add RTree classes

[anneal.git] / src / com / infomatiq / jsi / rtree / RTree.java

//   RTree.java
//   Java Spatial Index Library
//   Copyright (C) 2002 Infomatiq Limited
//  
//  This library is free software; you can redistribute it and/or
//  modify it under the terms of the GNU Lesser General Public
//  License as published by the Free Software Foundation; either
//  version 2.1 of the License, or (at your option) any later version.
//  
//  This library is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//  Lesser General Public License for more details.
//  
//  You should have received a copy of the GNU Lesser General Public
//  License along with this library; if not, write to the Free Software
//  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

package com.infomatiq.jsi.rtree;

import gnu.trove.TIntArrayList;
import gnu.trove.TIntObjectHashMap;
import gnu.trove.TIntProcedure;
import gnu.trove.TIntStack;
import java.util.Properties;

import com.infomatiq.jsi.IntProcedure;
import com.infomatiq.jsi.Point;
import com.infomatiq.jsi.Rectangle;
import com.infomatiq.jsi.SpatialIndex;

/**
 * <p>This is a lightweight RTree implementation, specifically designed 
 * for the following features (in order of importance): 
 * <ul>
 * <li>Fast intersection query performance. To achieve this, the RTree 
 * uses only main memory to store entries. Obviously this will only improve
 * performance if there is enough physical memory to avoid paging.</li>
 * <li>Low memory requirements.</li>
 * <li>Fast add performance.</li>
 * </ul></p> 
 * 
 * <p>The main reason for the high speed of this RTree implementation is the 
 * avoidance of the creation of unnecessary objects, mainly achieved by using
 * primitive collections from the trove4j library.</p>
 * 
 * @author aled.morris@infomatiq.co.uk
 * @version 1.0b2
 */
public class RTree implements SpatialIndex {
  
  private static final String version = "1.0b2";
  
  // parameters of the tree
  private final static int DEFAULT_MAX_NODE_ENTRIES = 10;
  int maxNodeEntries;
  int minNodeEntries;
  
  // map of nodeId -> node object
  // [x] TODO eliminate this map - it should not be needed. Nodes
  // can be found by traversing the tree.
  private TIntObjectHashMap nodeMap = new TIntObjectHashMap();
  
  // internal consistency checking - set to true if debugging tree corruption
  private final static boolean INTERNAL_CONSISTENCY_CHECKING = false;
  
  // used to mark the status of entries during a node split
  private final static int ENTRY_STATUS_ASSIGNED = 0;
  private final static int ENTRY_STATUS_UNASSIGNED = 1; 
  private byte[] entryStatus = null;
  private byte[] initialEntryStatus = null;
  
  // stacks used to store nodeId and entry index of each node 
  // from the root down to the leaf. Enables fast lookup
  // of nodes when a split is propagated up the tree.
  private TIntStack parents = new TIntStack();
  private TIntStack parentsEntry = new TIntStack();
  
  // initialisation
  private int treeHeight = 1; // leaves are always level 1
  private int rootNodeId = 0;
  private int size = 0;
  
  // Enables creation of new nodes
  private int highestUsedNodeId = rootNodeId; 
  
  // Deleted node objects are retained in the nodeMap, 
  // so that they can be reused. Store the IDs of nodes
  // which can be reused.
  private TIntStack deletedNodeIds = new TIntStack();
  
  // List of nearest rectangles. Use a member variable to
  // avoid recreating the object each time nearest() is called.
  private TIntArrayList nearestIds = new TIntArrayList();
  
  // Inner class used as a bridge between the trove4j TIntProcedure
  // and the SpatialIndex IntProcedure. This is used because 
  // the nearest rectangles must be stored as they are found, in
  // case a closer one is found later. 
  // 
  // A single instance of this class is used to avoid creating a new 
  // one every time nearest() is called.
  private class TIntProcedureVisit implements TIntProcedure {
        public IntProcedure m_intProcedure = null;
        
        public void setProcedure(IntProcedure ip) {
          m_intProcedure = ip;
        }
        public boolean execute(int i) {
          m_intProcedure.execute(i);
          return true;
        }
  }; 
  private TIntProcedureVisit visitProc = new TIntProcedureVisit();
  
  /**
   * Constructor. Use init() method to initialize parameters of the RTree.
   */
  public RTree() {  
    return; // NOP    
  }
  
  //-------------------------------------------------------------------------
  // public implementation of SpatialIndex interface:
  //  init(Properties)
  //  add(Rectangle, int)
  //  delete(Rectangle, int)
  //  nearest(Point, IntProcedure, float)
  //  intersects(Rectangle, IntProcedure)
  //  contains(Rectangle, IntProcedure)
  //  size()
  //-------------------------------------------------------------------------
  /**
   * <p>Initialize implementation dependent properties of the RTree.
   * Currently implemented properties are:
   * <ul>
   * <li>MaxNodeEntries</li> This specifies the maximum number of entries
   * in a node. The default value is 10, which is used if the property is
   * not specified, or is less than 2.
   * <li>MinNodeEntries</li> This specifies the minimum number of entries
   * in a node. The default value is half of the MaxNodeEntries value (rounded
   * down), which is used if the property is not specified or is less than 1.
   * </ul></p>
   * 
   * @see com.infomatiq.jsi.SpatialIndex#init(Properties)
   */
  public void init(Properties props) {
    maxNodeEntries = Integer.parseInt(props.getProperty("MaxNodeEntries", "0"));
    minNodeEntries = Integer.parseInt(props.getProperty("MinNodeEntries", "0"));
    
    // Obviously a node with less than 2 entries cannot be split.
    // The node splitting algorithm will work with only 2 entries
    // per node, but will be inefficient.
    if (maxNodeEntries < 2) { 
      System.err.println("Invalid MaxNodeEntries = " + maxNodeEntries + " Resetting to default value of " + DEFAULT_MAX_NODE_ENTRIES);
      maxNodeEntries = DEFAULT_MAX_NODE_ENTRIES;
    }
    
    // The MinNodeEntries must be less than or equal to (int) (MaxNodeEntries / 2)
    if (minNodeEntries < 1 || minNodeEntries > maxNodeEntries / 2) {
      System.err.println("MinNodeEntries must be between 1 and MaxNodeEntries / 2");
      minNodeEntries = maxNodeEntries / 2;
    }
    
    entryStatus = new byte[maxNodeEntries];  
    initialEntryStatus = new byte[maxNodeEntries];
    
    for (int i = 0; i < maxNodeEntries; i++) {
      initialEntryStatus[i] = ENTRY_STATUS_UNASSIGNED;
    }
    
    Node root = new Node(rootNodeId, 1, maxNodeEntries);
    nodeMap.put(rootNodeId, root);
    
  }
  
  /**
   * @see com.infomatiq.jsi.SpatialIndex#add(Rectangle, int)
   */
  public void add(Rectangle r, int id) {
      /*
    if (log.isDebugEnabled()) {
    //////log.debug("Adding rectangle " + r + ", id " + id);
    }
      */
    add(r.copy(), id, 1); 
    
    size++; 
  }
  
  /**
   * Adds a new entry at a specified level in the tree
   */
  private void add(Rectangle r, int id, int level) {
    // I1 [Find position for new record] Invoke ChooseLeaf to select a 
    // leaf node L in which to place r
    Node n = chooseNode(r, level);
    Node newLeaf = null;
    
    // I2 [Add record to leaf node] If L has room for another entry, 
    // install E. Otherwise invoke SplitNode to obtain L and LL containing
    // E and all the old entries of L
    if (n.entryCount < maxNodeEntries) {
      n.addEntryNoCopy(r, id);
    } else {
      newLeaf = splitNode(n, r, id);  
    }
    
    // I3 [Propagate changes upwards] Invoke AdjustTree on L, also passing LL
    // if a split was performed
    Node newNode = adjustTree(n, newLeaf); 

    // I4 [Grow tree taller] If node split propagation caused the root to 
    // split, create a new root whose children are the two resulting nodes.
    if (newNode != null) {
      int oldRootNodeId = rootNodeId;
      Node oldRoot = getNode(oldRootNodeId);
      
      rootNodeId = getNextNodeId();
      treeHeight++;
      Node root = new Node(rootNodeId, treeHeight, maxNodeEntries);
      root.addEntry(newNode.mbr, newNode.nodeId);
      root.addEntry(oldRoot.mbr, oldRoot.nodeId);
      nodeMap.put(rootNodeId, root);
    }
    
    if (INTERNAL_CONSISTENCY_CHECKING) {
      checkConsistency(rootNodeId, treeHeight, null);
    }
  } 
  
  /**
   * @see com.infomatiq.jsi.SpatialIndex#delete(Rectangle, int)
   */
  public boolean delete(Rectangle r, int id) {
   // FindLeaf algorithm inlined here. Note the "official" algorithm 
   // searches all overlapping entries. This seems inefficient to me, 
   // as an entry is only worth searching if it contains (NOT overlaps)
   // the rectangle we are searching for.
   //
   // Also the algorithm has been changed so that it is not recursive.
    
    // FL1 [Search subtrees] If root is not a leaf, check each entry 
    // to determine if it contains r. For each entry found, invoke
    // findLeaf on the node pointed to by the entry, until r is found or
    // all entries have been checked.
        parents.clear();
        parents.push(rootNodeId);
        
        parentsEntry.clear();
        parentsEntry.push(-1);
        Node n = null;
        int foundIndex = -1;  // index of entry to be deleted in leaf
        
        while (foundIndex == -1 && parents.size() > 0) {
          n = getNode(parents.peek());
          int startIndex = parentsEntry.peek() + 1;
      
      if (!n.isLeaf()) {
          /*
            //deleteLog.debug("searching node " + n.nodeId + ", from index " + startIndex);
          */
                  boolean contains = false;
        for (int i = startIndex; i < n.entryCount; i++) {
                    if (n.entries[i].contains(r)) {
                      parents.push(n.ids[i]);
                      parentsEntry.pop();
                      parentsEntry.push(i); // this becomes the start index when the child has been searched
                      parentsEntry.push(-1);
                      contains = true;
            break; // ie go to next iteration of while()
                    }
                  }
        if (contains) {
          continue;
        }
      } else {
        foundIndex = n.findEntry(r, id);        
      }
      
      parents.pop();
      parentsEntry.pop();
        } // while not found
        
        if (foundIndex != -1) {
          n.deleteEntry(foundIndex, minNodeEntries);
      condenseTree(n);
      size--;
        }
    
    return (foundIndex != -1);
  }
  
  /**
   * @see com.infomatiq.jsi.SpatialIndex#nearest(Point, IntProcedure, float)
   */
  public void nearest(Point p, IntProcedure v, float furthestDistance) {
    Node rootNode = getNode(rootNodeId);
   
    nearest(p, rootNode, furthestDistance);
   
    visitProc.setProcedure(v);
    nearestIds.forEach(visitProc);
    nearestIds.clear();
  }
   
  /**
   * @see com.infomatiq.jsi.SpatialIndex#intersects(Rectangle, IntProcedure)
   */
  public void intersects(Rectangle r, IntProcedure v) {
    Node rootNode = getNode(rootNodeId);
    intersects(r, v, rootNode);
  }

  /**
   * @see com.infomatiq.jsi.SpatialIndex#contains(Rectangle, IntProcedure)
   */
  public void contains(Rectangle r, IntProcedure v) {
    // find all rectangles in the tree that are contained by the passed rectangle
    // written to be non-recursive (should model other searches on this?)
        
    parents.clear();
    parents.push(rootNodeId);
    
    parentsEntry.clear();
    parentsEntry.push(-1);
    
    // TODO: possible shortcut here - could test for intersection with the 
    // MBR of the root node. If no intersection, return immediately.
    
    while (parents.size() > 0) {
      Node n = getNode(parents.peek());
      int startIndex = parentsEntry.peek() + 1;
      
      if (!n.isLeaf()) {
        // go through every entry in the index node to check
        // if it intersects the passed rectangle. If so, it 
        // could contain entries that are contained.
        boolean intersects = false;
        for (int i = startIndex; i < n.entryCount; i++) {
          if (r.intersects(n.entries[i])) {
            parents.push(n.ids[i]);
            parentsEntry.pop();
            parentsEntry.push(i); // this becomes the start index when the child has been searched
            parentsEntry.push(-1);
            intersects = true;
            break; // ie go to next iteration of while()
          }
        }
        if (intersects) {
          continue;
        }
      } else {
        // go through every entry in the leaf to check if 
        // it is contained by the passed rectangle
        for (int i = 0; i < n.entryCount; i++) {
          if (r.contains(n.entries[i])) {
            v.execute(n.ids[i]);
          } 
        }                       
      }
      parents.pop();
      parentsEntry.pop();  
    }
  }

  /**
   * @see com.infomatiq.jsi.SpatialIndex#size()
   */
  public int size() {
    return size;
  }

  /**
   * @see com.infomatiq.jsi.SpatialIndex#getBounds()
   */
  public Rectangle getBounds() {
    Rectangle bounds = null;
    
    Node n = getNode(getRootNodeId());
    if (n != null && n.getMBR() != null) {
      bounds = n.getMBR().copy();
    }
    return bounds;
  }
    
  /**
   * @see com.infomatiq.jsi.SpatialIndex#getVersion()
   */
  public String getVersion() {
    return "RTree-" + version;
  }
  //-------------------------------------------------------------------------
  // end of SpatialIndex methods
  //-------------------------------------------------------------------------
  
  /**
   * Get the next available node ID. Reuse deleted node IDs if
   * possible
   */
  private int getNextNodeId() {
    int nextNodeId = 0;
    if (deletedNodeIds.size() > 0) {
      nextNodeId = deletedNodeIds.pop();
    } else {
      nextNodeId = 1 + highestUsedNodeId++;
    }
    return nextNodeId;
  }

  /**
   * Get a node object, given the ID of the node.
   */
  public Node getNode(int index) {
    return (Node) nodeMap.get(index);
  }

  /**
   * Get the highest used node ID
   */  
  public int getHighestUsedNodeId() {
    return highestUsedNodeId;
  }

  /**
   * Get the root node ID
   */
  public int getRootNodeId() {
    return rootNodeId; 
  }
      
  /**
   * Split a node. Algorithm is taken pretty much verbatim from
   * Guttman's original paper.
   * 
   * @return new node object.
   */
  private Node splitNode(Node n, Rectangle newRect, int newId) {
    // [Pick first entry for each group] Apply algorithm pickSeeds to 
    // choose two entries to be the first elements of the groups. Assign
    // each to a group.
    
    // debug code
    float initialArea = 0;
    /*
    if (log.isDebugEnabled()) {
      Rectangle union = n.mbr.union(newRect);
      initialArea = union.area();
    }
    */ 
    System.arraycopy(initialEntryStatus, 0, entryStatus, 0, maxNodeEntries);
    
    Node newNode = null;
    newNode = new Node(getNextNodeId(), n.level, maxNodeEntries);
    nodeMap.put(newNode.nodeId, newNode);
    
    pickSeeds(n, newRect, newId, newNode); // this also sets the entryCount to 1
    
    // [Check if done] If all entries have been assigned, stop. If one
    // group has so few entries that all the rest must be assigned to it in 
    // order for it to have the minimum number m, assign them and stop. 
    while (n.entryCount + newNode.entryCount < maxNodeEntries + 1) {
      if (maxNodeEntries + 1 - newNode.entryCount == minNodeEntries) {
        // assign all remaining entries to original node
        for (int i = 0; i < maxNodeEntries; i++) {
          if (entryStatus[i] == ENTRY_STATUS_UNASSIGNED) {
            entryStatus[i] = ENTRY_STATUS_ASSIGNED;
            n.mbr.add(n.entries[i]);
            n.entryCount++;
          }
        }
        break;
      }   
      if (maxNodeEntries + 1 - n.entryCount == minNodeEntries) {
        // assign all remaining entries to new node
        for (int i = 0; i < maxNodeEntries; i++) {
          if (entryStatus[i] == ENTRY_STATUS_UNASSIGNED) {
            entryStatus[i] = ENTRY_STATUS_ASSIGNED;
            newNode.addEntryNoCopy(n.entries[i], n.ids[i]);
            n.entries[i] = null;
          }
        }
        break;
      }
      
      // [Select entry to assign] Invoke algorithm pickNext to choose the
      // next entry to assign. Add it to the group whose covering rectangle 
      // will have to be enlarged least to accommodate it. Resolve ties
      // by adding the entry to the group with smaller area, then to the 
      // the one with fewer entries, then to either. Repeat from S2
      pickNext(n, newNode);   
    }
      
    n.reorganize(this);
    
    // check that the MBR stored for each node is correct.
    if (INTERNAL_CONSISTENCY_CHECKING) {
      if (!n.mbr.equals(calculateMBR(n))) {
          throw new Error("Error: splitNode old node MBR wrong");
      }
      
      if (!newNode.mbr.equals(calculateMBR(newNode))) {
        throw new Error("Error: splitNode new node MBR wrong");
      }
    }
    
    // debug code
    /*
    if (log.isDebugEnabled()) {
      float newArea = n.mbr.area() + newNode.mbr.area();
      float percentageIncrease = (100 * (newArea - initialArea)) / initialArea;
      //log.debug("Node " + n.nodeId + " split. New area increased by " + percentageIncrease + "%");   
    }
    */
    return newNode;
  }
  
  /**
   * Pick the seeds used to split a node.
   * Select two entries to be the first elements of the groups
   */
  private void pickSeeds(Node n, Rectangle newRect, int newId, Node newNode) {
    // Find extreme rectangles along all dimension. Along each dimension,
    // find the entry whose rectangle has the highest low side, and the one 
    // with the lowest high side. Record the separation.
    float maxNormalizedSeparation = 0;
    int highestLowIndex = 0;
    int lowestHighIndex = 0;
    
    // for the purposes of picking seeds, take the MBR of the node to include
    // the new rectangle aswell.
    n.mbr.add(newRect);
    
    /*
    if (log.isDebugEnabled()) {
        //log.debug("pickSeeds(): NodeId = " + n.nodeId + ", newRect = " + newRect);
    }
    */
    
    for (int d = 0; d < Rectangle.DIMENSIONS; d++) {
      float tempHighestLow = newRect.min[d];
      int tempHighestLowIndex = -1; // -1 indicates the new rectangle is the seed
      
      float tempLowestHigh = newRect.max[d];
      int tempLowestHighIndex = -1;
      
      for (int i = 0; i < n.entryCount; i++) {
        float tempLow = n.entries[i].min[d];
        if (tempLow >= tempHighestLow) {
           tempHighestLow = tempLow;
           tempHighestLowIndex = i;
        } else {  // ensure that the same index cannot be both lowestHigh and highestLow
          float tempHigh = n.entries[i].max[d];
          if (tempHigh <= tempLowestHigh) {
            tempLowestHigh = tempHigh;
            tempLowestHighIndex = i;
          }
        }
      
        // PS2 [Adjust for shape of the rectangle cluster] Normalize the separations
        // by dividing by the widths of the entire set along the corresponding
        // dimension
        float normalizedSeparation = (tempHighestLow - tempLowestHigh) / (n.mbr.max[d] - n.mbr.min[d]);
        
        if (normalizedSeparation > 1 || normalizedSeparation < -1) {
          throw new Error("Invalid normalized separation");
        }
      
        /*
        if (log.isDebugEnabled()) {
            log.debug("Entry " + i + ", dimension " + d + ": HighestLow = " + tempHighestLow + 
                    " (index " + tempHighestLowIndex + ")" + ", LowestHigh = " +
                    tempLowestHigh + " (index " + tempLowestHighIndex + ", NormalizedSeparation = " + normalizedSeparation);
        }
        */
        
        // PS3 [Select the most extreme pair] Choose the pair with the greatest
        // normalized separation along any dimension.
        if (normalizedSeparation > maxNormalizedSeparation) {
          maxNormalizedSeparation = normalizedSeparation;
          highestLowIndex = tempHighestLowIndex;
          lowestHighIndex = tempLowestHighIndex;
        }
      }
    }
      
    // highestLowIndex is the seed for the new node.
    if (highestLowIndex == -1) {
      newNode.addEntry(newRect, newId);
    } else {
      newNode.addEntryNoCopy(n.entries[highestLowIndex], n.ids[highestLowIndex]);
      n.entries[highestLowIndex] = null;
      
      // move the new rectangle into the space vacated by the seed for the new node
      n.entries[highestLowIndex] = newRect;
      n.ids[highestLowIndex] = newId;
    }
    
    // lowestHighIndex is the seed for the original node. 
    if (lowestHighIndex == -1) {
      lowestHighIndex = highestLowIndex;
    }
    
    entryStatus[lowestHighIndex] = ENTRY_STATUS_ASSIGNED;
    n.entryCount = 1;
    n.mbr.set(n.entries[lowestHighIndex].min, n.entries[lowestHighIndex].max);
  }

  /** 
   * Pick the next entry to be assigned to a group during a node split.
   * 
   * [Determine cost of putting each entry in each group] For each 
   * entry not yet in a group, calculate the area increase required
   * in the covering rectangles of each group  
   */
  private int pickNext(Node n, Node newNode) {
    float maxDifference = Float.NEGATIVE_INFINITY;
    int next = 0;
    int nextGroup = 0;
    
    maxDifference = Float.NEGATIVE_INFINITY;
   
    /*
    if (log.isDebugEnabled()) {
        //log.debug("pickNext()");
    }
    */
   
    for (int i = 0; i < maxNodeEntries; i++) {
      if (entryStatus[i] == ENTRY_STATUS_UNASSIGNED) {
        
        if (n.entries[i] == null) {
          throw new Error("Error: Node " + n.nodeId + ", entry " + i + " is null");
        }
        
        float nIncrease = n.mbr.enlargement(n.entries[i]);
        float newNodeIncrease = newNode.mbr.enlargement(n.entries[i]);
        float difference = Math.abs(nIncrease - newNodeIncrease);
         
        if (difference > maxDifference) {
          next = i;
          
          if (nIncrease < newNodeIncrease) {
            nextGroup = 0; 
          } else if (newNodeIncrease < nIncrease) {
            nextGroup = 1;
          } else if (n.mbr.area() < newNode.mbr.area()) {
            nextGroup = 0;
          } else if (newNode.mbr.area() < n.mbr.area()) {
            nextGroup = 1;
          } else if (newNode.entryCount < maxNodeEntries / 2) {
            nextGroup = 0;
          } else {
            nextGroup = 1;
          }
          maxDifference = difference; 
        }
        /*
        if (log.isDebugEnabled()) {
            log.debug("Entry " + i + " group0 increase = " + nIncrease + ", group1 increase = " + newNodeIncrease +
                    ", diff = " + difference + ", MaxDiff = " + maxDifference + " (entry " + next + ")");
        }
        */
      }
    }
    
    entryStatus[next] = ENTRY_STATUS_ASSIGNED;
      
    if (nextGroup == 0) {
      n.mbr.add(n.entries[next]);
      n.entryCount++;
    } else {
      // move to new node.
      newNode.addEntryNoCopy(n.entries[next], n.ids[next]);
      n.entries[next] = null;
    }
    
    return next; 
  }

  /**
   * Recursively searches the tree for the nearest entry. Other queries
   * call execute() on an IntProcedure when a matching entry is found; 
   * however nearest() must store the entry Ids as it searches the tree,
   * in case a nearer entry is found.
   * Uses the member variable nearestIds to store the nearest
   * entry IDs.
   * 
   * [x] TODO rewrite this to be non-recursive?
   */
  private float nearest(Point p, Node n, float nearestDistance) {
    for (int i = 0; i < n.entryCount; i++) {
      float tempDistance = n.entries[i].distance(p);  
      if (n.isLeaf()) { // for leaves, the distance is an actual nearest distance 
        if (tempDistance < nearestDistance) {
          nearestDistance = tempDistance;
          nearestIds.clear();
        }
        if (tempDistance <= nearestDistance) {
          nearestIds.add(n.ids[i]);
        }     
      } else { // for index nodes, only go into them if they potentially could have
               // a rectangle nearer than actualNearest
         if (tempDistance <= nearestDistance) {
           // search the child node
           nearestDistance = nearest(p, getNode(n.ids[i]), nearestDistance);
         }
      }
    }
    return nearestDistance;
  }
  
  /** 
   * Recursively searches the tree for all intersecting entries.
   * Immediately calls execute() on the passed IntProcedure when 
   * a matching entry is found.
   * 
   * [x] TODO rewrite this to be non-recursive? Make sure it
   * doesn't slow it down.
   */
  private void intersects(Rectangle r, IntProcedure v, Node n) {
    for (int i = 0; i < n.entryCount; i++) {
      if (r.intersects(n.entries[i])) {
        if (n.isLeaf()) {
          v.execute(n.ids[i]);
        } else {
          Node childNode = getNode(n.ids[i]);
          intersects(r, v, childNode);
        }
      }
    }
  }

  /**
   * Used by delete(). Ensures that all nodes from the passed node
   * up to the root have the minimum number of entries.
   * 
   * Note that the parent and parentEntry stacks are expected to
   * contain the nodeIds of all parents up to the root.
   */
    private Rectangle oldRectangle = new Rectangle(0, 0, 0, 0, 0, 0);
  private void condenseTree(Node l) {
    // CT1 [Initialize] Set n=l. Set the list of eliminated
    // nodes to be empty.
    Node n = l;
    Node parent = null;
    int parentEntry = 0;
    
    TIntStack eliminatedNodeIds = new TIntStack();
  
    // CT2 [Find parent entry] If N is the root, go to CT6. Otherwise 
    // let P be the parent of N, and let En be N's entry in P  
    while (n.level != treeHeight) {
      parent = getNode(parents.pop());
      parentEntry = parentsEntry.pop();
      
      // CT3 [Eliminiate under-full node] If N has too few entries,
      // delete En from P and add N to the list of eliminated nodes
      if (n.entryCount < minNodeEntries) {
        parent.deleteEntry(parentEntry, minNodeEntries);
        eliminatedNodeIds.push(n.nodeId);
      } else {
        // CT4 [Adjust covering rectangle] If N has not been eliminated,
        // adjust EnI to tightly contain all entries in N
        if (!n.mbr.equals(parent.entries[parentEntry])) {
          oldRectangle.set(parent.entries[parentEntry].min, parent.entries[parentEntry].max);
          parent.entries[parentEntry].set(n.mbr.min, n.mbr.max);
          parent.recalculateMBR(oldRectangle);
        }
      }
      // CT5 [Move up one level in tree] Set N=P and repeat from CT2
      n = parent;
    }
    
    // CT6 [Reinsert orphaned entries] Reinsert all entries of nodes in set Q.
    // Entries from eliminated leaf nodes are reinserted in tree leaves as in 
    // Insert(), but entries from higher level nodes must be placed higher in 
    // the tree, so that leaves of their dependent subtrees will be on the same
    // level as leaves of the main tree
    while (eliminatedNodeIds.size() > 0) {
      Node e = getNode(eliminatedNodeIds.pop());
      for (int j = 0; j < e.entryCount; j++) {
        add(e.entries[j], e.ids[j], e.level); 
        e.entries[j] = null;
      }
      e.entryCount = 0;
      deletedNodeIds.push(e.nodeId);
    }
  }

  /**
   *  Used by add(). Chooses a leaf to add the rectangle to.
   */
  private Node chooseNode(Rectangle r, int level) {
    // CL1 [Initialize] Set N to be the root node
    Node n = getNode(rootNodeId);
    parents.clear();
    parentsEntry.clear();
     
    // CL2 [Leaf check] If N is a leaf, return N
    while (true) {
      if (n == null) {
        throw new Error("Could not get root node (" + rootNodeId + ")");  
      }
   
      if (n.level == level) {
        return n;
      }
      
      // CL3 [Choose subtree] If N is not at the desired level, let F be the entry in N 
      // whose rectangle FI needs least enlargement to include EI. Resolve
      // ties by choosing the entry with the rectangle of smaller area.
      float leastEnlargement = n.getEntry(0).enlargement(r);
      int index = 0; // index of rectangle in subtree
      for (int i = 1; i < n.entryCount; i++) {
        Rectangle tempRectangle = n.getEntry(i);
        float tempEnlargement = tempRectangle.enlargement(r);
        if ((tempEnlargement < leastEnlargement) ||
            ((tempEnlargement == leastEnlargement) && 
             (tempRectangle.area() < n.getEntry(index).area()))) {
          index = i;
          leastEnlargement = tempEnlargement;
        }
      }
      
      parents.push(n.nodeId);
      parentsEntry.push(index);
    
      // CL4 [Descend until a leaf is reached] Set N to be the child node 
      // pointed to by Fp and repeat from CL2
      n = getNode(n.ids[index]);
    }
  }
  
  /**
   * Ascend from a leaf node L to the root, adjusting covering rectangles and
   * propagating node splits as necessary.
   */
  private Node adjustTree(Node n, Node nn) {
    // AT1 [Initialize] Set N=L. If L was split previously, set NN to be 
    // the resulting second node.
    
    // AT2 [Check if done] If N is the root, stop
    while (n.level != treeHeight) {
    
      // AT3 [Adjust covering rectangle in parent entry] Let P be the parent 
      // node of N, and let En be N's entry in P. Adjust EnI so that it tightly
      // encloses all entry rectangles in N.
      Node parent = getNode(parents.pop());
      int entry = parentsEntry.pop(); 
      
      if (parent.ids[entry] != n.nodeId) {
        throw new Error("Error: entry " + entry + " in node " + 
             parent.nodeId + " should point to node " + 
             n.nodeId + "; actually points to node " + parent.ids[entry]);
      }
      
      if (!parent.entries[entry].equals(n.mbr)) {
        parent.entries[entry].set(n.mbr.min, n.mbr.max);
        parent.mbr.set(parent.entries[0].min, parent.entries[0].max);
        for (int i = 1; i < parent.entryCount; i++) {
          parent.mbr.add(parent.entries[i]);
        }
      }
      
      // AT4 [Propagate node split upward] If N has a partner NN resulting from 
      // an earlier split, create a new entry Enn with Ennp pointing to NN and 
      // Enni enclosing all rectangles in NN. Add Enn to P if there is room. 
      // Otherwise, invoke splitNode to produce P and PP containing Enn and
      // all P's old entries.
      Node newNode = null;
      if (nn != null) {
        if (parent.entryCount < maxNodeEntries) {
          parent.addEntry(nn.mbr, nn.nodeId);
        } else {
          newNode = splitNode(parent, nn.mbr.copy(), nn.nodeId);
        }
      }
      
      // AT5 [Move up to next level] Set N = P and set NN = PP if a split 
      // occurred. Repeat from AT2
      n = parent;
      nn = newNode;
      
      parent = null;
      newNode = null;
    }
    
    return nn;
  }
  
  /**
   * Check the consistency of the tree.
   */
  private void checkConsistency(int nodeId, int expectedLevel, Rectangle expectedMBR) {
    // go through the tree, and check that the internal data structures of 
    // the tree are not corrupted.    
    Node n = getNode(nodeId);
    
    if (n == null) {
      throw new Error("Error: Could not read node " + nodeId);
    }
    
    if (n.level != expectedLevel) {
      throw new Error("Error: Node " + nodeId + ", expected level " + expectedLevel + ", actual level " + n.level);
    }
    
    Rectangle calculatedMBR = calculateMBR(n);
    
    if (!n.mbr.equals(calculatedMBR)) {
      throw new Error("Error: Node " + nodeId + ", calculated MBR does not equal stored MBR");
    }
    
    if (expectedMBR != null && !n.mbr.equals(expectedMBR)) {
      throw new Error("Error: Node " + nodeId + ", expected MBR (from parent) does not equal stored MBR");
    }
    
    // Check for corruption where a parent entry is the same object as the child MBR
    if (expectedMBR != null && n.mbr.sameObject(expectedMBR)) {
      throw new Error("Error: Node " + nodeId + " MBR using same rectangle object as parent's entry");
    }
    
    for (int i = 0; i < n.entryCount; i++) {
      if (n.entries[i] == null) {
        throw new Error("Error: Node " + nodeId + ", Entry " + i + " is null");
      }     
      
      if (n.level > 1) { // if not a leaf
        checkConsistency(n.ids[i], n.level - 1, n.entries[i]); 
      }   
    } 
  }
  
  /**
   * Given a node object, calculate the node MBR from it's entries.
   * Used in consistency checking
   */
  private Rectangle calculateMBR(Node n) {
    Rectangle mbr = new Rectangle(n.entries[0].min, n.entries[0].max);
    
    for (int i = 1; i < n.entryCount; i++) {
      mbr.add(n.entries[i]);
    }
    return mbr; 
  }
}