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