Clear And Efficient 3D Range Tree Implementation

Question

I\'m working on this project where I have to search for objects in 3d space, and efficiency is a huge concern, I think Range Tree is perfect for what I\'m tryin

Answer 1

I just read the wikipedia article. Lets see if I can write an n dimensional range tree. Because anything worth doing in 3 dimensions is worth doing in n.

So the basic part of an n-dimensional range tree is that it can be recursively defined in terms of lower dimensional range trees.

Some property classes to work with relatively generic value types. Specialize element_properties to set the scalar type of whatever your n-dimensional value is, and specialize get(T const&) to get the ith dimension of your n-dimensional value.

#include 
#include 
#include 
#include 
#include 
#include 
#include 

void Assert(bool test) {
  if (!test)
  {
    std::cout << "Assert failed" << std::endl;
    exit(-1);
  }
}
template
struct Print {
  static void Do(Args... args) {}
};
template
struct Print {
  static void Do(Arg arg, Tail... args) {
      std::cout << arg;
      Print::Do(args...);
  }
};
template
void Debug(Args... args) {
    std::cout << "DEBUG:[";
    Print::Do(args...);
    std::cout << "]\n";
}

template
struct element_properties {
  typedef typename T::value_type value_type;
};
template<>
struct element_properties {
  typedef int value_type;
};
template
typename element_properties::value_type get( T const & t );

template
typename element_properties::value_type get( int i ) { return i; }

template
typename element_properties>::value_type get( std::vector const& v) {
  return v[d];
}

template::value_type> >
struct range_tree {
  typedef typename element_properties::value_type value_type;
  struct sorter {
    bool operator()( T const& left, T const& right ) const {
      return Order()( get(left), get(right) );
    }
  };
  struct printer {
    std::string operator()( T const& t ) const {
      std::string retval = "[ ";
      retval += print_elements( t );
      retval += "]";
      return retval;
    }
    std::string print_elements( T const& t ) const {
      std::stringstream ss;
      typedef typename range_tree::printer next_printer;
      ss << next_printer().print_elements(t);
      ss << get(t) << " ";
      return ss.str();
    }
  };
  template
  range_tree( Iterator begin, Iterator end ) {
    std::sort( begin, end, sorter() );
    root.reset( new tree_node( begin, end ) );
  }

  template
  void walk(Func f) const {
      if (root) root->walk(f);
  }
  template
  void walk(Func f) {
      if (root) root->walk(f);
  }
  struct tree_node {
    std::unique_ptr< range_tree > subtree;
    T value;
    template
    void walk(Func f) const {
      if (n==dim && !left && !right)
        f(value);
      if (left)
        left->walk(f);
      if (right)
        right->walk(f);
      if (subtree)
        subtree->walk(f);
    }
    template
    void walk(Func f) {
      if (n==dim && !left && !right)
        f(value);
      if (left)
        left->walk(f);
      if (right)
        right->walk(f);
      if (subtree)
        subtree->walk(f);
    }
    void find_path( T const& t, std::vector< tree_node const* >& vec ) {
      vec.push_back(this);
      if ( sorter()(t, value) ) {
        if (left)
          left->find_path(t, vec);
      } else if (sorter()(value, t)) {
        if (right)
          right->find_path(t, vec);
      } else {
        // found it!
        return;
      }
    }
    std::vector< tree_node const* > range_search( T const& left, T const& right )
    {
      std::vector left_path;
      std::vector right_path;
      find_path( left, left_path );
      find_path( right, right_path );
      // erase common path:
      {
        auto it1 = left_path.begin();
        auto it2 = right_path.begin();
        for( ; it1 != left_path.end() && it2 != right_path.end(); ++it1, ++it2) {
          if (*it1 != *it2)
          {
            Debug( "Different: ", printer()( (*it1)->value ), ", ", printer()( (*it2)->value ) );
            break;
          }

          Debug( "Identical: ", printer()( (*it1)->value ), ", ", printer()( (*it2)->value ) );
        }
        // remove identical prefixes:
        if (it2 == right_path.end() && it2 != right_path.begin())
            --it2;
        if (it1 == left_path.end() && it1 != left_path.begin())
            --it1;
        right_path.erase( right_path.begin(), it2 );
        left_path.erase( left_path.begin(), it1 );
      }
      for (auto it = left_path.begin(); it != left_path.end(); ++it) {
        if (*it && (*it)->right) {
          Debug( "Has right child: ", printer()( (*it)->value ) );
          *it = (*it)->right.get();
          Debug( "It is: ", printer()( (*it)->value ) );
        } else {
          Debug( "Has no right child: ", printer()( (*it)->value ) );
          if ( sorter()( (*it)->value, left) || sorter()( right, (*it)->value) ) {
            Debug( printer()( (*it)->value ), "<", printer()( left ), " so erased" );
            *it = 0;
          }
        }
      }
      for (auto it = right_path.begin(); it != right_path.end(); ++it) {
        if (*it && (*it)->left) {
          Debug( "Has left child: ", printer()( (*it)->value ) );
          *it = (*it)->left.get();
          Debug( "It is: ", printer()( (*it)->value ) );
        } else {
          Debug( "Has no left child: ", printer()( (*it)->value ) );
          if ( sorter()( (*it)->value, left) || sorter()( right, (*it)->value) ) {
            Debug( printer()( right ), "<", printer()( (*it)->value ), " so erased" );
            *it = 0;
          }
        }
      }
      left_path.insert( left_path.end(), right_path.begin(), right_path.end() );
      // remove duds and duplicates:
      auto highwater = std::remove_if( left_path.begin(), left_path.end(), []( tree_node const* n) { return n==0; } );
      std::sort( left_path.begin(), highwater );
      left_path.erase( std::unique( left_path.begin(), highwater ), left_path.end() );
      return left_path;
    }

    std::unique_ptr left;
    std::unique_ptr right;
    // rounds down:
    template
    static Iterator middle( Iterator begin, Iterator end ) {
      return (end-begin-1)/2 + begin ;
    }
    template
    tree_node( Iterator begin, Iterator end ):value(*middle(begin,end)) {
      Debug( "Inserted ", get(value), " at level ", dim );
      Iterator mid = middle(begin,end);
      Assert( begin != end );
      if (begin +1 != end) { // not a leaf
        Debug( "Not a leaf at level ", dim );
        ++mid; // so *mid was the last element in the left sub tree 
        Assert(mid!=begin);
        Assert(mid!=end);
        left.reset( new tree_node( begin, mid ) );
        right.reset( new tree_node( mid, end ) );
      } else {
        Debug( "Leaf at level ", dim );
      }
      if (dim > 0) {
        subtree.reset( new range_tree( begin, end ) );
      }
    }
  };
  std::unique_ptr root;
};
// makes the code above a tad easier:
template
struct range_tree< T, 0, Order > {
  typedef typename element_properties::value_type value_type;
  struct printer { templatestd::string print_elements(Unused const&) {return std::string();} };
  range_tree(...) {};
  struct tree_node {}; // maybe some stub functions in here
  template
  void walk(Func f) {}
};

int main() {
  typedef std::vector vector_type;
  std::vector test;
  test.push_back( vector_type{5,2} );
  test.push_back( vector_type{2,3} );
  range_tree< vector_type, 2 > tree( test.begin(), test.end() );
  std::cout << "Walking dim 2:";
  auto print_node = [](vector_type const& v){ std::cout << "(" << v[0] << "," << v[1] << ")"; };
  tree.walk<2>( print_node );
  std::cout << "\nWalking dim 1:";
  tree.walk<1>( print_node );
  std::cout << "\n";

  std::cout << "Range search from {3,3} to {10,10}\n";
  auto nodes = tree.root->range_search( vector_type{3,3}, vector_type{10,10} );
  for (auto it = nodes.begin(); it != nodes.end(); ++it)
  {
    (*it)->walk<2>( print_node );
  }
}

which is pretty damn close to an n-dimensional range tree. The 0 dimension tree naturally contains nothing.

Basic facilities to search (in one dimension at a time) have been added now. You can manually do the recursions into lower dimensions, or it up so that the range_search always returns level 1 tree_node*s.