QuadTree.h

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//     ____   ______ __
//    / __ \ / ____// /
//   / /_/ // /    / /
//  / ____// /___ / /___   PixInsight Class Library
// /_/     \____//_____/   PCL 2.6.11
// ----------------------------------------------------------------------------
// pcl/QuadTree.h - Released 2024-05-07T15:27:32Z
// ----------------------------------------------------------------------------
// This file is part of the PixInsight Class Library (PCL).
// PCL is a multiplatform C++ framework for development of PixInsight modules.
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// ----------------------------------------------------------------------------
 
#ifndef __PCL_QuadTree_h
#define __PCL_QuadTree_h
 
 
#include <pcl/Defs.h>
 
#include <pcl/Array.h>
#include <pcl/Rectangle.h>
#include <pcl/Vector.h>
 
namespace pcl
{
 
// ----------------------------------------------------------------------------
 
/*
 * Default bucket capacity for point region quadtree generation.
 */
#define __PCL_QUADTREE_DEFAULT_BUCKET_CAPACITY  40
 
/*
 * Default minimum allowed dimension of a quadtree node region.
 */
#define __PCL_QUADTREE_DEFAULT_EPSILON          1.0e-08
 
// ----------------------------------------------------------------------------
 
template <class T>
class QuadTree
{
public:
 
   using point = T;
 
   using component = typename point::component;
 
   using point_list = Array<point>;
 
   using rectangle = DRect;
 
   using coordinate = rectangle::component;
 
   // -------------------------------------------------------------------------
 
   struct Node
   {
      rectangle rect = 0.0;   
      Node*     nw = nullptr; 
      Node*     ne = nullptr; 
      Node*     sw = nullptr; 
      Node*     se = nullptr; 
 
#ifdef __PCL_QUADTREE_STRUCTURAL_NODE_HAS_DATA
      void* data = nullptr;
#endif
 
      Node() = default;
 
      Node( const rectangle& r )
         : rect( r )
      {
      }
 
      bool IsLeaf() const
      {
         return nw == nullptr && ne == nullptr && sw == nullptr && se == nullptr;
      }
 
      bool Intersects( const rectangle& r ) const
      {
         return rect.x1 >= r.x0 && rect.x0 <= r.x1 &&
                rect.y1 >= r.y0 && rect.y0 <= r.y1;
      }
 
      bool Includes( coordinate x, coordinate y ) const
      {
         return x >= rect.x0 && x <= rect.x1 &&
                y >= rect.y0 && y <= rect.y1;
      }
 
      bool Includes( const rectangle::point& p ) const
      {
         return Includes( p.x, p.y );
      }
 
      rectangle NWRect() const
      {
         return rectangle( rect.TopLeft(), rect.Center() );
      }
 
      rectangle NERect() const
      {
         return rectangle( rect.CenterTop(), rect.CenterRight() );
      }
 
      rectangle SWRect() const
      {
         return rectangle( rect.CenterLeft(), rect.CenterBottom() );
      }
 
      rectangle SERect() const
      {
         return rectangle( rect.Center(), rect.BottomRight() );
      }
   };
 
   // -------------------------------------------------------------------------
 
   struct LeafNode : public Node
   {
      point_list points;
 
#ifndef __PCL_QUADTREE_STRUCTURAL_NODE_HAS_DATA
 
      void* data = nullptr;
 
#endif
 
      LeafNode( const rectangle& r, const point_list& p )
         : Node( r )
         , points( p )
      {
         PCL_CHECK( !points.IsEmpty() )
      }
 
      LeafNode( const rectangle& r, const point& p )
         : Node( r )
      {
         points << p;
      }
 
      int Length() const
      {
         return int( points.Length() );
      }
   };
 
   // -------------------------------------------------------------------------
 
   QuadTree() = default;
 
   QuadTree( const point_list& points,
             int bucketCapacity = __PCL_QUADTREE_DEFAULT_BUCKET_CAPACITY,
             double epsilon = __PCL_QUADTREE_DEFAULT_EPSILON )
   {
      Build( points, bucketCapacity, epsilon );
   }
 
   QuadTree( const rectangle& rect, const point_list& points,
             int bucketCapacity = __PCL_QUADTREE_DEFAULT_BUCKET_CAPACITY,
             double epsilon = __PCL_QUADTREE_DEFAULT_EPSILON )
   {
      Build( rect, points, bucketCapacity, epsilon );
   }
 
   QuadTree( const QuadTree& ) = delete;
 
   QuadTree& operator =( const QuadTree& ) = delete;
 
   QuadTree( QuadTree&& x )
      : m_root( x.m_root )
      , m_bucketCapacity( x.m_bucketCapacity )
      , m_epsilon( x.m_epsilon )
      , m_length( x.m_length )
   {
      x.m_root = nullptr;
      x.m_length = 0;
   }
 
   QuadTree& operator =( QuadTree&& x )
   {
      if ( &x != this )
      {
         DestroyTree( m_root );
         m_root = x.m_root;
         m_bucketCapacity = x.m_bucketCapacity;
         m_epsilon = x.m_epsilon;
         m_length = x.m_length;
         x.m_root = nullptr;
         x.m_length = 0;
      }
      return *this;
   }
 
   ~QuadTree()
   {
      Clear();
   }
 
   void Clear()
   {
      DestroyTree( m_root );
      m_root = nullptr;
      m_length = 0;
   }
 
   void Build( const point_list& points,
               int bucketCapacity = __PCL_QUADTREE_DEFAULT_BUCKET_CAPACITY,
               double epsilon = __PCL_QUADTREE_DEFAULT_EPSILON )
   {
      Clear();
      m_bucketCapacity = Max( 1, bucketCapacity );
      m_epsilon = Max( 2*std::numeric_limits<coordinate>::epsilon(), epsilon );
 
      if ( !points.IsEmpty() )
      {
         component x = points[0][0];
         component y = points[0][1];
         rectangle rect( x, y, x, y );
         for ( const point& p : points )
         {
            x = p[0];
            y = p[1];
            if ( x < rect.x0 )
               rect.x0 = x;
            if ( y < rect.y0 )
               rect.y0 = y;
            if ( x > rect.x1 )
               rect.x1 = x;
            if ( y > rect.y1 )
               rect.y1 = y;
         }
         m_root = BuildTree( rect, points );
      }
   }
 
   void Build( const rectangle& rect, const point_list& points,
               int bucketCapacity = __PCL_QUADTREE_DEFAULT_BUCKET_CAPACITY,
               double epsilon = __PCL_QUADTREE_DEFAULT_EPSILON )
   {
      Clear();
      m_bucketCapacity = Max( 1, bucketCapacity );
      m_epsilon = Max( 2*std::numeric_limits<coordinate>::epsilon(), epsilon );
      if ( !points.IsEmpty() )
         m_root = BuildTree( rect.Ordered(), points );
   }
 
   point_list Search( const rectangle& rect ) const
   {
      point_list found;
      SearchTree( found, rect.Ordered(), m_root );
      return found;
   }
 
   template <class F>
   void Search( const rectangle& rect, F callback, void* data ) const
   {
      SearchTree( rect.Ordered(), callback, data, m_root );
   }
 
   void Insert( const point& pt )
   {
      if ( m_root != nullptr )
         InsertTree( pt, m_root );
      else
      {
         component x = pt[0];
         component y = pt[1];
         m_root = new LeafNode( rectangle( x, y, x, y ), pt );
      }
   }
 
   void Delete( const point& pt )
   {
      DeleteTree( pt, m_root );
   }
 
   void Delete( const rectangle& rect )
   {
      DeleteTree( rect.Ordered(), m_root );
   }
 
   int BucketCapacity() const
   {
      return m_bucketCapacity;
   }
 
   size_type Length() const
   {
      return m_length;
   }
 
   bool IsEmpty() const
   {
      return m_root == nullptr;
   }
 
   const Node* Root() const
   {
      return m_root;
   }
 
   Node* Root()
   {
      return m_root;
   }
 
   const LeafNode* LeafNodeAt( rectangle::point p ) const
   {
      return SearchLeafNode( p, m_root );
   }
 
   LeafNode* LeafNodeAt( rectangle::point p )
   {
      return SearchLeafNode( p, m_root );
   }
 
   const Node* NodeAt( rectangle::point p ) const
   {
      return SearchNode( p, m_root );
   }
 
   Node* NodeAt( rectangle::point p )
   {
      return SearchNode( p, m_root );
   }
 
   Node* SplitAt( rectangle::point p )
   {
      Node* node = SearchDeepestStructuralNodeAt( p, m_root );
      if ( node != nullptr )
      {
         Node** leaf = nullptr;
         if ( node->nw != nullptr && node->nw->Includes( p ) )
            leaf = &node->nw;
         else if ( node->ne != nullptr && node->ne->Includes( p ) )
            leaf = &node->ne;
         else if ( node->sw != nullptr && node->sw->Includes( p ) )
            leaf = &node->sw;
         else if ( node->se != nullptr && node->se->Includes( p ) )
            leaf = &node->se;
 
         if ( leaf != nullptr ) // cannot be false!
         {
            Node* newNode = SplitLeafNode( *leaf );
            if ( newNode != nullptr ) // should be true
            {
               delete static_cast<LeafNode*>( *leaf );
               *leaf = newNode;
            }
            return newNode;
         }
      }
 
      return nullptr;
   }
 
   template <class F>
   static void Traverse( const Node* node, F f )
   {
      if ( node != nullptr )
         if ( node->IsLeaf() )
            f( node->rect,
               static_cast<const LeafNode*>( node )->points,
               static_cast<const LeafNode*>( node )->data );
         else
         {
            Traverse( node->nw, f );
            Traverse( node->ne, f );
            Traverse( node->sw, f );
            Traverse( node->se, f );
         }
   }
 
   template <class F>
   static void Traverse( Node* node, F f )
   {
      if ( node != nullptr )
         if ( node->IsLeaf() )
            f( node->rect, static_cast<LeafNode*>( node )->points,
                           static_cast<LeafNode*>( node )->data );
         else
         {
            Traverse( node->nw, f );
            Traverse( node->ne, f );
            Traverse( node->sw, f );
            Traverse( node->se, f );
         }
   }
 
   template <class F>
   void Traverse( F f ) const
   {
      Traverse( m_root, f );
   }
 
   template <class F>
   void Traverse( F f )
   {
      Traverse( m_root, f );
   }
 
   static size_type NumberOfNodes( const Node* node )
   {
      size_type N = 0;
      GetNumberOfNodes( N, node );
      return N;
   }
 
   size_type NumberOfNodes() const
   {
      return NumberOfNodes( m_root );
   }
 
   static size_type NumberOfLeafNodes( const Node* node )
   {
      size_type N = 0;
      GetNumberOfLeafNodes( N, node );
      return N;
   }
 
   size_type NumberOfLeafNodes() const
   {
      return NumberOfLeafNodes( m_root );
   }
 
   static int Height( const Node* node )
   {
      return TreeHeight( node, 0 );
   }
 
   int Height() const
   {
      return Height( m_root );
   }
 
   friend void Swap( QuadTree& x1, QuadTree& x2 )
   {
      pcl::Swap( x1.m_root,           x2.m_root );
      pcl::Swap( x1.m_bucketCapacity, x2.m_bucketCapacity );
      pcl::Swap( x1.m_epsilon,        x2.m_epsilon );
      pcl::Swap( x1.m_length,         x2.m_length );
   }
 
private:
 
   Node*     m_root = nullptr;
   int       m_bucketCapacity = 0;
   double    m_epsilon = 0;
   size_type m_length = 0;
 
   Node* NewLeafNode( const rectangle& rect, const point_list& points )
   {
      m_length += points.Length();
      return new LeafNode( rect, points );
   }
 
   LeafNode* SearchLeafNode( const rectangle::point& p, const Node* node ) const
   {
      if ( node != nullptr )
         if ( node->Includes( p ) )
         {
            if ( node->IsLeaf() )
               return const_cast<LeafNode*>( static_cast<const LeafNode*>( node ) );
 
            LeafNode* child = SearchLeafNode( p, node->nw );
            if ( child == nullptr )
            {
               child = SearchLeafNode( p, node->ne );
               if ( child == nullptr )
               {
                  child = SearchLeafNode( p, node->sw );
                  if ( child == nullptr )
                     child = SearchLeafNode( p, node->se );
               }
            }
            return child;
         }
 
      return nullptr;
   }
 
   Node* SearchNode( const rectangle::point& p, const Node* node ) const
   {
      if ( node != nullptr )
         if ( node->Includes( p ) )
         {
            if ( node->IsLeaf() )
               return const_cast<Node*>( node );
 
            Node* child = SearchNode( p, node->nw );
            if ( child == nullptr )
            {
               child = SearchNode( p, node->ne );
               if ( child == nullptr )
               {
                  child = SearchNode( p, node->sw );
                  if ( child == nullptr )
                  {
                     child = SearchNode( p, node->se );
                     if ( child == nullptr )
                        return const_cast<Node*>( node );
                  }
               }
            }
            return child;
         }
 
      return nullptr;
   }
 
   Node* SearchDeepestStructuralNodeAt( const rectangle::point& p, const Node* node ) const
   {
      if ( node != nullptr )
         if ( !node->IsLeaf() )
            if ( node->Includes( p ) )
            {
               Node* child = SearchDeepestStructuralNodeAt( p, node->nw );
               if ( child == nullptr )
               {
                  child = SearchDeepestStructuralNodeAt( p, node->ne );
                  if ( child == nullptr )
                  {
                     child = SearchDeepestStructuralNodeAt( p, node->sw );
                     if ( child == nullptr )
                     {
                        child = SearchDeepestStructuralNodeAt( p, node->se );
                        if ( child == nullptr )
                           return const_cast<Node*>( node );
                     }
                  }
               }
               return child;
            }
 
      return nullptr;
   }
 
   Node* BuildTree( const rectangle& rect, const point_list& points )
   {
      if ( points.IsEmpty() )
         return nullptr;
 
      if ( points.Length() <= size_type( m_bucketCapacity ) )
         return NewLeafNode( rect, points );
 
      double x2 = (rect.x0 + rect.x1)/2;
      double y2 = (rect.y0 + rect.y1)/2;
      // Prevent geometrically degenerate subtrees. For safety, we enforce
      // minimum region dimensions larger than twice the machine epsilon for
      // the rectangle coordinate type.
      if ( x2 - rect.x0 < m_epsilon || rect.x1 - x2 < m_epsilon ||
           y2 - rect.y0 < m_epsilon || rect.y1 - y2 < m_epsilon )
      {
         return NewLeafNode( rect, points );
      }
 
      point_list nw, ne, sw, se;
      for ( const point& p : points )
      {
         component x = p[0];
         component y = p[1];
         if ( x <= x2 )
         {
            if ( y <= y2 )
               nw << p;
            else
               sw << p;
         }
         else
         {
            if ( y <= y2 )
               ne << p;
            else
               se << p;
         }
      }
 
      Node* node = new Node( rect );
      node->nw = BuildTree( rectangle( rect.x0, rect.y0,      x2,      y2 ), nw );
      node->ne = BuildTree( rectangle(      x2, rect.y0, rect.x1,      y2 ), ne );
      node->sw = BuildTree( rectangle( rect.x0,      y2,      x2, rect.y1 ), sw );
      node->se = BuildTree( rectangle(      x2,      y2, rect.x1, rect.y1 ), se );
 
      // Further degeneracies may result, e.g. if the point class is not
      // behaving as expected. Do not allow them.
      if ( node->IsLeaf() )
      {
         delete node;
         return NewLeafNode( rect, points );
      }
 
      return node;
   }
 
   Node* SplitLeafNode( const Node* node )
   {
      if ( node == nullptr || !node->IsLeaf() )
         return nullptr;
 
      double x2 = (node->rect.x0 + node->rect.x1)/2;
      double y2 = (node->rect.y0 + node->rect.y1)/2;
      // Prevent geometrically degenerate subtrees. For safety, we enforce
      // minimum region dimensions larger than twice the machine epsilon for
      // the rectangle coordinate type.
      if ( x2 - node->rect.x0 < m_epsilon || node->rect.x1 - x2 < m_epsilon ||
           y2 - node->rect.y0 < m_epsilon || node->rect.y1 - y2 < m_epsilon )
      {
         return nullptr;
      }
 
      const LeafNode* leaf = static_cast<const LeafNode*>( node );
      point_list nw, ne, sw, se;
      for ( const point& p : leaf->points )
      {
         component x = p[0];
         component y = p[1];
         if ( x <= x2 )
         {
            if ( y <= y2 )
               nw << p;
            else
               sw << p;
         }
         else
         {
            if ( y <= y2 )
               ne << p;
            else
               se << p;
         }
      }
 
      size_type savedLength = m_length;
      Node* newNode = new Node( node->rect );
      newNode->nw = BuildTree( rectangle( node->rect.x0, node->rect.y0,      x2,      y2 ), nw );
      newNode->ne = BuildTree( rectangle(      x2, node->rect.y0, node->rect.x1,      y2 ), ne );
      newNode->sw = BuildTree( rectangle( node->rect.x0,      y2,      x2, node->rect.y1 ), sw );
      newNode->se = BuildTree( rectangle(      x2,      y2, node->rect.x1, node->rect.y1 ), se );
      m_length = savedLength;
 
      // Further degeneracies may result, e.g. if the point class is not
      // behaving as expected. Do not allow them.
      if ( newNode->IsLeaf() )
      {
         delete newNode;
         return nullptr;
      }
 
      return newNode;
   }
 
   void SearchTree( point_list& found, const rectangle& rect, const Node* node ) const
   {
      if ( node != nullptr )
         if ( node->Intersects( rect ) )
            if ( node->IsLeaf() )
            {
               const LeafNode* leaf = static_cast<const LeafNode*>( node );
               for ( const point& p : leaf->points )
               {
                  component x = p[0];
                  if ( x >= rect.x0 )
                     if ( x <= rect.x1 )
                     {
                        component y = p[1];
                        if ( y >= rect.y0 )
                           if ( y <= rect.y1 )
                              found << p;
                     }
               }
            }
            else
            {
               SearchTree( found, rect, node->nw );
               SearchTree( found, rect, node->ne );
               SearchTree( found, rect, node->sw );
               SearchTree( found, rect, node->se );
            }
   }
 
   template <class F>
   void SearchTree( const rectangle& rect, F callback, void* data, const Node* node ) const
   {
      if ( node != nullptr )
         if ( node->Intersects( rect ) )
            if ( node->IsLeaf() )
            {
               const LeafNode* leaf = static_cast<const LeafNode*>( node );
               for ( const point& p : leaf->points )
               {
                  component x = p[0];
                  if ( x >= rect.x0 )
                     if ( x <= rect.x1 )
                     {
                        component y = p[1];
                        if ( y >= rect.y0 )
                           if ( y <= rect.y1 )
                              callback( p, data );
                     }
               }
            }
            else
            {
               SearchTree( rect, callback, data, node->nw );
               SearchTree( rect, callback, data, node->ne );
               SearchTree( rect, callback, data, node->sw );
               SearchTree( rect, callback, data, node->se );
            }
   }
 
   void InsertTree( const point& pt, Node*& node )
   {
      PCL_CHECK( node != nullptr )
 
      component x = pt[0];
      component y = pt[1];
 
      if ( x < node->rect.x0 )
         node->rect.x0 = x;
      else if ( x > node->rect.x1 )
         node->rect.x1 = x;
 
      if ( y < node->rect.y0 )
         node->rect.y0 = y;
      else if ( y > node->rect.y1 )
         node->rect.y1 = y;
 
      if ( node->IsLeaf() )
      {
         LeafNode* leaf = static_cast<LeafNode*>( node );
         if ( leaf->Length() < m_bucketCapacity )
            leaf->points << pt;
         else
         {
            rectangle rect = leaf->rect;
            double x2 = (rect.x0 + rect.x1)/2;
            double y2 = (rect.y0 + rect.y1)/2;
            // Prevent geometrically degenerate subtrees. For safety, we
            // enforce minimum region dimensions larger than twice the
            // machine epsilon for the rectangle coordinate type.
            if ( x2 - rect.x0 < m_epsilon || rect.x1 - x2 < m_epsilon ||
                 y2 - rect.y0 < m_epsilon || rect.y1 - y2 < m_epsilon )
            {
               leaf->points << pt;
            }
            else
            {
               point_list nw, ne, sw, se;
               for ( const point& p : leaf->points )
               {
                  component x = p[0];
                  component y = p[1];
                  if ( x <= x2 )
                  {
                     if ( y <= y2 )
                        nw << p;
                     else
                        sw << p;
                  }
                  else
                  {
                     if ( y <= y2 )
                        ne << p;
                     else
                        se << p;
                  }
               }
 
               if ( x <= x2 )
               {
                  if ( y <= y2 )
                     nw << pt;
                  else
                     sw << pt;
               }
               else
               {
                  if ( y <= y2 )
                     ne << pt;
                  else
                     se << pt;
               }
 
               delete leaf;
 
               node = new Node( rect );
 
               if ( !nw.IsEmpty() )
                  node->nw = new LeafNode( rectangle( rect.x0, rect.y0, x2, y2 ), nw );
               if ( !ne.IsEmpty() )
                  node->ne = new LeafNode( rectangle( x2, rect.y0, rect.x1, y2 ), ne );
               if ( !sw.IsEmpty() )
                  node->sw = new LeafNode( rectangle( rect.x0, y2, x2, rect.y1 ), sw );
               if ( !se.IsEmpty() )
                  node->se = new LeafNode( rectangle( x2, y2, rect.x1, rect.y1 ), se );
            }
         }
 
         ++m_length;
      }
      else
      {
         rectangle rect = node->rect;
         double x2 = (rect.x0 + rect.x1)/2;
         double y2 = (rect.y0 + rect.y1)/2;
         if ( pt[0] <= x2 )
         {
            if ( pt[1] <= y2 )
            {
               if ( node->nw == nullptr )
                  node->nw = new LeafNode( rectangle( rect.x0, rect.y0, x2, y2 ), pt );
               else
                  InsertTree( pt, node->nw );
            }
            else
            {
               if ( node->sw == nullptr )
                  node->sw = new LeafNode( rectangle( rect.x0, y2, x2, rect.y1 ), pt );
               else
                  InsertTree( pt, node->sw );
            }
         }
         else
         {
            if ( pt[1] <= y2 )
            {
               if ( node->ne == nullptr )
                  node->ne = new LeafNode( rectangle( x2, rect.y0, rect.x1, y2 ), pt );
               else
                  InsertTree( pt, node->ne );
            }
            else
            {
               if ( node->se == nullptr )
                  node->se = new LeafNode( rectangle( x2, y2, rect.x1, rect.y1 ), pt );
               else
                  InsertTree( pt, node->se );
            }
         }
      }
   }
 
   void DeleteTree( const rectangle& rect, Node*& node )
   {
      if ( node != nullptr )
         if ( node->Intersects( rect ) )
         {
            if ( node->IsLeaf() )
            {
               LeafNode* leaf = static_cast<LeafNode*>( node );
               point_list points;
               for ( const point& p : leaf->points )
               {
                  component x = p[0];
                  if ( x >= rect.x0 )
                     if ( x <= rect.x1 )
                     {
                        component y = p[1];
                        if ( y >= rect.y0 )
                           if ( y <= rect.y1 )
                           {
                              --m_length;
                              continue;
                           }
                     }
                  points << p;
               }
 
               if ( points.IsEmpty() )
               {
                  delete leaf;
                  node = nullptr;
               }
               else
                  leaf->points = points;
            }
            else
            {
               DeleteTree( rect, node->nw );
               DeleteTree( rect, node->ne );
               DeleteTree( rect, node->sw );
               DeleteTree( rect, node->se );
 
               if ( node->IsLeaf() )
               {
                  delete node;
                  node = nullptr;
               }
            }
         }
   }
 
   void DeleteTree( const point& pt, Node*& node )
   {
      if ( node != nullptr )
      {
         component x = pt[0];
         component y = pt[1];
         if ( node->Includes( x, y ) )
            if ( node->IsLeaf() )
            {
               LeafNode* leaf = static_cast<LeafNode*>( node );
               point_list points;
               for ( const point& p : leaf->points )
               {
                  if ( p[0] == x )
                     if ( p[1] == y )
                     {
                        --m_length;
                        continue;
                     }
                  points << p;
               }
 
               if ( points.IsEmpty() )
               {
                  delete leaf;
                  node = nullptr;
               }
               else
                  leaf->points = points;
            }
            else
            {
               DeleteTree( pt, node->nw );
               DeleteTree( pt, node->ne );
               DeleteTree( pt, node->sw );
               DeleteTree( pt, node->se );
 
               if ( node->IsLeaf() )
               {
                  delete node;
                  node = nullptr;
               }
            }
      }
   }
 
   void DestroyTree( Node* node )
   {
      if ( node != nullptr )
         if ( node->IsLeaf() )
            delete static_cast<LeafNode*>( node );
         else
         {
            DestroyTree( node->nw );
            DestroyTree( node->ne );
            DestroyTree( node->sw );
            DestroyTree( node->se );
            delete node;
         }
   }
 
   static void GetNumberOfNodes( size_type& N, const Node* node )
   {
      if ( node != nullptr )
      {
         ++N;
         GetNumberOfNodes( N, node->nw );
         GetNumberOfNodes( N, node->ne );
         GetNumberOfNodes( N, node->sw );
         GetNumberOfNodes( N, node->se );
      }
   }
 
   static void GetNumberOfLeafNodes( size_type& N, const Node* node )
   {
      if ( node != nullptr )
      {
         if ( node->IsLeaf() )
            ++N;
         GetNumberOfLeafNodes( N, node->nw );
         GetNumberOfLeafNodes( N, node->ne );
         GetNumberOfLeafNodes( N, node->sw );
         GetNumberOfLeafNodes( N, node->se );
      }
   }
 
   static int TreeHeight( const Node* node, int h )
   {
      if ( node == nullptr )
         return h;
      return h + 1 + Max( Max( Max( TreeHeight( node->nw, h ),
                                    TreeHeight( node->ne, h ) ),
                                    TreeHeight( node->sw, h ) ),
                                    TreeHeight( node->se, h ) );
   }
};
 
// ----------------------------------------------------------------------------
 
} // pcl
 
#endif   // __PCL_QuadTree_h
 
// ----------------------------------------------------------------------------
// EOF pcl/QuadTree.h - Released 2024-05-07T15:27:32Z