element_tree.hpp

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/**
 * element_tree.hpp
 * Ryan H. Lewis
 * (C) 2012
 *
 * An element tree partitions a mesh composed of elements.
 * We subdivide the bounding box of a mesh, and each element is
 * either entirely on the left, entirely on the right, or crossing
 * the diving line. We build a tree on the mesh with this property.
 */
#include <vector>
#include <set>
#include <iostream>
#include <map>
#include <algorithm>
#include <bitset>
#include <numeric>
#include <cmath>
#include <tr1/unordered_map>
#include <limits>

#include "common_tree.hpp"

#ifndef ELEMENT_TREE_HPP
#define ELEMENT_TREE_HPP
namespace moab
{
// forward declarations

template < typename _Entity_handles, typename _Box, typename _Moab, typename _Parametrizer >
class Element_tree;

// non-exported functionality
namespace
{
    namespace _element_tree
    {
        template < typename Iterator >
        struct Iterator_comparator
        {
            typedef typename Iterator::value_type Value;
            bool operator()( const Value& a, const Value& b )
            {
                return a->second.second.to_ulong() < b->second.second.to_ulong();
            }
        };  // Iterator_comparator

        template < typename Data >
        struct Split_comparator
        {
            // we minimizes ||left| - |right|| + |middle|^2
            double split_objective( const Data& a ) const
            {
                if( a.second.sizes[2] == 0 || a.second.sizes[0] == 0 )
                {
                    return std::numeric_limits< std::size_t >::max();
                }
                const double total = a.second.sizes[0] + a.second.sizes[2];
                const int max      = 2 * ( a.second.sizes[2] > a.second.sizes[0] );

                return ( a.second.sizes[max] - a.second.sizes[2 * ( 1 - ( max == 2 ) )] ) / total;
            }
            bool operator()( const Data& a, const Data& b ) const
            {
                return split_objective( a ) < split_objective( b );
            }
        };  // Split_comparator

        template < typename Partition_data, typename Box >
        void correct_bounding_box( const Partition_data& data, Box& box, const int child )
        {
            const int dim = data.dim;
            switch( child )
            {
                case 0:
                    box.max[dim] = data.left_rightline;
                    break;
                case 1:
                    box.max[dim] = data.right_line;
                    box.min[dim] = data.left_line;
                    break;
                case 2:
                    box.min[dim] = data.right_leftline;
                    break;
            }
#ifdef ELEMENT_TREE_DEBUG
            print_vector( data.bounding_box.max );
            print_vector( data.bounding_box.min );
            print_vector( box.max );
            print_vector( box.min );
#endif
        }

        template < typename Box >
        struct _Partition_data
        {
            typedef _Partition_data< Box > Self;
            // default constructor
            _Partition_data() : sizes( 3, 0 ), dim( 0 ) {}
            _Partition_data( const Self& f )
            {
                *this = f;
            }
            _Partition_data( const Box& _box, int _dim )
                : sizes( 3, 0 ), bounding_box( _box ), split( ( _box.max[_dim] + _box.min[_dim] ) / 2.0 ),
                  left_line( split ), right_line( split ), dim( _dim )
            {
            }
            _Partition_data& operator=( const Self& f )
            {
                sizes          = f.sizes;
                bounding_box   = f.bounding_box;
                split          = f.split;
                left_line      = f.left_line;
                right_line     = f.right_line;
                right_leftline = f.right_leftline;
                left_rightline = f.left_rightline;
                dim            = f.dim;
                return *this;
            }
            std::vector< std::size_t > sizes;
            Box bounding_box;
            double split;
            double left_line;
            double right_line;
            double right_leftline;
            double left_rightline;
            int dim;
            std::size_t left() const
            {
                return sizes[0];
            }
            std::size_t middle() const
            {
                return sizes[1];
            }
            std::size_t right() const
            {
                return sizes[2];
            }
        };  // Partition_data

        template < typename _Entity_handles, typename _Entities >
        class _Node
        {
            // public types:
          public:
            typedef _Entity_handles Entity_handles;
            typedef _Entities Entities;

            // private types:
          private:
            typedef _Node< _Entity_handles, _Entities > Self;

            // Constructors
          public:
            // Default constructor
            _Node()
                : children( 3, -1 ), left_( children[0] ), middle_( children[1] ), right_( children[2] ), dim( -1 ),
                  split( 0 ), left_line( 0 ), right_line( 0 ), entities( 0 )
            {
            }

            // Copy constructor
            _Node( const Self& from )
                : children( from.children ), left_( children[0] ), middle_( children[1] ), right_( children[2] ),
                  dim( from.dim ), split( from.split ), left_line( from.left_line ), right_line( from.right_line ),
                  entities( from.entities )
            {
            }

          public:
            template < typename Iterator >
            void assign_entities( const Iterator& begin, const Iterator& end )
            {
                entities.reserve( std::distance( begin, end ) );
                for( Iterator i = begin; i != end; ++i )
                {
                    entities.push_back( std::make_pair( ( *i )->second.first, ( *i )->first ) );
                }
            }

            // Functionality
          public:
            bool leaf() const
            {
                return children[0] == -1 && children[1] == -1 && children[2] == -1;
            }
            Self& operator=( const Self& from )
            {
                children   = from.children;
                dim        = from.dim;
                left_      = from.left_;
                middle_    = from.middle_;
                right_     = from.right_;
                split      = from.split;
                left_line  = from.left_line;
                right_line = from.right_line;
                entities   = from.entities;
                return *this;
            }
            template < typename Box >
            Self& operator=( const _Partition_data< Box >& from )
            {
                dim        = from.dim;
                split      = from.split;
                left_line  = from.left_line;
                right_line = from.right_line;
                return *this;
            }
            // private data members:
          private:
            // indices of children
            std::vector< int > children;
            int &left_, middle_, right_;
            int dim;       // split dimension
            double split;  // split position
            double left_line;
            double right_line;
            Entities entities;

            // Element_tree can touch my privates.
            template < Entity_handles, typename B >
            friend class moab::Element_tree;
        };  // class Node

    }  // namespace _element_tree
}  // namespace

template < typename _Entity_handles, typename _Box, typename _Moab, typename _Parametrizer >
class Element_tree
{

    // public types
  public:
    typedef _Entity_handles Entity_handles;
    typedef _Box Box;
    typedef _Moab Moab;
    typedef _Parametrizer Parametrizer;
    typedef typename Entity_handles::value_type Entity_handle;

    // private types
  private:
    typedef Element_tree< _Entity_handles, _Box, _Moab, _Parametrizer > Self;
    typedef std::pair< Box, Entity_handle > Leaf_element;
    typedef _element_tree::_Node< Entity_handles, std::vector< Leaf_element > > Node;
// int is because we only need to store
#define MAX_ITERATIONS 2
    typedef common_tree::_Element_data< Box, std::bitset< NUM_DIM * MAX_ITERATIONS * 2 > > Element_data;
    typedef std::vector< Node > Nodes;
    // TODO: we really want an unordered map here, make sure this is kosher..
    typedef std::tr1::unordered_map< Entity_handle, Element_data > Element_map;
    typedef typename std::vector< typename Element_map::iterator > Element_list;
    typedef _element_tree::_Partition_data< Box > Partition_data;
    // public methods
  public:
    // Constructor
    Element_tree( Entity_handles& _entities, Moab& _moab, Box& _bounding_box, Parametrizer& _entity_contains )
        : entity_handles_( _entities ), tree_(), moab( _moab ), bounding_box( _bounding_box ),
          entity_contains( _entity_contains )
    {
        tree_.reserve( _entities.size() );
        Element_map element_map( _entities.size() );
        Partition_data _data;
        common_tree::construct_element_map( entity_handles_, element_map, _data.bounding_box, moab );
        bounding_box  = _data.bounding_box;
        _bounding_box = bounding_box;
        Element_list element_ordering( element_map.size() );
        std::size_t index = 0;
        for( typename Element_map::iterator i = element_map.begin(); i != element_map.end(); ++i, ++index )
        {
            element_ordering[index] = i;
        }
        // We only build nonempty trees
        if( element_ordering.size() )
        {
            // initially all bits are set
            std::bitset< 3 > directions( 7 );
            tree_.push_back( Node() );
            int depth = 0;
            build_tree( element_ordering.begin(), element_ordering.end(), 0, directions, _data, depth );
            std::cout << "depth: " << depth << std::endl;
        }
    }

    // Copy constructor
    Element_tree( Self& s )
        : entity_handles_( s.entity_handles_ ), tree_( s.tree_ ), moab( s.moab ), bounding_box( s.bounding_box )
    {
    }

    // private functionality
  private:
    template < typename Iterator, typename Split_data >
    void compute_split( Iterator& begin, Iterator& end, Split_data& split_data, bool iteration = false )
    {
        typedef typename Iterator::value_type::value_type Map_value_type;
        typedef typename Map_value_type::second_type::second_type Bitset;
        // we will update the left/right line
        double& left_line  = split_data.left_line;
        double& right_line = split_data.right_line;
        double& split      = split_data.split;
        const int& dim     = split_data.dim;
#ifdef ELEMENT_TREE_DEBUG
        std::cout << std::endl;
        std::cout << "-------------------" << std::endl;
        std::cout << "dim: " << dim << " split: " << split << std::endl;
        std::cout << "bounding_box min: ";
        print_vector( split_data.bounding_box.min );
        std::cout << "bounding_box max: ";
        print_vector( split_data.bounding_box.max );
#endif
        // for each elt determine if left/middle/right
        for( Iterator i = begin; i != end; ++i )
        {
            const Box& box = ( *i )->second.first;
            Bitset& bits   = ( *i )->second.second;
            // will be 0 if on left, will be 1 if in the middle
            // and 2 if on the right;
            const bool on_left   = ( box.max[dim] < split );
            const bool on_right  = ( box.min[dim] > split );
            const bool in_middle = !on_left && !on_right;
            // set the corresponding bits in the bit vector
            // looks like: [x_1 = 00 | x_2 = 00 | .. | z_1 = 00 | z_2 = 00]
            // two bits, left = 00, middle = 01, right = 10
            const int index = 4 * dim + 2 * iteration;
            if( on_left ) { split_data.sizes[0]++; }
            else if( in_middle )
            {
                split_data.sizes[1]++;
                bits.set( index, 1 );
                left_line  = std::min( left_line, box.min[dim] );
                right_line = std::max( right_line, box.max[dim] );
            }
            else if( on_right )
            {
                bits.set( index + 1, 1 );
                split_data.sizes[2]++;
            }
        }
#ifdef ELEMENT_TREE_DEBUG
        std::size_t _count = std::accumulate( split_data.sizes.begin(), split_data.sizes.end(), 0 );
        std::size_t total  = std::distance( begin, end );
        if( total != _count ) { std::cout << total << "vs. " << _count << std::endl; }
        std::cout << " left_line: " << left_line;
        std::cout << " right_line: " << right_line << std::endl;
        std::cout << "co/mputed partition size: ";
        print_vector( split_data.sizes );
        std::cout << "-------------------" << std::endl;
#endif
    }

    template < typename Split_data >
    bool update_split_line( Split_data& data ) const
    {
        const int max        = 2 * ( data.sizes[2] > data.sizes[0] );
        const int min        = 2 * ( 1 - ( max == 2 ) );
        bool one_side_empty  = data.sizes[max] == 0 || data.sizes[min] == 0;
        double balance_ratio = data.sizes[max] - data.sizes[min];
        // if ( !one_side_empty && balance_ratio < .05*total){ return false; }
        if( !one_side_empty )
        {
            // if we have some imbalance on left/right
            // try to fix the situation
            balance_ratio /= data.sizes[max];
            data.split += ( max - 1 ) * balance_ratio * ( data.split / 2.0 );
        }
        else
        {
            // if the (left) side is empty move the split line just past the
            // extent of the (left) line of the middle box.
            // if middle encompasses everything then wiggle
            // the split line a bit and hope for the best..
            const double left_distance  = std::abs( data.left_line - data.split );
            const double right_distance = std::abs( data.right_line - data.split );
            if( ( data.sizes[0] == 0 ) && ( data.sizes[2] != 0 ) ) { data.split += right_distance; }
            else if( data.sizes[2] == 0 && data.sizes[0] != 0 )
            {
                data.split -= left_distance;
            }
            else
            {
                data.split *= 1.05;
            }
        }
        data.left_line = data.right_line = data.split;
        data.sizes.assign( data.sizes.size(), 0 );
        return true;
    }

    template < typename Iterator, typename Split_data, typename Directions >
    void determine_split( Iterator& begin, Iterator& end, Split_data& data, const Directions& directions )
    {
        typedef typename Iterator::value_type Pair;
        typedef typename Pair::value_type Map_value_type;
        typedef typename Map_value_type::second_type::second_type Bitset;
        typedef typename Map_value_type::second_type::first_type Box;
        typedef typename std::map< std::size_t, Split_data > Splits;
        typedef typename Splits::value_type Split;
        typedef _element_tree::Split_comparator< Split > Comparator;
        Splits splits;
        for( std::size_t dir = 0; dir < directions.size(); ++dir )
        {
            if( directions.test( dir ) )
            {
                Split_data split_data( data.bounding_box, dir );
                compute_split( begin, end, split_data );
                splits.insert( std::make_pair( 2 * dir, split_data ) );
                if( update_split_line( split_data ) )
                {
                    compute_split( begin, end, split_data, true );
                    splits.insert( std::make_pair( 2 * dir + 1, split_data ) );
                }
            }
        }
        Split best = *std::min_element( splits.begin(), splits.end(), Comparator() );
#ifdef ELEMENT_TREE_DEBUG
        std::cout << "best: " << Comparator().split_objective( best ) << " ";
        print_vector( best.second.sizes );
#endif
        const int dir          = best.first / 2;
        const int iter         = best.first % 2;
        double& left_rightline = best.second.left_rightline = best.second.bounding_box.min[dir];
        double& right_leftline = best.second.right_leftline = best.second.bounding_box.max[dir];
        Bitset mask( 0 );
        mask.flip( 4 * dir + 2 * iter ).flip( 4 * dir + 2 * iter + 1 );
        for( Iterator i = begin; i != end; ++i )
        {
            Bitset& bits   = ( *i )->second.second;
            const Box& box = ( *i )->second.first;
            // replace 12 bits with just two.
            bits &= mask;
            bits >>= 4 * dir + 2 * iter;
            // if box is labeled left/right but properly contained
            // in the middle, move the element into the middle.
            // we can shrink the size of left/right
            switch( bits.to_ulong() )
            {
                case 0:
                    if( box.max[dir] > best.second.left_line )
                    {
                        left_rightline = std::max( left_rightline, box.max[dir] );
                    }
                    break;
                case 2:
                    if( box.min[dir] < best.second.right_line )
                    {
                        right_leftline = std::min( right_leftline, box.max[dir] );
                    }
                    break;
            }
        }
        data = best.second;
    }

// define here for now.
#define ELEMENTS_PER_LEAF 30
#define MAX_DEPTH         30
#define EPSILON           1e-1
    template < typename Iterator, typename Node_index, typename Directions, typename Partition_data >
    void build_tree( Iterator begin, Iterator end, const Node_index node, const Directions& directions,
                     Partition_data& _data, int& depth, const bool is_middle = false )
    {
        std::size_t number_elements = std::distance( begin, end );
        if( depth < MAX_DEPTH && number_elements > ELEMENTS_PER_LEAF && ( !is_middle || directions.any() ) )
        {
            determine_split( begin, end, _data, directions );
            // count_sort( begin, end, _data);
            std::sort( begin, end, _element_tree::Iterator_comparator< Iterator >() );
            // update the tree
            tree_[node] = _data;
            Iterator middle_begin( begin + _data.left() );
            Iterator middle_end( middle_begin + _data.middle() );
            std::vector< int > depths( 3, depth );
            // left subtree
            if( _data.left() > 0 )
            {
                Partition_data data( _data );
                tree_.push_back( Node() );
                tree_[node].children[0] = tree_.size() - 1;
                correct_bounding_box( _data, data.bounding_box, 0 );
                Directions new_directions( directions );
                const bool axis_is_very_small =
                    ( data.bounding_box.max[_data.dim] - data.bounding_box.min[_data.dim] < EPSILON );
                new_directions.set( _data.dim, axis_is_very_small );
                build_tree( begin, middle_begin, tree_[node].children[0], new_directions, data, ++depths[0],
                            is_middle );
            }
            // middle subtree
            if( _data.middle() > 0 )
            {
                Partition_data data( _data );
                tree_.push_back( Node() );
                tree_[node].children[1] = tree_.size() - 1;
                correct_bounding_box( _data, data.bounding_box, 1 );
                // force the middle subtree to split
                // in a different direction from this one
                Directions new_directions( directions );
                new_directions.flip( tree_[node].dim );
                bool axis_is_very_small =
                    ( data.bounding_box.max[_data.dim] - data.bounding_box.min[_data.dim] < EPSILON );
                new_directions.set( _data.dim, axis_is_very_small );
                build_tree( middle_begin, middle_end, tree_[node].children[1], new_directions, data, ++depths[1],
                            true );
            }
            // right subtree
            if( _data.right() > 0 )
            {
                Partition_data data( _data );
                tree_.push_back( Node() );
                tree_[node].children[2] = tree_.size() - 1;
                correct_bounding_box( _data, data.bounding_box, 2 );
                Directions new_directions( directions );
                const bool axis_is_very_small =
                    ( data.bounding_box.max[_data.dim] - data.bounding_box.min[_data.dim] < EPSILON );
                new_directions.set( _data.dim, axis_is_very_small );

                build_tree( middle_end, end, tree_[node].children[2], directions, data, ++depths[2], is_middle );
            }
            depth = *std::max_element( depths.begin(), depths.end() );
        }
        if( tree_[node].leaf() ) { common_tree::assign_entities( tree_[node].entities, begin, end ); }
    }

    template < typename Vector, typename Node_index, typename Result >
    Result& _find_point( const Vector& point, const Node_index& index, Result& result ) const
    {
        typedef typename Node::Entities::const_iterator Entity_iterator;
        typedef typename std::pair< bool, Vector > Return_type;
        const Node& node = tree_[index];
        if( node.leaf() )
        {
            // check each node
            for( Entity_iterator i = node.entities.begin(); i != node.entities.end(); ++i )
            {
                if( common_tree::box_contains_point( i->first, point ) )
                {
                    Return_type r = entity_contains( moab, i->second, point );
                    if( r.first ) { result = std::make_pair( i->second, r.second ); }
                    return result;
                }
            }
            return Result( 0, point );
        }
        if( point[node.dim] < node.left_line ) { return _find_point( point, node.left_, result ); }
        else if( point[node.dim] > node.right_line )
        {
            return _find_point( point, node.right_, result );
        }
        else
        {
            Entity_handle middle = _find_point( point, node.middle_, result );
            if( middle != 0 ) { return result; }
            if( point[node.dim] < node.split ) { return _find_point( point, node.left_, result ); }
            return _find_point( point, node.right_, result );
        }
    }

    // public functionality
  public:
    template < typename Vector, typename Result >
    Result& find( const Vector& point, Result& result ) const
    {
        typedef typename Vector::const_iterator Point_iterator;
        typedef typename Box::Pair Pair;
        typedef typename Pair::first_type Box_iterator;
        return _find_point( point, 0, result );
    }

    // public accessor methods
  public:
    // private data members
  private:
    const Entity_handles& entity_handles_;
    Nodes tree_;
    Moab& moab;
    Box bounding_box;
    Parametrizer entity_contains;

};  // class Element_tree

}  // namespace moab

#endif  // ELEMENT_TREE_HPP