree. Return what?
        return nodePlusOctant(nodeI, 0);
    }

    const node& nod = nodes_[nodeI];

    if (debug)
    {
        if (!nod.bb_.contains(sample))
        {
            FatalErrorInFunction
                << "Cannot find " << sample << " in node " << nodeI
                << abort(FatalError);
        }
    }

    direction octant = nod.bb_.subOctant(sample);

    labelBits index = nod.subNodes_[octant];

    if (isNode(index))
    {
        // Recurse
        return findNode(getNode(index), sample);
    }
    else if (isContent(index))
    {
        // Content. Return treenode+octant
        return nodePlusOctant(nodeI, octant);
    }
    else
    {
        // Empty. Return treenode+octant
        return nodePlusOctant(nodeI, octant);
    }
}


template<class Type>
template<class ... Args>
Foam::label Foam::indexedOctree<Type>::findInside
(
    const point& sample,
    const Args& ... args
) const
{
    if (nodes_.empty())
    {
        return -1;
    }

    labelBits index = findNode(0, sample);

    const node& nod = nodes_[getNode(index)];

    labelBits contentIndex = nod.subNodes_[getOctant(index)];

    // Need to check for the presence of content, in-case the node is empty
    if (isContent(contentIndex))
    {
        labelList indices = contents_[getContent(contentIndex)];

        forAll(indices, elemI)
        {
            label shapeI = indices[elemI];

            if (shapes_.contains(shapeI, sample, args ...))
            {
                return shapeI;
            }
        }
    }

    return -1;
}


template<class Type>
const Foam::labelList& Foam::indexedOctree<Type>::findIndices
(
    const point& sample
) const
{
    if (nodes_.empty())
    {
        return emptyList<label>();
    }

    labelBits index = findNode(0, sample);

    const node& nod = nodes_[getNode(index)];

    labelBits contentIndex = nod.subNodes_[getOctant(index)];

    // Need to check for the presence of content, in-case the node is empty
    if (isContent(contentIndex))
    {
        return contents_[getContent(contentIndex)];
    }
    else
    {
        return emptyList<label>();
    }
}


template<class Type>
Foam::volumeType Foam::indexedOctree<Type>::getVolumeType
(
    const point& sample
) const
{
    if (nodes_.empty())
    {
        return volumeType::unknown;
    }

    if (nodeTypes_.size() != 8*nodes_.size())
    {
        // Calculate type for every octant of node.

        nodeTypes_.setSize(8*nodes_.size());
        nodeTypes_ = volumeType::unknown;

        calcVolumeType(0);

        if (debug)
        {
            label nUnknown = 0;
            label nMixed = 0;
            label nInside = 0;
            label nOutside = 0;

            forAll(nodeTypes_, i)
            {
                volumeType type = volumeType::type(nodeTypes_.get(i));

                if (type == volumeType::unknown)
                {
                    nUnknown++;
                }
                else if (type == volumeType::mixed)
                {
                    nMixed++;
                }
                else if (type == volumeType::inside)
                {
                    nInside++;
                }
                else if (type == volumeType::outside)
                {
                    nOutside++;
                }
                else
                {
                    FatalErrorInFunction << abort(FatalError);
                }
            }

            Pout<< "indexedOctree<Type>::getVolumeType : "
                << " bb:" << bb()
                << " nodes_:" << nodes_.size()
                << " nodeTypes_:" << nodeTypes_.size()
                << " nUnknown:" << nUnknown
                << " nMixed:" << nMixed
                << " nInside:" << nInside
                << " nOutside:" << nOutside
                << endl;
        }
    }

    return getVolumeType(0, sample);
}


template<class Type>
template<class CompareOp>
void Foam::indexedOctree<Type>::findNear
(
    const scalar nearDist,
    const indexedOctree<Type>& tree2,
    CompareOp& cop
) const
{
    findNear
    (
        nearDist,
        true,
        *this,
        nodePlusOctant(0, 0),
        bb(),
        tree2,
        nodePlusOctant(0, 0),
        tree2.bb(),
        cop
    );
}


template<class Type>
void Foam::indexedOctree<Type>::print
(
    prefixOSstream& os,
    const bool printContents,
    const label nodeI
) const
{
    const node& nod = nodes_[nodeI];
    const treeBoundBox& bb = nod.bb_;

    os  << "nodeI:" << nodeI << " bb:" << bb << nl
        << "parent:" << nod.parent_ << nl
        << "n:" << countElements(nodePlusOctant(nodeI, 0)) << nl;

    for (direction octant = 0; octant < nod.subNodes_.size(); octant++)
    {
        const treeBoundBox subBb(bb.subBbox(octant));

        labelBits index = nod.subNodes_[octant];

        if (isNode(index))
        {
            // tree node.
            label subNodeI = getNode(index);

            os  << "octant:" << octant
                << " node: n:" << countElements(index)
                << " bb:" << subBb << endl;

            string oldPrefix = os.prefix();
            os.prefix() = "  " + oldPrefix;

            print(os, printContents, subNodeI);

            os.prefix() = oldPrefix;
        }
        else if (isContent(index))
        {
            const labelList& indices = contents_[getContent(index)];

            if (debug)
            {
                writeOBJ(nodeI, octant);
            }

            os  << "octant:" << octant
                << " content: n:" << indices.size()
                << " bb:" << subBb;

            if (printContents)
            {
                os << " contents:";
                forAll(indices, j)
                {
                    os  << ' ' << indices[j];
                }
            }
            os  << endl;
        }
        else
        {
            if (debug)
            {
                writeOBJ(nodeI, octant);
            }

            os  << "octant:" << octant << " empty:" << subBb << endl;
        }
    }
}


template<class Type>
bool Foam::indexedOctree<Type>::write(Ostream& os) const
{
    os << *this;

    return os.good();
}


template<class Type>
Foam::Ostream& Foam::operator<<(Ostream& os, const indexedOctree<Type>& t)
{
    return
        os  << t.bb() << token::SPACE << t.nodes()
            << token::SPACE << t.contents();
}


// ************************************************************************* //