AdaptiveKDTree.cpp

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/**\file AdaptiveKDTree.cpp
 */

#include "moab/AdaptiveKDTree.hpp"
#include "moab/Interface.hpp"
#include "moab/GeomUtil.hpp"
#include "moab/Range.hpp"
#include "moab/ElemEvaluator.hpp"
#include "moab/CpuTimer.hpp"
#include "Internals.hpp"
#include "moab/Util.hpp"
#include 

#include 
#include 
#include 
#include 
#include 

namespace moab
{

const char* AdaptiveKDTree::treeName = "AKDTree";

#define MB_AD_KD_TREE_DEFAULT_TAG_NAME

// If defined, use single tag for both axis and location of split plane
#define MB_AD_KD_TREE_USE_SINGLE_TAG

// No effect if MB_AD_KD_TREE_USE_SINGLE_TAG is not defined.
// If defined, store plane axis as double so tag has consistent
// type (doubles for both location and axis).  If not defined,
// store struct Plane as opaque.
#define MB_AD_KD_TREE_USE_TWO_DOUBLE_TAG

AdaptiveKDTree::AdaptiveKDTree( Interface* iface )
    : Tree( iface ), planeTag( 0 ), axisTag( 0 ), splitsPerDir( 3 ), planeSet( SUBDIVISION_SNAP ), spherical( false ),
      radius( 1.0 )
{
    boxTagName = treeName;

    ErrorCode rval = init();
    if( MB_SUCCESS != rval ) throw rval;
}

AdaptiveKDTree::AdaptiveKDTree( Interface* iface,
                                const Range& entities,
                                EntityHandle* tree_root_set,
                                FileOptions* opts )
    : Tree( iface ), planeTag( 0 ), axisTag( 0 ), splitsPerDir( 3 ), planeSet( SUBDIVISION_SNAP ), spherical( false ),
      radius( 1.0 )
{
    boxTagName = treeName;

    ErrorCode rval;
    if( opts )
    {
        rval = parse_options( *opts );
        if( MB_SUCCESS != rval ) throw rval;
    }

    rval = init();
    if( MB_SUCCESS != rval ) throw rval;

    rval = build_tree( entities, tree_root_set, opts );
    if( MB_SUCCESS != rval ) throw rval;
}

AdaptiveKDTree::~AdaptiveKDTree()
{
    if( !cleanUp ) return;

    if( myRoot )
    {
        reset_tree();
        myRoot = 0;
    }
}

ErrorCode AdaptiveKDTree::build_tree( const Range& entities, EntityHandle* tree_root_set, FileOptions* options )
{
    ErrorCode rval;
    CpuTimer cp;

    if( options )
    {
        rval = parse_options( *options );
        if( MB_SUCCESS != rval ) return rval;

        if( !options->all_seen() ) return MB_FAILURE;
    }

    // calculate bounding box of elements
    BoundBox box;
    rval = box.update( *moab(), entities, spherical, radius );
    if( MB_SUCCESS != rval ) return rval;

    // create tree root
    EntityHandle tmp_root;
    if( !tree_root_set ) tree_root_set = &tmp_root;
    rval = create_root( box.bMin.array(), box.bMax.array(), *tree_root_set );
    if( MB_SUCCESS != rval ) return rval;
    rval = moab()->add_entities( *tree_root_set, entities );
    if( MB_SUCCESS != rval ) return rval;

    AdaptiveKDTreeIter iter;
    iter.initialize( this, *tree_root_set, box.bMin.array(), box.bMax.array(), AdaptiveKDTreeIter::LEFT );

    std::vector< double > tmp_data;
    std::vector< EntityHandle > tmp_data2;
    for( ;; )
    {

        int pcount;
        rval = moab()->get_number_entities_by_handle( iter.handle(), pcount );
        if( MB_SUCCESS != rval ) break;

        const size_t p_count = pcount;
        Range best_left, best_right, best_both;
        Plane best_plane = { HUGE_VAL, -1 };
        if( (int)p_count > maxPerLeaf && (int)iter.depth() < maxDepth )
        {
            switch( planeSet )
            {
                case AdaptiveKDTree::SUBDIVISION:
                    rval = best_subdivision_plane( splitsPerDir, iter, best_left, best_right, best_both, best_plane,
                                                   minWidth );
                    break;
                case AdaptiveKDTree::SUBDIVISION_SNAP:
                    rval = best_subdivision_snap_plane( splitsPerDir, iter, best_left, best_right, best_both,
                                                        best_plane, tmp_data, minWidth );
                    break;
                case AdaptiveKDTree::VERTEX_MEDIAN:
                    rval = best_vertex_median_plane( splitsPerDir, iter, best_left, best_right, best_both, best_plane,
                                                     tmp_data, minWidth );
                    break;
                case AdaptiveKDTree::VERTEX_SAMPLE:
                    rval = best_vertex_sample_plane( splitsPerDir, iter, best_left, best_right, best_both, best_plane,
                                                     tmp_data, tmp_data2, minWidth );
                    break;
                default:
                    rval = MB_FAILURE;
            }

            if( MB_SUCCESS != rval ) return rval;
        }

        if( best_plane.norm >= 0 )
        {
            best_left.merge( best_both );
            best_right.merge( best_both );
            rval = split_leaf( iter, best_plane, best_left, best_right );
            if( MB_SUCCESS != rval ) return rval;
        }
        else
        {
            rval = iter.step();
            if( MB_ENTITY_NOT_FOUND == rval )
            {
                rval               = treeStats.compute_stats( mbImpl, myRoot );
                treeStats.initTime = cp.time_elapsed();
                return rval;  // at end
            }
            else if( MB_SUCCESS != rval )
                break;
        }
    }

    reset_tree();

    treeStats.reset();

    return rval;
}

ErrorCode AdaptiveKDTree::parse_options( FileOptions& opts )
{
    ErrorCode rval = parse_common_options( opts );
    if( MB_SUCCESS != rval ) return rval;

    //  SPLITS_PER_DIR: number of candidate splits considered per direction; default = 3
    int tmp_int;
    rval = opts.get_int_option( "SPLITS_PER_DIR", tmp_int );
    if( MB_SUCCESS == rval ) splitsPerDir = tmp_int;

    //  PLANE_SET: method used to decide split planes; see CandidatePlaneSet enum (below)
    //           for possible values; default = 1 (SUBDIVISION_SNAP)
    rval = opts.get_int_option( "PLANE_SET", tmp_int );
    if( MB_SUCCESS == rval && ( tmp_int < SUBDIVISION || tmp_int > VERTEX_SAMPLE ) )
        return MB_FAILURE;
    else if( MB_ENTITY_NOT_FOUND == rval )
        planeSet = SUBDIVISION;
    else
        planeSet = (CandidatePlaneSet)( tmp_int );

    rval = opts.get_toggle_option( "SPHERICAL", false, spherical );
    if( MB_SUCCESS != rval ) spherical = false;

    double tmp = 1.0;
    rval       = opts.get_real_option( "RADIUS", tmp );
    if( MB_SUCCESS != rval )
        radius = 1.0;
    else
        radius = tmp;

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::make_tag( Interface* iface,
                                    std::string name,
                                    TagType storage,
                                    DataType type,
                                    int count,
                                    void* default_val,
                                    Tag& tag_handle,
                                    std::vector< Tag >& created_tags )
{
    ErrorCode rval =
        iface->tag_get_handle( name.c_str(), count, type, tag_handle, MB_TAG_CREAT | storage, default_val );

    if( MB_SUCCESS == rval )
    {
        if( std::find( created_tags.begin(), created_tags.end(), tag_handle ) == created_tags.end() )
            created_tags.push_back( tag_handle );
    }
    else
    {
        while( !created_tags.empty() )
        {
            iface->tag_delete( created_tags.back() );
            created_tags.pop_back();
        }

        planeTag = axisTag = (Tag)-1;
    }

    return rval;
}

ErrorCode AdaptiveKDTree::init()
{
    std::vector< Tag > ctl;

#ifndef MB_AD_KD_TREE_USE_SINGLE_TAG
    // create two tags, one for axis direction and one for axis coordinate
    std::string n1( treeName ), n2( treeName );
    n1 += "_coord";
    n2 += "_norm";
    ErrorCode rval = make_tag( moab(), n1, MB_TAG_DENSE, MB_TYPE_DOUBLE, 1, 0, planeTag, ctl );
    if( MB_SUCCESS != rval ) return rval;
    rval = make_tag( moab(), n2, MB_TAG_DENSE, MB_TYPE_INT, 1, 0, axisTag, ctl );
    if( MB_SUCCESS != rval ) return rval;

#elif defined( MB_AD_KD_TREE_USE_TWO_DOUBLE_TAG )
    // create tag to hold two doubles, one for location and one for axis
    std::string double_tag_name = std::string( treeName ) + std::string( "_coord_norm" );
    ErrorCode rval = make_tag( moab(), double_tag_name, MB_TAG_DENSE, MB_TYPE_DOUBLE, 2, 0, planeTag, ctl );
    if( MB_SUCCESS != rval ) return rval;
#else
    // create opaque tag to hold struct Plane
    ErrorCode rval = make_tag( moab(), tagname, MB_TAG_DENSE, MB_TYPE_OPAQUE, sizeof( Plane ), 0, planeTag, ctl );
    if( MB_SUCCESS != rval ) return rval;

#ifdef MOAB_HAVE_HDF5
    // create a mesh tag holding the HDF5 type for a struct Plane
    Tag type_tag;
    std::string type_tag_name = "__hdf5_tag_type_";
    type_tag_name += boxTagName;
    rval = make_tag( moab(), type_tag_name, MB_TAG_MESH, MB_TYPE_OPAQUE, sizeof( hid_t ), 0, type_tag, ctl );
    if( MB_SUCCESS != rval ) return rval;
    // create HDF5 type object describing struct Plane
    Plane p;
    hid_t handle = H5Tcreate( H5T_COMPOUND, sizeof( Plane ) );
    H5Tinsert( handle, "coord", &( p.coord ) - &p, H5T_NATIVE_DOUBLE );
    H5Tinsert( handle, "norm", &( p.axis ) - &p, H5T_NATIVE_INT );
    EntityHandle root = 0;
    rval              = mbImpl->tag_set_data( type_tag, &root, 1, &handle );
    if( MB_SUCCESS != rval ) return rval;
#endif
#endif

    return rval;
}

ErrorCode AdaptiveKDTree::get_split_plane( EntityHandle entity, Plane& plane )
{
#ifndef MB_AD_KD_TREE_USE_SINGLE_TAG
    ErrorCode r1, r2;
    r1 = moab()->tag_get_data( planeTag, &entity, 1, &plane.coord );
    r2 = moab()->tag_get_data( axisTag, &entity, 1, &plane.norm );
    return MB_SUCCESS == r1 ? r2 : r1;
#elif defined( MB_AD_KD_TREE_USE_TWO_DOUBLE_TAG )
    double values[2];
    ErrorCode rval = moab()->tag_get_data( planeTag, &entity, 1, values );
    plane.coord    = values[0];
    plane.norm     = (int)values[1];
    return rval;
#else
    return moab()->tag_get_data( planeTag, &entity, 1, &plane );
#endif
}

ErrorCode AdaptiveKDTree::set_split_plane( EntityHandle entity, const Plane& plane )
{
#ifndef MB_AD_KD_TREE_USE_SINGLE_TAG
    ErrorCode r1, r2;
    r1 = moab()->tag_set_data( planeTag, &entity, 1, &plane.coord );
    r2 = moab()->tag_set_data( axisTag, &entity, 1, &plane.norm );
    return MB_SUCCESS == r1 ? r2 : r1;
#elif defined( MB_AD_KD_TREE_USE_TWO_DOUBLE_TAG )
    double values[2] = { plane.coord, static_cast< double >( plane.norm ) };
    return moab()->tag_set_data( planeTag, &entity, 1, values );
#else
    return moab()->tag_set_data( planeTag, &entity, 1, &plane );
#endif
}

ErrorCode AdaptiveKDTree::get_tree_iterator( EntityHandle root, AdaptiveKDTreeIter& iter )
{
    double box[6];
    ErrorCode rval = moab()->tag_get_data( boxTag, &root, 1, box );
    if( MB_SUCCESS != rval ) return rval;

    return get_sub_tree_iterator( root, box, box + 3, iter );
}

ErrorCode AdaptiveKDTree::get_last_iterator( EntityHandle root, AdaptiveKDTreeIter& iter )
{
    double box[6];
    ErrorCode rval = moab()->tag_get_data( boxTag, &root, 1, box );
    if( MB_SUCCESS != rval ) return rval;

    return iter.initialize( this, root, box, box + 3, AdaptiveKDTreeIter::RIGHT );
}

ErrorCode AdaptiveKDTree::get_sub_tree_iterator( EntityHandle root,
                                                 const double min[3],
                                                 const double max[3],
                                                 AdaptiveKDTreeIter& result )
{
    return result.initialize( this, root, min, max, AdaptiveKDTreeIter::LEFT );
}

ErrorCode AdaptiveKDTree::split_leaf( AdaptiveKDTreeIter& leaf, Plane plane, EntityHandle& left, EntityHandle& right )
{
    ErrorCode rval;

    rval = moab()->create_meshset( meshsetFlags, left );
    if( MB_SUCCESS != rval ) return rval;

    rval = moab()->create_meshset( meshsetFlags, right );
    if( MB_SUCCESS != rval )
    {
        moab()->delete_entities( &left, 1 );
        return rval;
    }

    if( MB_SUCCESS != set_split_plane( leaf.handle(), plane ) ||
        MB_SUCCESS != moab()->add_child_meshset( leaf.handle(), left ) ||
        MB_SUCCESS != moab()->add_child_meshset( leaf.handle(), right ) ||
        MB_SUCCESS != leaf.step_to_first_leaf( AdaptiveKDTreeIter::LEFT ) )
    {
        EntityHandle children[] = { left, right };
        moab()->delete_entities( children, 2 );
        return MB_FAILURE;
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::split_leaf( AdaptiveKDTreeIter& leaf, Plane plane )
{
    EntityHandle left, right;
    return split_leaf( leaf, plane, left, right );
}

ErrorCode AdaptiveKDTree::split_leaf( AdaptiveKDTreeIter& leaf,
                                      Plane plane,
                                      const Range& left_entities,
                                      const Range& right_entities )
{
    EntityHandle left, right, parent = leaf.handle();
    ErrorCode rval = split_leaf( leaf, plane, left, right );
    if( MB_SUCCESS != rval ) return rval;

    if( MB_SUCCESS == moab()->add_entities( left, left_entities ) &&
        MB_SUCCESS == moab()->add_entities( right, right_entities ) &&
        MB_SUCCESS == moab()->clear_meshset( &parent, 1 ) )
        return MB_SUCCESS;

    moab()->remove_child_meshset( parent, left );
    moab()->remove_child_meshset( parent, right );
    EntityHandle children[] = { left, right };
    moab()->delete_entities( children, 2 );
    return MB_FAILURE;
}

ErrorCode AdaptiveKDTree::split_leaf( AdaptiveKDTreeIter& leaf,
                                      Plane plane,
                                      const std::vector< EntityHandle >& left_entities,
                                      const std::vector< EntityHandle >& right_entities )
{
    EntityHandle left, right, parent = leaf.handle();
    ErrorCode rval = split_leaf( leaf, plane, left, right );
    if( MB_SUCCESS != rval ) return rval;

    if( MB_SUCCESS == moab()->add_entities( left, &left_entities[0], left_entities.size() ) &&
        MB_SUCCESS == moab()->add_entities( right, &right_entities[0], right_entities.size() ) &&
        MB_SUCCESS == moab()->clear_meshset( &parent, 1 ) )
        return MB_SUCCESS;

    moab()->remove_child_meshset( parent, left );
    moab()->remove_child_meshset( parent, right );
    EntityHandle children[] = { left, right };
    moab()->delete_entities( children, 2 );
    return MB_FAILURE;
}

ErrorCode AdaptiveKDTree::merge_leaf( AdaptiveKDTreeIter& iter )
{
    ErrorCode rval;
    if( iter.depth() == 1 )  // at root
        return MB_FAILURE;

    // Move iter to parent

    AdaptiveKDTreeIter::StackObj node = iter.mStack.back();
    iter.mStack.pop_back();

    iter.childVect.clear();
    rval = moab()->get_child_meshsets( iter.mStack.back().entity, iter.childVect );
    if( MB_SUCCESS != rval ) return rval;
    Plane plane;
    rval = get_split_plane( iter.mStack.back().entity, plane );
    if( MB_SUCCESS != rval ) return rval;

    int child_idx = iter.childVect[0] == node.entity ? 0 : 1;
    assert( iter.childVect[child_idx] == node.entity );
    iter.mBox[1 - child_idx][plane.norm] = node.coord;

    // Get all entities from children and put them in parent
    EntityHandle parent = iter.handle();
    moab()->remove_child_meshset( parent, iter.childVect[0] );
    moab()->remove_child_meshset( parent, iter.childVect[1] );
    std::vector< EntityHandle > stack( iter.childVect );

    Range range;
    while( !stack.empty() )
    {
        EntityHandle h = stack.back();
        stack.pop_back();
        range.clear();
        rval = moab()->get_entities_by_handle( h, range );
        if( MB_SUCCESS != rval ) return rval;
        rval = moab()->add_entities( parent, range );
        if( MB_SUCCESS != rval ) return rval;

        iter.childVect.clear();
        rval = moab()->get_child_meshsets( h, iter.childVect );MB_CHK_ERR( rval );
        if( !iter.childVect.empty() )
        {
            moab()->remove_child_meshset( h, iter.childVect[0] );
            moab()->remove_child_meshset( h, iter.childVect[1] );
            stack.push_back( iter.childVect[0] );
            stack.push_back( iter.childVect[1] );
        }

        rval = moab()->delete_entities( &h, 1 );
        if( MB_SUCCESS != rval ) return rval;
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTreeIter::initialize( AdaptiveKDTree* ttool,
                                          EntityHandle root,
                                          const double bmin[3],
                                          const double bmax[3],
                                          Direction direction )
{
    mStack.clear();
    treeTool      = ttool;
    mBox[BMIN][0] = bmin[0];
    mBox[BMIN][1] = bmin[1];
    mBox[BMIN][2] = bmin[2];
    mBox[BMAX][0] = bmax[0];
    mBox[BMAX][1] = bmax[1];
    mBox[BMAX][2] = bmax[2];
    mStack.push_back( StackObj( root, 0 ) );
    return step_to_first_leaf( direction );
}

ErrorCode AdaptiveKDTreeIter::step_to_first_leaf( Direction direction )
{
    ErrorCode rval;
    AdaptiveKDTree::Plane plane;
    const Direction opposite = static_cast< Direction >( 1 - direction );

    for( ;; )
    {
        childVect.clear();
        treeTool->treeStats.nodesVisited++;  // not sure whether this is the visit or the push_back below
        rval = treeTool->moab()->get_child_meshsets( mStack.back().entity, childVect );
        if( MB_SUCCESS != rval ) return rval;
        if( childVect.empty() )
        {  // leaf
            treeTool->treeStats.leavesVisited++;
            break;
        }

        rval = treeTool->get_split_plane( mStack.back().entity, plane );
        if( MB_SUCCESS != rval ) return rval;

        mStack.push_back( StackObj( childVect[direction], mBox[opposite][plane.norm] ) );
        mBox[opposite][plane.norm] = plane.coord;
    }
    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTreeIter::step( Direction direction )
{
    StackObj node, parent;
    ErrorCode rval;
    AdaptiveKDTree::Plane plane;
    const Direction opposite = static_cast< Direction >( 1 - direction );

    // If stack is empty, then either this iterator is uninitialized
    // or we reached the end of the iteration (and return
    // MB_ENTITY_NOT_FOUND) already.
    if( mStack.empty() ) return MB_FAILURE;

    // Pop the current node from the stack.
    // The stack should then contain the parent of the current node.
    // If the stack is empty after this pop, then we've reached the end.
    node = mStack.back();
    mStack.pop_back();
    treeTool->treeStats.nodesVisited++;
    if( mStack.empty() ) treeTool->treeStats.leavesVisited++;

    while( !mStack.empty() )
    {
        // Get data for parent entity
        parent = mStack.back();
        childVect.clear();
        rval = treeTool->moab()->get_child_meshsets( parent.entity, childVect );
        if( MB_SUCCESS != rval ) return rval;
        rval = treeTool->get_split_plane( parent.entity, plane );
        if( MB_SUCCESS != rval ) return rval;

        // If we're at the left child
        if( childVect[opposite] == node.entity )
        {
            // change from box of left child to box of parent
            mBox[direction][plane.norm] = node.coord;
            // push right child on stack
            node.entity = childVect[direction];
            treeTool->treeStats.nodesVisited++;  // changed node
            node.coord = mBox[opposite][plane.norm];
            mStack.push_back( node );
            // change from box of parent to box of right child
            mBox[opposite][plane.norm] = plane.coord;
            // descend to left-most leaf of the right child
            return step_to_first_leaf( opposite );
        }

        // The current node is the right child of the parent,
        // continue up the tree.
        assert( childVect[direction] == node.entity );
        mBox[opposite][plane.norm] = node.coord;
        node                       = parent;
        treeTool->treeStats.nodesVisited++;
        mStack.pop_back();
    }

    return MB_ENTITY_NOT_FOUND;
}

ErrorCode AdaptiveKDTreeIter::get_neighbors( AdaptiveKDTree::Axis norm,
                                             bool neg,
                                             std::vector< AdaptiveKDTreeIter >& results,
                                             double epsilon ) const
{
    StackObj node, parent;
    ErrorCode rval;
    AdaptiveKDTree::Plane plane;
    int child_idx;

    // Find tree node at which the specified side of the box
    // for this node was created.
    AdaptiveKDTreeIter iter( *this );  // temporary iterator (don't modify *this)
    node = iter.mStack.back();
    iter.mStack.pop_back();
    for( ;; )
    {
        // reached the root - original node was on boundary (no neighbors)
        if( iter.mStack.empty() ) return MB_SUCCESS;

        // get parent node data
        parent = iter.mStack.back();
        iter.childVect.clear();
        rval = treeTool->moab()->get_child_meshsets( parent.entity, iter.childVect );
        if( MB_SUCCESS != rval ) return rval;
        rval = treeTool->get_split_plane( parent.entity, plane );
        if( MB_SUCCESS != rval ) return rval;

        child_idx = iter.childVect[0] == node.entity ? 0 : 1;
        assert( iter.childVect[child_idx] == node.entity );

        // if we found the split plane for the desired side
        // push neighbor on stack and stop
        if( plane.norm == norm && (int)neg == child_idx )
        {
            // change from box of previous child to box of parent
            iter.mBox[1 - child_idx][plane.norm] = node.coord;
            // push other child of parent onto stack
            node.entity = iter.childVect[1 - child_idx];
            node.coord  = iter.mBox[child_idx][plane.norm];
            iter.mStack.push_back( node );
            // change from parent box to box of new child
            iter.mBox[child_idx][plane.norm] = plane.coord;
            break;
        }

        // continue up the tree
        iter.mBox[1 - child_idx][plane.norm] = node.coord;
        node                                 = parent;
        iter.mStack.pop_back();
    }

    // now move down tree, searching for adjacent boxes
    std::vector< AdaptiveKDTreeIter > list;
    // loop over all potential paths to neighbors (until list is empty)
    for( ;; )
    {
        // follow a single path to a leaf, append any other potential
        // paths to neighbors to 'list'
        node = iter.mStack.back();
        for( ;; )
        {
            iter.childVect.clear();
            rval = treeTool->moab()->get_child_meshsets( node.entity, iter.childVect );
            if( MB_SUCCESS != rval ) return rval;

            // if leaf
            if( iter.childVect.empty() )
            {
                results.push_back( iter );
                break;
            }

            rval = treeTool->get_split_plane( node.entity, plane );
            if( MB_SUCCESS != rval ) return rval;

            // if split parallel to side
            if( plane.norm == norm )
            {
                // continue with whichever child is on the correct side of the split
                node.entity = iter.childVect[neg];
                node.coord  = iter.mBox[1 - neg][plane.norm];
                iter.mStack.push_back( node );
                iter.mBox[1 - neg][plane.norm] = plane.coord;
            }
            // if left child is adjacent
            else if( this->mBox[BMIN][plane.norm] - plane.coord <= epsilon )
            {
                // if right child is also adjacent, add to list
                if( plane.coord - this->mBox[BMAX][plane.norm] <= epsilon )
                {
                    list.push_back( iter );
                    list.back().mStack.push_back( StackObj( iter.childVect[1], iter.mBox[BMIN][plane.norm] ) );
                    list.back().mBox[BMIN][plane.norm] = plane.coord;
                }
                // continue with left child
                node.entity = iter.childVect[0];
                node.coord  = iter.mBox[BMAX][plane.norm];
                iter.mStack.push_back( node );
                iter.mBox[BMAX][plane.norm] = plane.coord;
            }
            // right child is adjacent
            else
            {
                // if left child is not adjacent, right must be or something
                // is really messed up.
                assert( plane.coord - this->mBox[BMAX][plane.norm] <= epsilon );
                // continue with left child
                node.entity = iter.childVect[1];
                node.coord  = iter.mBox[BMIN][plane.norm];
                iter.mStack.push_back( node );
                iter.mBox[BMIN][plane.norm] = plane.coord;
            }
        }

        if( list.empty() ) break;

        iter = list.back();
        list.pop_back();
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTreeIter::sibling_side( AdaptiveKDTree::Axis& axis_out, bool& neg_out ) const
{
    if( mStack.size() < 2 )  // at tree root
        return MB_ENTITY_NOT_FOUND;

    EntityHandle parent = mStack[mStack.size() - 2].entity;
    AdaptiveKDTree::Plane plane;
    ErrorCode rval = tool()->get_split_plane( parent, plane );
    if( MB_SUCCESS != rval ) return MB_FAILURE;

    childVect.clear();
    rval = tool()->moab()->get_child_meshsets( parent, childVect );
    if( MB_SUCCESS != rval || childVect.size() != 2 ) return MB_FAILURE;

    axis_out = static_cast< AdaptiveKDTree::Axis >( plane.norm );
    neg_out  = ( childVect[1] == handle() );
    assert( childVect[neg_out] == handle() );
    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTreeIter::get_parent_split_plane( AdaptiveKDTree::Plane& plane ) const
{
    if( mStack.size() < 2 )  // at tree root
        return MB_ENTITY_NOT_FOUND;

    EntityHandle parent = mStack[mStack.size() - 2].entity;
    return tool()->get_split_plane( parent, plane );
}

bool AdaptiveKDTreeIter::is_sibling( const AdaptiveKDTreeIter& other_leaf ) const
{
    const size_t s = mStack.size();
    return ( s > 1 ) && ( s == other_leaf.mStack.size() ) &&
           ( other_leaf.mStack[s - 2].entity == mStack[s - 2].entity ) && other_leaf.handle() != handle();
}

bool AdaptiveKDTreeIter::is_sibling( EntityHandle other_leaf ) const
{
    if( mStack.size() < 2 || other_leaf == handle() ) return false;
    EntityHandle parent = mStack[mStack.size() - 2].entity;
    childVect.clear();
    ErrorCode rval = tool()->moab()->get_child_meshsets( parent, childVect );
    if( MB_SUCCESS != rval || childVect.size() != 2 )
    {
        assert( false );
        return false;
    }
    return childVect[0] == other_leaf || childVect[1] == other_leaf;
}

bool AdaptiveKDTreeIter::sibling_is_forward() const
{
    if( mStack.size() < 2 )  // if root
        return false;
    EntityHandle parent = mStack[mStack.size() - 2].entity;
    childVect.clear();
    ErrorCode rval = tool()->moab()->get_child_meshsets( parent, childVect );
    if( MB_SUCCESS != rval || childVect.size() != 2 )
    {
        assert( false );
        return false;
    }
    return childVect[0] == handle();
}

bool AdaptiveKDTreeIter::intersect_ray( const double ray_point[3],
                                        const double ray_vect[3],
                                        double& t_enter,
                                        double& t_exit ) const
{
    treeTool->treeStats.traversalLeafObjectTests++;
    return GeomUtil::ray_box_intersect( CartVect( box_min() ), CartVect( box_max() ), CartVect( ray_point ),
                                        CartVect( ray_vect ), t_enter, t_exit );
}

ErrorCode AdaptiveKDTree::intersect_children_with_elems( const Range& elems,
                                                         AdaptiveKDTree::Plane plane,
                                                         double eps,
                                                         CartVect box_min,
                                                         CartVect box_max,
                                                         Range& left_tris,
                                                         Range& right_tris,
                                                         Range& both_tris,
                                                         double& metric_value )
{
    left_tris.clear();
    right_tris.clear();
    both_tris.clear();
    CartVect coords[16];

    // get extents of boxes for left and right sides
    BoundBox left_box( box_min, box_max ), right_box( box_min, box_max );
    right_box.bMin             = box_min;
    left_box.bMax              = box_max;
    right_box.bMin[plane.norm] = left_box.bMax[plane.norm] = plane.coord;
    const CartVect left_cen                                = 0.5 * ( left_box.bMax + box_min );
    const CartVect left_dim                                = 0.5 * ( left_box.bMax - box_min );
    const CartVect right_cen                               = 0.5 * ( box_max + right_box.bMin );
    const CartVect right_dim                               = 0.5 * ( box_max - right_box.bMin );
    const CartVect dim                                     = box_max - box_min;
    const double max_tol                                   = std::max( dim[0], std::max( dim[1], dim[2] ) ) / 10;

    // test each entity
    ErrorCode rval;
    int count, count2;
    const EntityHandle *conn, *conn2;

    const Range::const_iterator elem_begin = elems.lower_bound( MBEDGE );
    const Range::const_iterator poly_begin = elems.lower_bound( MBPOLYHEDRON, elem_begin );
    const Range::const_iterator set_begin  = elems.lower_bound( MBENTITYSET, poly_begin );
    Range::iterator left_ins               = left_tris.begin();
    Range::iterator right_ins              = right_tris.begin();
    Range::iterator both_ins               = both_tris.begin();
    Range::const_iterator i;

    // vertices
    for( i = elems.begin(); i != elem_begin; ++i )
    {
        tree_stats().constructLeafObjectTests++;
        rval = moab()->get_coords( &*i, 1, coords[0].array() );
        if( MB_SUCCESS != rval ) return rval;

        bool lo = false, ro = false;
        if( coords[0][plane.norm] <= plane.coord ) lo = true;
        if( coords[0][plane.norm] >= plane.coord ) ro = true;

        if( lo && ro )
            both_ins = both_tris.insert( both_ins, *i, *i );
        else if( lo )
            left_ins = left_tris.insert( left_ins, *i, *i );
        else  // if (ro)
            right_ins = right_tris.insert( right_ins, *i, *i );
    }

    // non-polyhedron elements
    std::vector< EntityHandle > dum_vector;
    for( i = elem_begin; i != poly_begin; ++i )
    {
        tree_stats().constructLeafObjectTests++;
        rval = moab()->get_connectivity( *i, conn, count, true, &dum_vector );
        if( MB_SUCCESS != rval ) return rval;
        if( count > (int)( sizeof( coords ) / sizeof( coords[0] ) ) ) return MB_FAILURE;
        rval = moab()->get_coords( &conn[0], count, coords[0].array() );
        if( MB_SUCCESS != rval ) return rval;

        bool lo = false, ro = false;
        for( int j = 0; j < count; ++j )
        {
            if( coords[j][plane.norm] <= plane.coord ) lo = true;
            if( coords[j][plane.norm] >= plane.coord ) ro = true;
        }

        // Triangle must be in at least one leaf.  If test against plane
        // identified that leaf, then we're done.  If triangle is on both
        // sides of plane, do more precise test to ensure that it is really
        // in both.
        //        BoundBox box;
        //        box.update(*moab(), *i);
        if( lo && ro )
        {
            double tol = eps;
            lo = ro = false;
            while( !lo && !ro && tol <= max_tol )
            {
                tree_stats().boxElemTests += 2;
                lo = GeomUtil::box_elem_overlap( coords, TYPE_FROM_HANDLE( *i ), left_cen, left_dim + CartVect( tol ),
                                                 count );
                ro = GeomUtil::box_elem_overlap( coords, TYPE_FROM_HANDLE( *i ), right_cen, right_dim + CartVect( tol ),
                                                 count );

                tol *= 10.0;
            }
        }
        if( lo && ro )
            both_ins = both_tris.insert( both_ins, *i, *i );
        else if( lo )
            left_ins = left_tris.insert( left_ins, *i, *i );
        else if( ro )
            right_ins = right_tris.insert( right_ins, *i, *i );
    }

    // polyhedra
    for( i = poly_begin; i != set_begin; ++i )
    {
        tree_stats().constructLeafObjectTests++;
        rval = moab()->get_connectivity( *i, conn, count, true );
        if( MB_SUCCESS != rval ) return rval;

        // just check the bounding box of the polyhedron
        bool lo = false, ro = false;
        for( int j = 0; j < count; ++j )
        {
            rval = moab()->get_connectivity( conn[j], conn2, count2, true );
            if( MB_SUCCESS != rval ) return rval;

            for( int k = 0; k < count2; ++k )
            {
                rval = moab()->get_coords( conn2 + k, 1, coords[0].array() );
                if( MB_SUCCESS != rval ) return rval;
                if( coords[0][plane.norm] <= plane.coord ) lo = true;
                if( coords[0][plane.norm] >= plane.coord ) ro = true;
            }
        }

        if( lo && ro )
            both_ins = both_tris.insert( both_ins, *i, *i );
        else if( lo )
            left_ins = left_tris.insert( left_ins, *i, *i );
        else if( ro )
            right_ins = right_tris.insert( right_ins, *i, *i );
    }

    // sets
    BoundBox tbox;
    for( i = set_begin; i != elems.end(); ++i )
    {
        tree_stats().constructLeafObjectTests++;
        rval = tbox.update( *moab(), *i, spherical, radius );
        if( MB_SUCCESS != rval ) return rval;

        bool lo = false, ro = false;
        if( tbox.bMin[plane.norm] <= plane.coord ) lo = true;
        if( tbox.bMax[plane.norm] >= plane.coord ) ro = true;

        if( lo && ro )
            both_ins = both_tris.insert( both_ins, *i, *i );
        else if( lo )
            left_ins = left_tris.insert( left_ins, *i, *i );
        else  // if (ro)
            right_ins = right_tris.insert( right_ins, *i, *i );
    }

    CartVect box_dim  = box_max - box_min;
    double area_left  = left_dim[0] * left_dim[1] + left_dim[1] * left_dim[2] + left_dim[2] * left_dim[0];
    double area_right = right_dim[0] * right_dim[1] + right_dim[1] * right_dim[2] + right_dim[2] * right_dim[0];
    double area_both  = box_dim[0] * box_dim[1] + box_dim[1] * box_dim[2] + box_dim[2] * box_dim[0];
    metric_value = ( area_left * left_tris.size() + area_right * right_tris.size() ) / area_both + both_tris.size();
    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::best_subdivision_plane( int num_planes,
                                                  const AdaptiveKDTreeIter& iter,
                                                  Range& best_left,
                                                  Range& best_right,
                                                  Range& best_both,
                                                  AdaptiveKDTree::Plane& best_plane,
                                                  double eps )
{
    double metric_val = std::numeric_limits< unsigned >::max();

    ErrorCode r;
    const CartVect box_min( iter.box_min() );
    const CartVect box_max( iter.box_max() );
    const CartVect diff( box_max - box_min );

    Range entities;
    r = iter.tool()->moab()->get_entities_by_handle( iter.handle(), entities );
    if( MB_SUCCESS != r ) return r;
    const size_t p_count = entities.size();

    for( int axis = 0; axis < 3; ++axis )
    {
        int plane_count = num_planes;
        if( ( num_planes + 1 ) * eps >= diff[axis] ) plane_count = (int)( diff[axis] / eps ) - 1;

        for( int p = 1; p <= plane_count; ++p )
        {
            AdaptiveKDTree::Plane plane = { box_min[axis] + ( p / ( 1.0 + plane_count ) ) * diff[axis], axis };
            Range left, right, both;
            double val;
            r = intersect_children_with_elems( entities, plane, eps, box_min, box_max, left, right, both, val );
            if( MB_SUCCESS != r ) return r;
            const size_t sdiff = p_count - both.size();
            if( left.size() == sdiff || right.size() == sdiff ) continue;

            if( val >= metric_val ) continue;

            metric_val = val;
            best_plane = plane;
            best_left.swap( left );
            best_right.swap( right );
            best_both.swap( both );
        }
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::best_subdivision_snap_plane( int num_planes,
                                                       const AdaptiveKDTreeIter& iter,
                                                       Range& best_left,
                                                       Range& best_right,
                                                       Range& best_both,
                                                       AdaptiveKDTree::Plane& best_plane,
                                                       std::vector< double >& tmp_data,
                                                       double eps )
{
    double metric_val = std::numeric_limits< unsigned >::max();

    ErrorCode r;
    // const CartVect tol(eps*diff);

    Range entities, vertices;
    r = iter.tool()->moab()->get_entities_by_handle( iter.handle(), entities );
    if( MB_SUCCESS != r ) return r;
    const size_t p_count = entities.size();
    r                    = iter.tool()->moab()->get_adjacencies( entities, 0, false, vertices, Interface::UNION );
    if( MB_SUCCESS != r ) return r;

    unsigned int nverts = vertices.size();
    tmp_data.resize( 3 * nverts );
    r = iter.tool()->moab()->get_coords( vertices, &tmp_data[0], &tmp_data[nverts], &tmp_data[2 * nverts] );
    if( MB_SUCCESS != r ) return r;

    // calculate bounding box of vertices
    // decide based on the actual box the splitting plane
    // do not decide based on iterator box.
    // it could be too big
    // BoundBox box;
    // r = box.update(*moab(), vertices);
    CartVect box_min;
    CartVect box_max;
    for( int dir = 0; dir < 3; dir++ )
    {
        double amin = tmp_data[dir * nverts];
        double amax = amin;
        double* p   = &tmp_data[dir * nverts + 1];
        for( unsigned int i = 1; i < nverts; i++ )
        {
            if( *p < amin ) amin = *p;
            if( *p > amax ) amax = *p;
            p++;
        }
        box_min[dir] = amin;
        box_max[dir] = amax;
    }
    CartVect diff( box_max - box_min );

    for( int axis = 0; axis < 3; ++axis )
    {
        int plane_count = num_planes;

        // if num_planes results in width < eps, reset the plane count
        if( ( num_planes + 1 ) * eps >= diff[axis] ) plane_count = (int)( diff[axis] / eps ) - 1;

        for( int p = 1; p <= plane_count; ++p )
        {

            // coord of this plane on axis
            double coord = box_min[axis] + ( p / ( 1.0 + plane_count ) ) * diff[axis];

            // find closest vertex coordinate to this plane position
            unsigned int istrt   = axis * nverts;
            double closest_coord = tmp_data[istrt];
            for( unsigned i = 1; i < nverts; ++i )
                if( fabs( coord - tmp_data[istrt + i] ) < fabs( coord - closest_coord ) )
                    closest_coord = tmp_data[istrt + i];
            if( closest_coord - box_min[axis] <= eps || box_max[axis] - closest_coord <= eps ) continue;

            // seprate elems into left/right/both, and compute separating metric
            AdaptiveKDTree::Plane plane = { closest_coord, axis };
            Range left, right, both;
            double val;
            r = intersect_children_with_elems( entities, plane, eps, box_min, box_max, left, right, both, val );
            if( MB_SUCCESS != r ) return r;
            const size_t d = p_count - both.size();
            if( left.size() == d || right.size() == d ) continue;

            if( val >= metric_val ) continue;

            metric_val = val;
            best_plane = plane;
            best_left.swap( left );
            best_right.swap( right );
            best_both.swap( both );
        }
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::best_vertex_median_plane( int num_planes,
                                                    const AdaptiveKDTreeIter& iter,
                                                    Range& best_left,
                                                    Range& best_right,
                                                    Range& best_both,
                                                    AdaptiveKDTree::Plane& best_plane,
                                                    std::vector< double >& coords,
                                                    double eps )
{
    double metric_val = std::numeric_limits< unsigned >::max();

    ErrorCode r;
    const CartVect box_min( iter.box_min() );
    const CartVect box_max( iter.box_max() );

    Range entities, vertices;
    r = iter.tool()->moab()->get_entities_by_handle( iter.handle(), entities );
    if( MB_SUCCESS != r ) return r;
    const size_t p_count = entities.size();
    r                    = iter.tool()->moab()->get_adjacencies( entities, 0, false, vertices, Interface::UNION );
    if( MB_SUCCESS != r ) return r;

    coords.resize( vertices.size() );
    for( int axis = 0; axis < 3; ++axis )
    {
        if( box_max[axis] - box_min[axis] <= 2 * eps ) continue;

        double* ptrs[] = { 0, 0, 0 };
        ptrs[axis]     = &coords[0];
        r              = iter.tool()->moab()->get_coords( vertices, ptrs[0], ptrs[1], ptrs[2] );
        if( MB_SUCCESS != r ) return r;

        std::sort( coords.begin(), coords.end() );
        std::vector< double >::iterator citer;
        citer              = std::upper_bound( coords.begin(), coords.end(), box_min[axis] + eps );
        const size_t count = std::upper_bound( citer, coords.end(), box_max[axis] - eps ) - citer;
        size_t step;
        int np = num_planes;
        if( count < 2 * (size_t)num_planes )
        {
            step = 1;
            np   = count - 1;
        }
        else
        {
            step = count / ( num_planes + 1 );
        }

        for( int p = 1; p <= np; ++p )
        {

            citer += step;
            AdaptiveKDTree::Plane plane = { *citer, axis };
            Range left, right, both;
            double val;
            r = intersect_children_with_elems( entities, plane, eps, box_min, box_max, left, right, both, val );
            if( MB_SUCCESS != r ) return r;
            const size_t diff = p_count - both.size();
            if( left.size() == diff || right.size() == diff ) continue;

            if( val >= metric_val ) continue;

            metric_val = val;
            best_plane = plane;
            best_left.swap( left );
            best_right.swap( right );
            best_both.swap( both );
        }
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::best_vertex_sample_plane( int num_planes,
                                                    const AdaptiveKDTreeIter& iter,
                                                    Range& best_left,
                                                    Range& best_right,
                                                    Range& best_both,
                                                    AdaptiveKDTree::Plane& best_plane,
                                                    std::vector< double >& coords,
                                                    std::vector< EntityHandle >& indices,
                                                    double eps )
{
    const size_t random_elem_threshold = 20 * num_planes;
    double metric_val                  = std::numeric_limits< unsigned >::max();

    ErrorCode r;
    const CartVect box_min( iter.box_min() );
    const CartVect box_max( iter.box_max() );

    Range entities, vertices;
    r = iter.tool()->moab()->get_entities_by_handle( iter.handle(), entities );
    if( MB_SUCCESS != r ) return r;

    // We are selecting random vertex coordinates to use for candidate split
    // planes.  So if element list is large, begin by selecting random elements.
    const size_t p_count = entities.size();
    coords.resize( 3 * num_planes );
    if( p_count < random_elem_threshold )
    {
        r = iter.tool()->moab()->get_adjacencies( entities, 0, false, vertices, Interface::UNION );
        if( MB_SUCCESS != r ) return r;
    }
    else
    {
        indices.resize( random_elem_threshold );
        const int num_rand = p_count / RAND_MAX + 1;
        for( size_t j = 0; j < random_elem_threshold; ++j )
        {
            size_t rnd = rand();
            for( int i = num_rand; i > 1; --i )
                rnd *= rand();
            rnd %= p_count;
            indices[j] = entities[rnd];
        }
        r = iter.tool()->moab()->get_adjacencies( &indices[0], random_elem_threshold, 0, false, vertices,
                                                  Interface::UNION );
        if( MB_SUCCESS != r ) return r;
    }

    coords.resize( vertices.size() );
    for( int axis = 0; axis < 3; ++axis )
    {
        if( box_max[axis] - box_min[axis] <= 2 * eps ) continue;

        double* ptrs[] = { 0, 0, 0 };
        ptrs[axis]     = &coords[0];
        r              = iter.tool()->moab()->get_coords( vertices, ptrs[0], ptrs[1], ptrs[2] );
        if( MB_SUCCESS != r ) return r;

        size_t num_valid_coords = 0;
        for( size_t i = 0; i < coords.size(); ++i )
            if( coords[i] > box_min[axis] + eps && coords[i] < box_max[axis] - eps ) ++num_valid_coords;

        if( 2 * (size_t)num_planes > num_valid_coords )
        {
            indices.clear();
            for( size_t i = 0; i < coords.size(); ++i )
                if( coords[i] > box_min[axis] + eps && coords[i] < box_max[axis] - eps ) indices.push_back( i );
        }
        else
        {
            indices.resize( num_planes );
            // make sure random indices are sufficient to cover entire range
            const int num_rand = coords.size() / RAND_MAX + 1;
            for( int j = 0; j < num_planes; ++j )
            {
                size_t rnd;
                do
                {
                    rnd = rand();
                    for( int i = num_rand; i > 1; --i )
                        rnd *= rand();
                    rnd %= coords.size();
                } while( coords[rnd] <= box_min[axis] + eps || coords[rnd] >= box_max[axis] - eps );
                indices[j] = rnd;
            }
        }

        for( unsigned p = 0; p < indices.size(); ++p )
        {

            AdaptiveKDTree::Plane plane = { coords[indices[p]], axis };
            Range left, right, both;
            double val;
            r = intersect_children_with_elems( entities, plane, eps, box_min, box_max, left, right, both, val );
            if( MB_SUCCESS != r ) return r;
            const size_t diff = p_count - both.size();
            if( left.size() == diff || right.size() == diff ) continue;

            if( val >= metric_val ) continue;

            metric_val = val;
            best_plane = plane;
            best_left.swap( left );
            best_right.swap( right );
            best_both.swap( both );
        }
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::point_search( const double* point,
                                        EntityHandle& leaf_out,
                                        const double iter_tol,
                                        const double inside_tol,
                                        bool* multiple_leaves,
                                        EntityHandle* start_node,
                                        CartVect* params )
{
    std::vector< EntityHandle > children;
    Plane plane;

    treeStats.numTraversals++;
    leaf_out = 0;
    BoundBox box;
    // kdtrees never have multiple leaves containing a pt
    if( multiple_leaves ) *multiple_leaves = false;

    EntityHandle node = ( start_node ? *start_node : myRoot );

    treeStats.nodesVisited++;
    ErrorCode rval = get_bounding_box( box, &node );
    if( MB_SUCCESS != rval ) return rval;
    if( !box.contains_point( point, iter_tol ) ) return MB_SUCCESS;

    rval = moab()->get_child_meshsets( node, children );
    if( MB_SUCCESS != rval ) return rval;

    while( !children.empty() )
    {
        treeStats.nodesVisited++;

        rval = get_split_plane( node, plane );
        if( MB_SUCCESS != rval ) return rval;

        const double d = point[plane.norm] - plane.coord;
        node           = children[( d > 0.0 )];

        children.clear();
        rval = moab()->get_child_meshsets( node, children );
        if( MB_SUCCESS != rval ) return rval;
    }

    treeStats.leavesVisited++;
    if( myEval && params )
    {
        rval = myEval->find_containing_entity( node, point, iter_tol, inside_tol, leaf_out, params->array(),
                                               &treeStats.traversalLeafObjectTests );
        if( MB_SUCCESS != rval ) return rval;
    }
    else
        leaf_out = node;

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::point_search( const double* point,
                                        AdaptiveKDTreeIter& leaf_it,
                                        const double iter_tol,
                                        const double /*inside_tol*/,
                                        bool* multiple_leaves,
                                        EntityHandle* start_node )
{
    ErrorCode rval;
    treeStats.numTraversals++;

    // kdtrees never have multiple leaves containing a pt
    if( multiple_leaves ) *multiple_leaves = false;

    leaf_it.mBox[0] = boundBox.bMin;
    leaf_it.mBox[1] = boundBox.bMax;

    // test that point is inside tree
    if( !boundBox.contains_point( point, iter_tol ) )
    {
        treeStats.nodesVisited++;
        return MB_ENTITY_NOT_FOUND;
    }

    // initialize iterator at tree root
    leaf_it.treeTool = this;
    leaf_it.mStack.clear();
    leaf_it.mStack.push_back( AdaptiveKDTreeIter::StackObj( ( start_node ? *start_node : myRoot ), 0 ) );

    // loop until we reach a leaf
    AdaptiveKDTree::Plane plane;
    for( ;; )
    {
        treeStats.nodesVisited++;

        // get children
        leaf_it.childVect.clear();
        rval = moab()->get_child_meshsets( leaf_it.handle(), leaf_it.childVect );
        if( MB_SUCCESS != rval ) return rval;

        // if no children, then at leaf (done)
        if( leaf_it.childVect.empty() )
        {
            treeStats.leavesVisited++;
            break;
        }

        // get split plane
        rval = get_split_plane( leaf_it.handle(), plane );
        if( MB_SUCCESS != rval ) return rval;

        // step iterator to appropriate child
        // idx: 0->left, 1->right
        const int idx = ( point[plane.norm] > plane.coord );
        leaf_it.mStack.push_back(
            AdaptiveKDTreeIter::StackObj( leaf_it.childVect[idx], leaf_it.mBox[1 - idx][plane.norm] ) );
        leaf_it.mBox[1 - idx][plane.norm] = plane.coord;
    }

    return MB_SUCCESS;
}

struct NodeDistance
{
    EntityHandle handle;
    CartVect dist;  // from_point - closest_point_on_box
};

ErrorCode AdaptiveKDTree::distance_search( const double from_point[3],
                                           const double distance,
                                           std::vector< EntityHandle >& result_list,
                                           const double iter_tol,
                                           const double inside_tol,
                                           std::vector< double >* result_dists,
                                           std::vector< CartVect >* result_params,
                                           EntityHandle* tree_root )
{
    treeStats.numTraversals++;
    const double dist_sqr = distance * distance;
    const CartVect from( from_point );
    std::vector< NodeDistance > list,
        result_list_nodes;  // list of subtrees to traverse, and results
                            // pre-allocate space for default max tree depth
    list.reserve( maxDepth );

    // misc temporary values
    Plane plane;
    NodeDistance node;
    ErrorCode rval;
    std::vector< EntityHandle > children;

    // Get distance from input position to bounding box of tree
    // (zero if inside box)
    BoundBox box;
    rval = get_bounding_box( box );
    if( MB_SUCCESS == rval && !box.contains_point( from_point, iter_tol ) )
    {
        treeStats.nodesVisited++;
        return MB_SUCCESS;
    }

    // if bounding box is not available (e.g. not starting from true root)
    // just start with zero.  Less efficient, but will work.
    node.dist = CartVect( 0.0 );
    if( MB_SUCCESS == rval )
    {
        for( int i = 0; i < 3; ++i )
        {
            if( from_point[i] < box.bMin[i] )
                node.dist[i] = box.bMin[i] - from_point[i];
            else if( from_point[i] > box.bMax[i] )
                node.dist[i] = from_point[i] - box.bMax[i];
        }
        if( node.dist % node.dist > dist_sqr )
        {
            treeStats.nodesVisited++;
            return MB_SUCCESS;
        }
    }

    // begin with root in list
    node.handle = ( tree_root ? *tree_root : myRoot );
    list.push_back( node );

    while( !list.empty() )
    {

        node = list.back();
        list.pop_back();
        treeStats.nodesVisited++;

        // If leaf node, test contained triangles
        children.clear();
        rval = moab()->get_child_meshsets( node.handle, children );
        if( children.empty() )
        {
            treeStats.leavesVisited++;
            if( myEval && result_params )
            {
                EntityHandle ent;
                CartVect params;
                rval = myEval->find_containing_entity( node.handle, from_point, iter_tol, inside_tol, ent,
                                                       params.array(), &treeStats.traversalLeafObjectTests );
                if( MB_SUCCESS != rval )
                    return rval;
                else if( ent )
                {
                    result_list.push_back( ent );
                    result_params->push_back( params );
                    if( result_dists ) result_dists->push_back( 0.0 );
                }
            }
            else
            {
                result_list_nodes.push_back( node );
                continue;
            }
        }

        // If not leaf node, add children to working list
        rval = get_split_plane( node.handle, plane );
        if( MB_SUCCESS != rval ) return rval;

        const double d = from[plane.norm] - plane.coord;

        // right of plane?
        if( d > 0 )
        {
            node.handle = children[1];
            list.push_back( node );
            // if the split plane is close to the input point, add
            // the left child also (we'll check the exact distance
            /// when we pop it from the list.)
            if( d <= distance )
            {
                node.dist[plane.norm] = d;
                if( node.dist % node.dist <= dist_sqr )
                {
                    node.handle = children[0];
                    list.push_back( node );
                }
            }
        }
        // left of plane
        else
        {
            node.handle = children[0];
            list.push_back( node );
            // if the split plane is close to the input point, add
            // the right child also (we'll check the exact distance
            /// when we pop it from the list.)
            if( -d <= distance )
            {
                node.dist[plane.norm] = -d;
                if( node.dist % node.dist <= dist_sqr )
                {
                    node.handle = children[1];
                    list.push_back( node );
                }
            }
        }
    }

    if( myEval && result_params ) return MB_SUCCESS;

    // separate loops to avoid if test inside loop

    result_list.reserve( result_list_nodes.size() );
    for( std::vector< NodeDistance >::iterator vit = result_list_nodes.begin(); vit != result_list_nodes.end(); ++vit )
        result_list.push_back( ( *vit ).handle );

    if( result_dists && distance > 0.0 )
    {
        result_dists->reserve( result_list_nodes.size() );
        for( std::vector< NodeDistance >::iterator vit = result_list_nodes.begin(); vit != result_list_nodes.end();
             ++vit )
            result_dists->push_back( ( *vit ).dist.length() );
    }

    return MB_SUCCESS;
}

static ErrorCode closest_to_triangles( Interface* moab,
                                       const Range& tris,
                                       const CartVect& from,
                                       double& shortest_dist_sqr,
                                       CartVect& closest_pt,
                                       EntityHandle& closest_tri )
{
    ErrorCode rval;
    CartVect pos, diff, verts[3];
    const EntityHandle* conn = NULL;
    int len                  = 0;

    for( Range::iterator i = tris.begin(); i != tris.end(); ++i )
    {
        rval = moab->get_connectivity( *i, conn, len );
        if( MB_SUCCESS != rval ) return rval;

        rval = moab->get_coords( conn, 3, verts[0].array() );
        if( MB_SUCCESS != rval ) return rval;

        GeomUtil::closest_location_on_tri( from, verts, pos );
        diff            = pos - from;
        double dist_sqr = diff % diff;
        if( dist_sqr < shortest_dist_sqr )
        {
            // new closest location
            shortest_dist_sqr = dist_sqr;
            closest_pt        = pos;
            closest_tri       = *i;
        }
    }

    return MB_SUCCESS;
}

static ErrorCode closest_to_triangles( Interface* moab,
                                       EntityHandle set_handle,
                                       const CartVect& from,
                                       double& shortest_dist_sqr,
                                       CartVect& closest_pt,
                                       EntityHandle& closest_tri )
{
    ErrorCode rval;
    Range tris;

    rval = moab->get_entities_by_type( set_handle, MBTRI, tris );
    if( MB_SUCCESS != rval ) return rval;

    return closest_to_triangles( moab, tris, from, shortest_dist_sqr, closest_pt, closest_tri );
}

ErrorCode AdaptiveKDTree::find_close_triangle( EntityHandle root,
                                               const double from[3],
                                               double pt[3],
                                               EntityHandle& triangle )
{
    ErrorCode rval;
    Range tris;
    Plane split;
    std::vector< EntityHandle > stack;
    std::vector< EntityHandle > children( 2 );
    stack.reserve( 30 );
    assert( root );
    stack.push_back( root );

    while( !stack.empty() )
    {
        EntityHandle node = stack.back();
        stack.pop_back();

        for( ;; )
        {  // loop until we find a leaf

            children.clear();
            rval = moab()->get_child_meshsets( node, children );
            if( MB_SUCCESS != rval ) return rval;

            // loop termination criterion
            if( children.empty() ) break;

            // if not a leaf, get split plane
            rval = get_split_plane( node, split );
            if( MB_SUCCESS != rval ) return rval;

            // continue down the side that contains the point,
            // and push the other side onto the stack in case
            // we need to check it later.
            int rs = split.right_side( from );
            node   = children[rs];
            stack.push_back( children[1 - rs] );
        }

        // We should now be at a leaf.
        // If it has some triangles, we're done.
        // If not, continue searching for another leaf.
        tris.clear();
        rval = moab()->get_entities_by_type( node, MBTRI, tris );
        if( !tris.empty() )
        {
            double dist_sqr = HUGE_VAL;
            CartVect point( pt );
            rval = closest_to_triangles( moab(), tris, CartVect( from ), dist_sqr, point, triangle );
            point.get( pt );
            return rval;
        }
    }

    // If we got here, then we traversed the entire tree
    // and all the leaves were empty.
    return MB_ENTITY_NOT_FOUND;
}

/** Find the triangles in a set that are closer to the input
 *  position than any triangles in the 'closest_tris' list.
 *
 *  closest_tris is assumed to contain a list of triangles for
 *  which the first is the closest known triangle to the input
 *  position and the first entry in 'closest_pts' is the closest
 *  location on that triangle.  Any other values in the lists must
 *  be other triangles for which the closest point is within the
 *  input tolerance of the closest closest point.  This function
 *  will update the lists as appropriate if any closer triangles
 *  or triangles within the tolerance of the current closest location
 *  are found.  The first entry is maintained as the closest of the
 *  list of triangles.
 */
/*
  static ErrorCode closest_to_triangles( Interface* moab,
  EntityHandle set_handle,
  double tolerance,
  const CartVect& from,
  std::vector& closest_tris,
  std::vector& closest_pts )
  {
  ErrorCode rval;
  Range tris;
  CartVect pos, diff, verts[3];
  const EntityHandle* conn;
  int len;
  double shortest_dist_sqr = HUGE_VAL;
  if (!closest_pts.empty()) {
  diff = from - closest_pts.front();
  shortest_dist_sqr = diff % diff;
  }

  rval = moab->get_entities_by_type( set_handle, MBTRI, tris );
  if (MB_SUCCESS != rval)
  return rval;

  for (Range::iterator i = tris.begin(); i != tris.end(); ++i) {
  rval = moab->get_connectivity( *i, conn, len );
  if (MB_SUCCESS != rval)
  return rval;

  rval = moab->get_coords( conn, 3, verts[0].array() );
  if (MB_SUCCESS != rval)
  return rval;

  GeomUtil::closest_location_on_tri( from, verts, pos );
  diff = pos - from;
  double dist_sqr = diff % diff;
  if (dist_sqr < shortest_dist_sqr) {
    // new closest location
    shortest_dist_sqr = dist_sqr;

    if (closest_pts.empty()) {
    closest_tris.push_back( *i );
    closest_pts.push_back( pos );
    }
      // if have a previous closest location
      else {
        // if previous closest is more than 2*tolerance away
          // from new closest, then nothing in the list can
          // be within tolerance of new closest point.
          diff = pos - closest_pts.front();
          dist_sqr = diff % diff;
          if (dist_sqr > 4.0 * tolerance * tolerance) {
          closest_tris.clear();
          closest_pts.clear();
          closest_tris.push_back( *i );
          closest_pts.push_back( pos );
          }
            // otherwise need to remove any triangles that are
              // not within tolerance of the new closest point.
              else {
              unsigned r = 0, w = 0;
              for (r = 0; r < closest_pts.size(); ++r) {
              diff = pos - closest_pts[r];
              if (diff % diff <= tolerance*tolerance) {
              closest_pts[w] = closest_pts[r];
              closest_tris[w] = closest_tris[r];
              ++w;
              }
              }
              closest_pts.resize( w + 1 );
              closest_tris.resize( w + 1 );
                // always put the closest one in the front
                if (w > 0) {
                closest_pts.back() = closest_pts.front();
                closest_tris.back() = closest_tris.front();
                }
                closest_pts.front() = pos;
                closest_tris.front() = *i;
                }
                }
                }
                else {
                  // If within tolerance of old closest triangle,
                    // add this one to the list.
                    diff = closest_pts.front() - pos;
                    if (diff % diff <= tolerance*tolerance) {
                    closest_pts.push_back( pos );
                    closest_tris.push_back( *i );
                    }
                    }
                    }

                    return MB_SUCCESS;
                    }
*/

ErrorCode AdaptiveKDTree::closest_triangle( EntityHandle tree_root,
                                            const double from_coords[3],
                                            double closest_point_out[3],
                                            EntityHandle& triangle_out )
{
    ErrorCode rval;
    double shortest_dist_sqr = HUGE_VAL;
    std::vector< EntityHandle > leaves;
    const CartVect from( from_coords );
    CartVect closest_pt;

    // Find the leaf containing the input point
    // This search does not take into account any bounding box for the
    // tree, so it always returns one leaf.
    assert( tree_root );
    rval = find_close_triangle( tree_root, from_coords, closest_pt.array(), triangle_out );
    if( MB_SUCCESS != rval ) return rval;

    // Find any other leaves for which the bounding box is within
    // the same distance from the input point as the current closest
    // point is.
    CartVect diff = closest_pt - from;
    rval = distance_search( from_coords, sqrt( diff % diff ), leaves, 1.0e-10, 1.0e-6, NULL, NULL, &tree_root );
    if( MB_SUCCESS != rval ) return rval;

    // Check any close leaves to see if they contain triangles that
    // are as close to or closer than the current closest triangle(s).
    for( unsigned i = 0; i < leaves.size(); ++i )
    {
        rval = closest_to_triangles( moab(), leaves[i], from, shortest_dist_sqr, closest_pt, triangle_out );
        if( MB_SUCCESS != rval ) return rval;
    }

    // pass back resulting position
    closest_pt.get( closest_point_out );
    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::sphere_intersect_triangles( EntityHandle tree_root,
                                                      const double center[3],
                                                      double rad,
                                                      std::vector< EntityHandle >& triangles )
{
    ErrorCode rval;
    std::vector< EntityHandle > leaves;
    const CartVect from( center );
    CartVect closest_pt;
    const EntityHandle* conn;
    CartVect coords[3];
    int conn_len;

    // get leaves of tree that intersect sphere
    assert( tree_root );
    rval = distance_search( center, rad, leaves, 1.0e-10, 1.0e-6, NULL, NULL, &tree_root );
    if( MB_SUCCESS != rval ) return rval;

    // search each leaf for triangles intersecting sphere
    for( unsigned i = 0; i < leaves.size(); ++i )
    {
        Range tris;
        rval = moab()->get_entities_by_type( leaves[i], MBTRI, tris );
        if( MB_SUCCESS != rval ) return rval;

        for( Range::iterator j = tris.begin(); j != tris.end(); ++j )
        {
            rval = moab()->get_connectivity( *j, conn, conn_len );
            if( MB_SUCCESS != rval ) return rval;
            rval = moab()->get_coords( conn, 3, coords[0].array() );
            if( MB_SUCCESS != rval ) return rval;
            GeomUtil::closest_location_on_tri( from, coords, closest_pt );
            closest_pt -= from;
            if( ( closest_pt % closest_pt ) <= ( rad * rad ) ) triangles.push_back( *j );
        }
    }

    // remove duplicates from triangle list
    std::sort( triangles.begin(), triangles.end() );
    triangles.erase( std::unique( triangles.begin(), triangles.end() ), triangles.end() );
    return MB_SUCCESS;
}

struct NodeSeg
{
    NodeSeg( EntityHandle h, double b, double e ) : handle( h ), beg( b ), end( e ) {}
    EntityHandle handle;
    double beg, end;
};

ErrorCode AdaptiveKDTree::ray_intersect_triangles( EntityHandle root,
                                                   const double tol,
                                                   const double ray_dir_in[3],
                                                   const double ray_pt_in[3],
                                                   std::vector< EntityHandle >& tris_out,
                                                   std::vector< double >& dists_out,
                                                   int max_ints,
                                                   double ray_end )
{
    ErrorCode rval;
    double ray_beg = 0.0;
    if( ray_end < 0.0 ) ray_end = HUGE_VAL;

    // if root has bounding box, trim ray to that box
    CartVect tvec( tol );
    BoundBox box;
    const CartVect ray_pt( ray_pt_in ), ray_dir( ray_dir_in );
    rval = get_bounding_box( box );
    if( MB_SUCCESS == rval )
    {
        if( !GeomUtil::segment_box_intersect( box.bMin - tvec, box.bMax + tvec, ray_pt, ray_dir, ray_beg, ray_end ) )
            return MB_SUCCESS;  // ray misses entire tree.
    }

    Range tris;
    Range::iterator iter;
    CartVect tri_coords[3];
    const EntityHandle* tri_conn;
    int conn_len;
    double tri_t;

    Plane plane;
    std::vector< EntityHandle > children;
    std::vector< NodeSeg > list;
    NodeSeg seg( root, ray_beg, ray_end );
    list.push_back( seg );

    while( !list.empty() )
    {
        seg = list.back();
        list.pop_back();

        // If we are limited to a certain number of intersections
        // (max_ints != 0), then ray_end will contain the distance
        // to the furthest intersection we have so far.  If the
        // tree node is further than that, skip it.
        if( seg.beg > ray_end ) continue;

        // Check if at a leaf
        children.clear();
        rval = moab()->get_child_meshsets( seg.handle, children );
        if( MB_SUCCESS != rval ) return rval;
        if( children.empty() )
        {  // leaf

            tris.clear();
            rval = moab()->get_entities_by_type( seg.handle, MBTRI, tris );
            if( MB_SUCCESS != rval ) return rval;

            for( iter = tris.begin(); iter != tris.end(); ++iter )
            {
                rval = moab()->get_connectivity( *iter, tri_conn, conn_len );
                if( MB_SUCCESS != rval ) return rval;
                rval = moab()->get_coords( tri_conn, 3, tri_coords[0].array() );
                if( MB_SUCCESS != rval ) return rval;

                if( GeomUtil::ray_tri_intersect( tri_coords, ray_pt, ray_dir, tri_t, &ray_end ) )
                {
                    if( !max_ints )
                    {
                        if( std::find( tris_out.begin(), tris_out.end(), *iter ) == tris_out.end() )
                        {
                            tris_out.push_back( *iter );
                            dists_out.push_back( tri_t );
                        }
                    }
                    else if( tri_t < ray_end )
                    {
                        if( std::find( tris_out.begin(), tris_out.end(), *iter ) == tris_out.end() )
                        {
                            if( tris_out.size() < (unsigned)max_ints )
                            {
                                tris_out.resize( tris_out.size() + 1 );
                                dists_out.resize( dists_out.size() + 1 );
                            }
                            int w = tris_out.size() - 1;
                            for( ; w > 0 && tri_t < dists_out[w - 1]; --w )
                            {
                                tris_out[w]  = tris_out[w - 1];
                                dists_out[w] = dists_out[w - 1];
                            }
                            tris_out[w]  = *iter;
                            dists_out[w] = tri_t;
                            if( tris_out.size() >= (unsigned)max_ints )
                                // when we have already reached the max intx points, we cans safely
                                // reset ray_end, because we will accept new points only "closer"
                                // than the last one
                                ray_end = dists_out.back();
                        }
                    }
                }
            }

            continue;
        }

        rval = get_split_plane( seg.handle, plane );
        if( MB_SUCCESS != rval ) return rval;

        // Consider two planes that are the split plane +/- the tolerance.
        // Calculate the segment parameter at which the line segment intersects
        // the true plane, and also the difference between that value and the
        // intersection with either of the +/- tol planes.
        const double inv_dir = 1.0 / ray_dir[plane.norm];                       // only do division once
        const double t       = ( plane.coord - ray_pt[plane.norm] ) * inv_dir;  // intersection with plane
        const double diff    = tol * inv_dir;                                   // t adjustment for +tol plane
            // const double t0 = t - diff; // intersection with -tol plane
            // const double t1 = t + diff; // intersection with +tol plane

        // The index of the child tree node (0 or 1) that is on the
        // side of the plane to which the ray direction points.  That is,
        // if the ray direction is opposite the plane normal, the index
        // of the child corresponding to the side beneath the plane.  If
        // the ray direction is the same as the plane normal, the index
        // of the child corresponding to the side above the plane.
        const int fwd_child = ( ray_dir[plane.norm] > 0.0 );

        // Note: we maintain seg.beg <= seg.end at all times, so assume that here.

        // If segment is parallel to plane
        if( !Util::is_finite( t ) )
        {
            if( ray_pt[plane.norm] - tol <= plane.coord ) list.push_back( NodeSeg( children[0], seg.beg, seg.end ) );
            if( ray_pt[plane.norm] + tol >= plane.coord ) list.push_back( NodeSeg( children[1], seg.beg, seg.end ) );
        }
        // If segment is entirely to one side of plane such that the
        // intersection with the split plane is past the end of the segment
        else if( seg.end + diff < t )
        {
            // If segment direction is opposite that of plane normal, then
            // being past the end of the segment means that we are to the
            // right (or above) the plane and what the right child (index == 1).
            // Otherwise we want the left child (index == 0);
            list.push_back( NodeSeg( children[1 - fwd_child], seg.beg, seg.end ) );
        }
        // If the segment is entirely to one side of the plane such that
        // the intersection with the split plane is before the start of the
        // segment
        else if( seg.beg - diff > t )
        {
            // If segment direction is opposite that of plane normal, then
            // being before the start of the segment means that we are to the
            // left (or below) the plane and what the left child (index == 0).
            // Otherwise we want the right child (index == 1);
            list.push_back( NodeSeg( children[fwd_child], seg.beg, seg.end ) );
        }
        // Otherwise we must intersect the plane.
        // Note: be careful not to grow the segment if t is slightly
        // outside the current segment, as doing so would effectively
        // increase the tolerance as we descend the tree.
        else if( t <= seg.beg )
        {
            list.push_back( NodeSeg( children[1 - fwd_child], seg.beg, seg.beg ) );
            list.push_back( NodeSeg( children[fwd_child], seg.beg, seg.end ) );
        }
        else if( t >= seg.end )
        {
            list.push_back( NodeSeg( children[1 - fwd_child], seg.beg, seg.end ) );
            list.push_back( NodeSeg( children[fwd_child], seg.end, seg.end ) );
        }
        else
        {
            list.push_back( NodeSeg( children[1 - fwd_child], seg.beg, t ) );
            list.push_back( NodeSeg( children[fwd_child], t, seg.end ) );
        }
    }

    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::compute_depth( EntityHandle root, unsigned int& min_depth, unsigned int& max_depth )
{
    AdaptiveKDTreeIter iter;
    get_tree_iterator( root, iter );
    iter.step_to_first_leaf( AdaptiveKDTreeIter::LEFT );
    min_depth = max_depth = iter.depth();

    int num_of_elements = 0, max, min;
    moab()->get_number_entities_by_handle( iter.handle(), num_of_elements );
    max = min = num_of_elements;
    int k     = 0;
    while( MB_SUCCESS == iter.step() )
    {
        int temp = 0;
        moab()->get_number_entities_by_handle( iter.handle(), temp );
        max = std::max( max, temp );
        min = std::min( min, temp );
        if( iter.depth() > max_depth )
            max_depth = iter.depth();
        else if( iter.depth() < min_depth )
            min_depth = iter.depth();
        ++k;
    }
    return MB_SUCCESS;
}

ErrorCode AdaptiveKDTree::get_info( EntityHandle root, double bmin[3], double bmax[3], unsigned int& dep )
{
    BoundBox box;
    ErrorCode result = get_bounding_box( box, &root );
    if( MB_SUCCESS != result ) return result;
    box.bMin.get( bmin );
    box.bMax.get( bmax );

    unsigned min_depth;
    return compute_depth( root, min_depth, dep );
}

static std::string mem_to_string( unsigned long mem )
{
    char unit[3] = "B";
    if( mem > 9 * 1024 )
    {
        mem = ( mem + 512 ) / 1024;
        strcpy( unit, "kB" );
    }
    if( mem > 9 * 1024 )
    {
        mem = ( mem + 512 ) / 1024;
        strcpy( unit, "MB" );
    }
    if( mem > 9 * 1024 )
    {
        mem = ( mem + 512 ) / 1024;
        strcpy( unit, "GB" );
    }
    char buffer[256];
    sprintf( buffer, "%lu %s", mem, unit );
    return buffer;
}

template < typename T >
struct SimpleStat
{
    T min, max, sum, sqr;
    size_t count;
    SimpleStat();
    void add( T value );
    double avg() const
    {
        return (double)sum / count;
    }
    double rms() const
    {
        return sqrt( (double)sqr / count );
    }
    double dev() const
    {
        return ( count > 1
                     ? sqrt( ( count * (double)sqr - (double)sum * (double)sum ) / ( (double)count * ( count - 1 ) ) )
                     : 0.0 );
    }
};

template < typename T >
SimpleStat< T >::SimpleStat()
    : min( std::numeric_limits< T >::max() ), max( std::numeric_limits< T >::min() ), sum( 0 ), sqr( 0 ), count( 0 )
{
}

template < typename T >
void SimpleStat< T >::add( T value )
{
    if( value < min ) min = value;
    if( value > max ) max = value;
    sum += value;
    sqr += value * value;
    ++count;
}

ErrorCode AdaptiveKDTree::print()
{
    Range range;

    Range tree_sets, elem2d, elem3d, verts, all;
    moab()->get_child_meshsets( myRoot, tree_sets, 0 );
    for( Range::iterator rit = tree_sets.begin(); rit != tree_sets.end(); ++rit )
    {
        moab()->get_entities_by_dimension( *rit, 2, elem2d );
        moab()->get_entities_by_dimension( *rit, 3, elem3d );
        moab()->get_entities_by_type( *rit, MBVERTEX, verts );
    }
    all.merge( verts );
    all.merge( elem2d );
    all.merge( elem3d );
    tree_sets.insert( myRoot );
    unsigned long long set_used, set_amortized, set_store_used, set_store_amortized, set_tag_used, set_tag_amortized,
        elem_used, elem_amortized;
    moab()->estimated_memory_use( tree_sets, &set_used, &set_amortized, &set_store_used, &set_store_amortized, 0, 0, 0,
                                  0, &set_tag_used, &set_tag_amortized );
    moab()->estimated_memory_use( all, &elem_used, &elem_amortized );

    int num_2d = 0, num_3d = 0;
    ;
    moab()->get_number_entities_by_dimension( 0, 2, num_2d );
    moab()->get_number_entities_by_dimension( 0, 3, num_3d );

    BoundBox box;
    ErrorCode rval = get_bounding_box( box, &myRoot );
    if( MB_SUCCESS != rval || box == BoundBox() ) throw rval;
    double diff[3]        = { box.bMax[0] - box.bMin[0], box.bMax[1] - box.bMin[1], box.bMax[2] - box.bMin[2] };
    double tree_vol       = diff[0] * diff[1] * diff[2];
    double tree_surf_area = 2 * ( diff[0] * diff[1] + diff[1] * diff[2] + diff[2] * diff[0] );

    SimpleStat< unsigned > depth, size;
    SimpleStat< double > vol, surf;

    AdaptiveKDTreeIter iter;
    get_tree_iterator( myRoot, iter );
    do
    {
        depth.add( iter.depth() );

        int num_leaf_elem;
        moab()->get_number_entities_by_handle( iter.handle(), num_leaf_elem );
        size.add( num_leaf_elem );

        const double* n = iter.box_min();
        const double* x = iter.box_max();
        double dims[3]  = { x[0] - n[0], x[1] - n[1], x[2] - n[2] };

        double leaf_vol = dims[0] * dims[1] * dims[2];
        vol.add( leaf_vol );

        double area = 2.0 * ( dims[0] * dims[1] + dims[1] * dims[2] + dims[2] * dims[0] );
        surf.add( area );

    } while( MB_SUCCESS == iter.step() );

    printf( "------------------------------------------------------------------\n" );
    printf( "tree volume:      %f\n", tree_vol );
    printf( "total elements:   %d\n", num_2d + num_3d );
    printf( "number of leaves: %lu\n", (unsigned long)depth.count );
    printf( "number of nodes:  %lu\n", (unsigned long)tree_sets.size() );
    printf( "volume ratio:     %0.2f%%\n", 100 * ( vol.sum / tree_vol ) );
    printf( "surface ratio:    %0.2f%%\n", 100 * ( surf.sum / tree_surf_area ) );
    printf( "\nmemory:           used  amortized\n" );
    printf( "            ---------- ----------\n" );
    printf( "elements    %10s %10s\n", mem_to_string( elem_used ).c_str(), mem_to_string( elem_amortized ).c_str() );
    printf( "sets (total)%10s %10s\n", mem_to_string( set_used ).c_str(), mem_to_string( set_amortized ).c_str() );
    printf( "sets        %10s %10s\n", mem_to_string( set_store_used ).c_str(),
            mem_to_string( set_store_amortized ).c_str() );
    printf( "set tags    %10s %10s\n", mem_to_string( set_tag_used ).c_str(),
            mem_to_string( set_tag_amortized ).c_str() );
    printf( "\nleaf stats:        min        avg        rms        max    std.dev\n" );
    printf( "            ---------- ---------- ---------- ---------- ----------\n" );
    printf( "depth       %10u %10.1f %10.1f %10u %10.2f\n", depth.min, depth.avg(), depth.rms(), depth.max,
            depth.dev() );
    printf( "triangles   %10u %10.1f %10.1f %10u %10.2f\n", size.min, size.avg(), size.rms(), size.max, size.dev() );
    printf( "volume      %10.2g %10.2g %10.2g %10.2g %10.2g\n", vol.min, vol.avg(), vol.rms(), vol.max, vol.dev() );
    printf( "surf. area  %10.2g %10.2g %10.2g %10.2g %10.2g\n", surf.min, surf.avg(), surf.rms(), surf.max,
            surf.dev() );
    printf( "------------------------------------------------------------------\n" );

    return MB_SUCCESS;
}

}  // namespace moab