vtkKdTree.cxx

/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkKdTree.cxx

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/

/*----------------------------------------------------------------------------
 Copyright (c) Sandia Corporation
 See Copyright.txt or http://www.paraview.org/HTML/Copyright.html for details.
----------------------------------------------------------------------------*/

#include "vtkKdTree.h"

#include "vtkKdNode.h"
#include "vtkBSPCuts.h"
#include "vtkBSPIntersections.h"
#include "vtkObjectFactory.h"
#include "vtkDataSet.h"
#include "vtkDataSetCollection.h"
#include "vtkFloatArray.h"
#include "vtkMath.h"
#include "vtkCell.h"
#include "vtkCellArray.h"
#include "vtkGarbageCollector.h"
#include "vtkIdList.h"
#include "vtkPolyData.h"
#include "vtkPoints.h"
#include "vtkIdTypeArray.h"
#include "vtkIntArray.h"
#include "vtkPointSet.h"
#include "vtkImageData.h"
#include "vtkUniformGrid.h"
#include "vtkRectilinearGrid.h"
#include "vtkCallbackCommand.h"

#ifdef _MSC_VER
#pragma warning ( disable : 4100 )
#endif
#include <vtkstd/algorithm>
#include <vtkstd/list>
#include <vtkstd/map>
#include <vtkstd/queue>
#include <vtkstd/set>


// Timing data ---------------------------------------------

#include "vtkTimerLog.h"

#define MSGSIZE 60

static char dots[MSGSIZE] = "...........................................................";
static char msg[MSGSIZE];

//-----------------------------------------------------------------------------
static void LastInputDeletedCallback(vtkObject *, unsigned long,
                                     void *_self, void *)
{
  vtkKdTree *self = reinterpret_cast<vtkKdTree *>(_self);

  self->InvalidateGeometry();
}

//----------------------------------------------------------------------------
static char * makeEntry(const char *s)
{
  memcpy(msg, dots, MSGSIZE);
  int len = static_cast<int>(strlen(s));
  len = (len >= MSGSIZE) ? MSGSIZE-1 : len;

  memcpy(msg, s, len);

  return msg;
}

#define TIMER(s)         \
  if (this->Timing)      \
    {                    \
    char *s2 = makeEntry(s);               \
    if (this->TimerLog == NULL){           \
      this->TimerLog = vtkTimerLog::New(); \
      }                                    \
    this->TimerLog->MarkStartEvent(s2);    \
    }

#define TIMERDONE(s) \
  if (this->Timing){ char *s2 = makeEntry(s); this->TimerLog->MarkEndEvent(s2); }

// Timing data ---------------------------------------------

// helper class for ordering the points in vtkKdTree::FindClosestNPoints()
namespace
{
  class OrderPoints
  {
  public:
    OrderPoints(int N) 
      {
        this->NumDesiredPoints = N;
        this->NumPoints = 0;
        this->LargestDist2 = VTK_LARGE_FLOAT;
      }

    void InsertPoint(float dist2, vtkIdType id)
      {
        if(dist2 <= this->LargestDist2 || this->NumPoints < this->NumDesiredPoints)
          {
          vtkstd::map<float, vtkstd::list<vtkIdType> >::iterator it=this->dist2ToIds.find(dist2);
          this->NumPoints++;
          if(it == this->dist2ToIds.end())
            {
            vtkstd::list<vtkIdType> idset;
            idset.push_back(id);
            this->dist2ToIds[dist2] = idset;
            }
          else
            {
            it->second.push_back(id);
            }
          if(this->NumPoints > this->NumDesiredPoints)
            {
            it=this->dist2ToIds.end(); 
            it--;
            if((this->NumPoints-it->second.size()) > this->NumDesiredPoints)
              {
              this->NumPoints -= it->second.size();
              vtkstd::map<float, vtkstd::list<vtkIdType> >::iterator it2 = it;
              it2--;
              this->LargestDist2 = it2->first;
              this->dist2ToIds.erase(it);
              }
            }
          }
      }
    void GetSortedIds(vtkIdList* ids)
      {
        ids->Reset();
        vtkIdType numIds = (this->NumDesiredPoints < this->NumPoints) 
          ? this->NumDesiredPoints : this->NumPoints;
        ids->SetNumberOfIds(numIds);
        vtkIdType counter = 0;
        vtkstd::map<float, vtkstd::list<vtkIdType> >::iterator it=this->dist2ToIds.begin();
        while(counter < numIds && it!=this->dist2ToIds.end())
          {
          vtkstd::list<vtkIdType>::iterator lit=it->second.begin();
          while(counter < numIds && lit!=it->second.end())
            {
            ids->InsertId(counter, *lit);
            counter++;
            lit++;
            }
          it++;
          }
      }

    float GetLargestDist2()
      {
        return this->LargestDist2;
      }
    
  private:
    size_t NumDesiredPoints, NumPoints;
    float LargestDist2;
    vtkstd::map<float, vtkstd::list<vtkIdType> > dist2ToIds; // map from dist^2 to a list of ids
  };
}

vtkStandardNewMacro(vtkKdTree);

//----------------------------------------------------------------------------
vtkKdTree::vtkKdTree()
{
  this->FudgeFactor = 0;
  this->MaxWidth = 0.0;
  this->MaxLevel  = 20;
  this->Level    = 0;

  this->NumberOfRegionsOrLess = 0;
  this->NumberOfRegionsOrMore = 0;

  this->ValidDirections =
  (1 << vtkKdTree::XDIM) | (1 << vtkKdTree::YDIM) | (1 << vtkKdTree::ZDIM);

  this->MinCells = 100;
  this->NumberOfRegions     = 0;

  this->DataSets = vtkDataSetCollection::New();

  this->Top      = NULL;
  this->RegionList   = NULL;

  this->Timing = 0;
  this->TimerLog = NULL;

  this->IncludeRegionBoundaryCells = 0;
  this->GenerateRepresentationUsingDataBounds = 0;

  this->InitializeCellLists();
  this->CellRegionList = NULL;

  this->NumberOfLocatorPoints = 0;
  this->LocatorPoints = NULL;
  this->LocatorIds = NULL;
  this->LocatorRegionLocation = NULL;

  this->LastDataCacheSize = 0;
  this->LastNumDataSets = 0;
  this->ClearLastBuildCache();

  this->BSPCalculator = NULL;
  this->Cuts = NULL;
  this->UserDefinedCuts = 0;

  this->Progress = 0;
  this->ProgressOffset = 0;
  this->ProgressScale = 1.0;
}

//----------------------------------------------------------------------------
void vtkKdTree::DeleteAllDescendants(vtkKdNode *nd)
{
  vtkKdNode *left = nd->GetLeft();
  vtkKdNode *right = nd->GetRight();

  if (left && left->GetLeft())
    {
    vtkKdTree::DeleteAllDescendants(left);
    }

  if (right && right->GetLeft())
    {
    vtkKdTree::DeleteAllDescendants(right);
    }

  if (left && right)
    {
    nd->DeleteChildNodes();   // undo AddChildNodes
    left->Delete();           // undo vtkKdNode::New()
    right->Delete();
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::InitializeCellLists()
{ 
  this->CellList.dataSet       = NULL;
  this->CellList.regionIds     = NULL;
  this->CellList.nRegions      = 0;
  this->CellList.cells         = NULL;
  this->CellList.boundaryCells = NULL;
  this->CellList.emptyList = NULL;
}

//----------------------------------------------------------------------------
void vtkKdTree::DeleteCellLists()
{ 
  int i;
  int num = this->CellList.nRegions;
  
  if (this->CellList.regionIds)
    {
    delete [] this->CellList.regionIds;
    }
  
  if (this->CellList.cells)
    {
    for (i=0; i<num; i++)
      {
      this->CellList.cells[i]->Delete();
      }

    delete [] this->CellList.cells;
    }

  if (this->CellList.boundaryCells) 
    {
    for (i=0; i<num; i++)
      {
      this->CellList.boundaryCells[i]->Delete();
      }
    delete [] this->CellList.boundaryCells;
    }

  if (this->CellList.emptyList)
    {
    this->CellList.emptyList->Delete();
    }

  this->InitializeCellLists();

  return;
}

//----------------------------------------------------------------------------
vtkKdTree::~vtkKdTree()
{
  if (this->DataSets)
    {
    this->DataSets->Delete();
    this->DataSets = NULL;
    }

  this->FreeSearchStructure();

  this->DeleteCellLists();

  if (this->CellRegionList)
    {
    delete [] this->CellRegionList;
    this->CellRegionList = NULL;
    }

  if (this->TimerLog)
    {
    this->TimerLog->Delete();
    }

  this->ClearLastBuildCache();

  this->SetCalculator(NULL);
  this->SetCuts(NULL);
}
//----------------------------------------------------------------------------
void vtkKdTree::SetCalculator(vtkKdNode *kd)
{
  if (this->BSPCalculator)
    {
    this->BSPCalculator->Delete();
    this->BSPCalculator = NULL;
    }

  if (!this->UserDefinedCuts)
    {
    this->SetCuts(NULL, 0);
    }

  if (kd == NULL)
    {
    return;
    }

  if (!this->UserDefinedCuts)
    {
    vtkBSPCuts *cuts = vtkBSPCuts::New();
    cuts->CreateCuts(kd);
    this->SetCuts(cuts, 0);
    }

  this->BSPCalculator = vtkBSPIntersections::New();
  this->BSPCalculator->SetCuts(this->Cuts);
}
//----------------------------------------------------------------------------
void vtkKdTree::SetCuts(vtkBSPCuts *cuts)
{
  this->SetCuts(cuts, 1);
}
//----------------------------------------------------------------------------
void vtkKdTree::SetCuts(vtkBSPCuts *cuts, int userDefined)
{
  if (userDefined != 0)
    {
    userDefined = 1;
    }

  if ((cuts == this->Cuts) && (userDefined == this->UserDefinedCuts))
    {
    return;
    }

  if (!this->Cuts || !this->Cuts->Equals(cuts))
    {
    this->Modified();
    }

  if (this->Cuts)
    {
    if (this->UserDefinedCuts)
      {
      this->Cuts->UnRegister(this);
      }
    else
      {
      this->Cuts->Delete();
      }

    this->Cuts = NULL;
    this->UserDefinedCuts = 0;
    }

  if (cuts == NULL)
    {
    return;
    }

  this->Cuts = cuts;
  this->UserDefinedCuts = userDefined;

  if (this->UserDefinedCuts)
    {
    this->Cuts->Register(this);
    }
}
//----------------------------------------------------------------------------
// Add and remove data sets.  We don't update this->Modify() here, because
// changing the data sets doesn't necessarily require rebuilding the
// k-d tree.  We only need to build a new k-d tree in BuildLocator if
// the geometry has changed, and we check for that with NewGeometry in
// BuildLocator.  We Modify() for changes that definitely require a
// rebuild of the tree, like changing the depth of the k-d tree.

void vtkKdTree::SetDataSet(vtkDataSet *set)
{
  this->DataSets->RemoveAllItems();
  this->AddDataSet(set);
}

void vtkKdTree::AddDataSet(vtkDataSet *set)
{
  if (set == NULL)
    {
    return;
    }

  if (this->DataSets->IsItemPresent(set))
    {
    return;
    }

  this->DataSets->AddItem(set);
}

void vtkKdTree::RemoveDataSet(vtkDataSet *set)
{
  this->DataSets->RemoveItem(set);
}

void vtkKdTree::RemoveDataSet(int index)
{
  this->DataSets->RemoveItem(index);
}

void vtkKdTree::RemoveAllDataSets()
{
  this->DataSets->RemoveAllItems();
}

//-----------------------------------------------------------------------------

int vtkKdTree::GetNumberOfDataSets()
{
  return this->DataSets->GetNumberOfItems();
}

int vtkKdTree::GetDataSetIndex(vtkDataSet *set)
{
  // This is weird, but IsItemPresent returns the index + 1 (so that 0
  // corresponds to item not present).
  return this->DataSets->IsItemPresent(set) - 1;
}

vtkDataSet *vtkKdTree::GetDataSet(int index)
{
  return this->DataSets->GetItem(index);
}

int vtkKdTree::GetDataSetsNumberOfCells(int from, int to)
{
  int numCells = 0;

  for (int i=from; i<=to; i++)
    {
    vtkDataSet *data = this->GetDataSet(i);
    if (data)
      {
      numCells += data->GetNumberOfCells();
      }
    }

  return numCells;
}

//----------------------------------------------------------------------------
int vtkKdTree::GetNumberOfCells()
{ 
  return this->GetDataSetsNumberOfCells(0, this->GetNumberOfDataSets()-1);
}

//----------------------------------------------------------------------------
void vtkKdTree::GetBounds(double *bounds)
{
  if (this->Top)
    {
    this->Top->GetBounds(bounds);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::GetRegionBounds(int regionID, double bounds[6])
{
  if ( (regionID < 0) || (regionID >= this->NumberOfRegions))
    {
    vtkErrorMacro( << "vtkKdTree::GetRegionBounds invalid region");
    return;
    }

  vtkKdNode *node = this->RegionList[regionID];

  node->GetBounds(bounds);
}

//----------------------------------------------------------------------------
void vtkKdTree::GetRegionDataBounds(int regionID, double bounds[6])
{
  if ( (regionID < 0) || (regionID >= this->NumberOfRegions))
    {
    vtkErrorMacro( << "vtkKdTree::GetRegionDataBounds invalid region");
    return;
    }

  vtkKdNode *node = this->RegionList[regionID];

  node->GetDataBounds(bounds);
}

//----------------------------------------------------------------------------
vtkKdNode **vtkKdTree::_GetRegionsAtLevel(int level, vtkKdNode **nodes, vtkKdNode *kd)
{
  if (level > 0)
    {
    vtkKdNode **nodes0 = _GetRegionsAtLevel(level-1, nodes, kd->GetLeft());
    vtkKdNode **nodes1 = _GetRegionsAtLevel(level-1, nodes0, kd->GetRight());

    return nodes1;
    }
  else
    {
    nodes[0] = kd;
    return nodes+1;
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::GetRegionsAtLevel(int level, vtkKdNode **nodes)
{
  if ( (level < 0) || (level > this->Level)) 
    {
    return;
    }

  vtkKdTree::_GetRegionsAtLevel(level, nodes, this->Top);

  return;
}

//----------------------------------------------------------------------------
void vtkKdTree::GetLeafNodeIds(vtkKdNode *node, vtkIntArray *ids)
{
  int id = node->GetID();

  if (id < 0)
    {
    vtkKdTree::GetLeafNodeIds(node->GetLeft(), ids);
    vtkKdTree::GetLeafNodeIds(node->GetRight(), ids);
    }
  else
    {
    ids->InsertNextValue(id);
    }
  return;
}

//----------------------------------------------------------------------------
float *vtkKdTree::ComputeCellCenters()
{
  vtkDataSet *allSets = NULL;
  return this->ComputeCellCenters(allSets);
}

//----------------------------------------------------------------------------
float *vtkKdTree::ComputeCellCenters(int set)
{
  vtkDataSet *data = this->GetDataSet(set);
  if (!data)
    {
    vtkErrorMacro(<<"vtkKdTree::ComputeCellCenters no such data set");
    return NULL;
    }
  return this->ComputeCellCenters(data);
}

//----------------------------------------------------------------------------
float *vtkKdTree::ComputeCellCenters(vtkDataSet *set)
{
  this->UpdateSubOperationProgress(0);
  int totalCells;

  if (set)
    {
    totalCells = set->GetNumberOfCells();
    }
  else
    {
    totalCells = this->GetNumberOfCells();   // all data sets
    }

  if (totalCells == 0) 
    {
    return NULL;
    }

  float *center = new float [3 * totalCells];

  if (!center)
    {
    return NULL;
    }

  int maxCellSize = 0;

  if (set)
    {
    maxCellSize = set->GetMaxCellSize();
    }
  else
    {
    vtkCollectionSimpleIterator cookie;
    this->DataSets->InitTraversal(cookie);
    for (vtkDataSet *iset = this->DataSets->GetNextDataSet(cookie);
         iset != NULL; iset = this->DataSets->GetNextDataSet(cookie))
      {
      int cellSize = iset->GetMaxCellSize();
      maxCellSize = (cellSize > maxCellSize) ? cellSize : maxCellSize;
      }
    }

  double *weights = new double [maxCellSize];

  float *cptr = center;
  double dcenter[3];

  if (set)
    {
    for (int j=0; j<totalCells; j++)
      {
      this->ComputeCellCenter(set->GetCell(j), dcenter, weights);
      cptr[0] = static_cast<float>(dcenter[0]);
      cptr[1] = static_cast<float>(dcenter[1]);
      cptr[2] = static_cast<float>(dcenter[2]);
      cptr += 3;
      if (j%1000 == 0)
        {
        this->UpdateSubOperationProgress(static_cast<double>(j)/totalCells);
        }
      }
    }
  else
    {
    vtkCollectionSimpleIterator cookie;
    this->DataSets->InitTraversal(cookie);
    for (vtkDataSet *iset = this->DataSets->GetNextDataSet(cookie);
         iset != NULL; iset = this->DataSets->GetNextDataSet(cookie))
      {
      int nCells = iset->GetNumberOfCells();

      for (int j=0; j<nCells; j++)
        {
        this->ComputeCellCenter(iset->GetCell(j), dcenter, weights);
        cptr[0] = static_cast<float>(dcenter[0]);
        cptr[1] = static_cast<float>(dcenter[1]);
        cptr[2] = static_cast<float>(dcenter[2]);
        cptr += 3;
        if (j%1000 == 0)
          {
          this->UpdateSubOperationProgress(static_cast<double>(j)/totalCells);
          }
        }
      }
    }

  delete [] weights;

  this->UpdateSubOperationProgress(1.0);
  return center;
}

//----------------------------------------------------------------------------
void vtkKdTree::ComputeCellCenter(vtkDataSet *set, int cellId, float *center)
{
  double dcenter[3];

  this->ComputeCellCenter(set, cellId, dcenter);

  center[0] = static_cast<float>(dcenter[0]);
  center[1] = static_cast<float>(dcenter[1]);
  center[2] = static_cast<float>(dcenter[2]);
}

//----------------------------------------------------------------------------
void vtkKdTree::ComputeCellCenter(vtkDataSet *set, int cellId, double *center)
{
  int setNum;

  if (set)
    {
    setNum = this->GetDataSetIndex(set);

    if ( setNum < 0)
      {
      vtkErrorMacro(<<"vtkKdTree::ComputeCellCenter invalid data set");
      return;
      } 
    }
  else
    {
    setNum = 0;
    set = this->GetDataSet();
    }
      
  if ( (cellId < 0) || (cellId >= set->GetNumberOfCells()))
    {
    vtkErrorMacro(<<"vtkKdTree::ComputeCellCenter invalid cell ID");
    return;
    }

  double *weights = new double [set->GetMaxCellSize()];

  this->ComputeCellCenter(set->GetCell(cellId), center, weights);

  delete [] weights;

  return;
}

//----------------------------------------------------------------------------
void vtkKdTree::ComputeCellCenter(vtkCell *cell, double *center,
                                  double *weights)
{
  double pcoords[3];
  
  int subId = cell->GetParametricCenter(pcoords);
    
  cell->EvaluateLocation(subId, pcoords, center, weights);
      
  return;
}

//----------------------------------------------------------------------------
// Build the kdtree structure based on location of cell centroids.
//
void vtkKdTree::BuildLocator()
{
  this->UpdateProgress(0);
  int nCells=0;
  int i;

  if ((this->Top != NULL) && 
      (this->BuildTime > this->GetMTime()) &&
      (this->NewGeometry() == 0))
    {
    return;
    }

  // Make sure input is up to date.
  for (i = 0; i < this->GetNumberOfDataSets(); i++)
    {
    this->GetDataSet(i)->Update();
    }

  nCells = this->GetNumberOfCells();

  if (nCells == 0)
    {
     vtkErrorMacro( << "vtkKdTree::BuildLocator - No cells to subdivide");
     return;
    }

  vtkDebugMacro( << "Creating Kdtree" );
  this->InvokeEvent(vtkCommand::StartEvent);

  if ((this->Timing) && (this->TimerLog == NULL))
    {
    this->TimerLog = vtkTimerLog::New();
    }

  TIMER("Set up to build k-d tree");

  this->FreeSearchStructure();

  // volume bounds - push out a little if flat

  double setBounds[6], volBounds[6];
  int first = 1;

  vtkCollectionSimpleIterator cookie;
  this->DataSets->InitTraversal(cookie);
  for (vtkDataSet *iset = this->DataSets->GetNextDataSet(cookie);
       iset != NULL; iset = this->DataSets->GetNextDataSet(cookie))
    {
    iset->Update();
    if (first)
      {
      iset->GetBounds(volBounds);
      first = 0;
      }
    else
      {
      iset->GetBounds(setBounds);
      if (setBounds[0] < volBounds[0]) 
        {
        volBounds[0] = setBounds[0];
        }
      if (setBounds[2] < volBounds[2]) 
        {
        volBounds[2] = setBounds[2];
        }
      if (setBounds[4] < volBounds[4]) 
        {
        volBounds[4] = setBounds[4];
        }
      if (setBounds[1] > volBounds[1]) 
        {
        volBounds[1] = setBounds[1];
        }
      if (setBounds[3] > volBounds[3]) 
        {
        volBounds[3] = setBounds[3];
        }
      if (setBounds[5] > volBounds[5]) 
        {
        volBounds[5] = setBounds[5];
        }
      }
    }

  double diff[3], aLittle = 0.0;
  this->MaxWidth = 0.0;

  for (i=0; i<3; i++)
    {
     diff[i] = volBounds[2*i+1] - volBounds[2*i];
     this->MaxWidth = static_cast<float>(
       (diff[i] > this->MaxWidth) ? diff[i] : this->MaxWidth);
    }

  this->FudgeFactor = this->MaxWidth * 10e-6;

  aLittle = this->MaxWidth / 100.0;

  for (i=0; i<3; i++)
    {
    if (diff[i] <= 0)
      {
      volBounds[2*i]   -= aLittle;
      volBounds[2*i+1] += aLittle;
      }
    else // need lower bound to be strictly less than any point in decomposition
      {
      volBounds[2*i] -= this->FudgeFactor;
      }
    }
  TIMERDONE("Set up to build k-d tree");

  if (this->UserDefinedCuts)
    {
    // Actually, we will not compute the k-d tree.  We will use a
    // k-d tree provided to us.

    int fail = this->ProcessUserDefinedCuts(volBounds);

    if (fail)
      {
      return;
      }
    }
  else
    {
    // cell centers - basis of spatial decomposition
  
    TIMER("Create centroid list");
    this->ProgressOffset = 0;
    this->ProgressScale = 0.3;
    float *ptarray = this->ComputeCellCenters();
  
    TIMERDONE("Create centroid list");
  
    if (!ptarray)
      {
      vtkErrorMacro( << "vtkKdTree::BuildLocator - insufficient memory");
      return;
      }
  
    // create kd tree structure that balances cell centers
  
    vtkKdNode *kd = this->Top = vtkKdNode::New();
  
    kd->SetBounds(volBounds[0], volBounds[1], 
                  volBounds[2], volBounds[3], 
                  volBounds[4], volBounds[5]);
  
    kd->SetNumberOfPoints(nCells);
  
    kd->SetDataBounds(volBounds[0], volBounds[1],
                      volBounds[2], volBounds[3],
                      volBounds[4], volBounds[5]); 
  
    TIMER("Build tree");
  
    this->ProgressOffset += this->ProgressScale;
    this->ProgressScale = 0.7;
    this->DivideRegion(kd, ptarray, NULL, 0);
  
    TIMERDONE("Build tree");
  
    // In the process of building the k-d tree regions,
    //   the cell centers became reordered, so no point
    //   in saving them, for example to build cell lists.
  
    delete [] ptarray;
    }

  this->SetActualLevel();
  this->BuildRegionList();

  this->InvokeEvent(vtkCommand::EndEvent);

  this->UpdateBuildTime();

  this->SetCalculator(this->Top);

  this->UpdateProgress(1.0);
  return;
}

int vtkKdTree::ProcessUserDefinedCuts(double *minBounds)
{
  if (!this->Cuts)
    {
    vtkErrorMacro(<< "vtkKdTree::ProcessUserDefinedCuts - no cuts" );
    return 1;
    }
  // Fix the bounds for the entire partitioning.  They must be at
  // least as large of the bounds of all the data sets.  

  vtkKdNode *kd = this->Cuts->GetKdNodeTree();
  double bounds[6];
  kd->GetBounds(bounds);
  int fixBounds = 0;

  for (int j=0; j<3; j++)
    {
    int min = 2*j;
    int max = min+1;

    if (minBounds[min] < bounds[min])
      {
      bounds[min] = minBounds[min]; 
      fixBounds = 1;
      }
    if (minBounds[max] > bounds[max])
      {
      bounds[max] = minBounds[max]; 
      fixBounds = 1;
      }
    }

  this->Top = vtkKdTree::CopyTree(kd);

  if (fixBounds)
    {
    this->SetNewBounds(bounds);
    }

  // We don't really know the data bounds, so we'll just set them
  // to the spatial bounds.  

  vtkKdTree::SetDataBoundsToSpatialBounds(this->Top);

  // And, we don't know how many points are in each region.  The number
  // in the provided vtkBSPCuts object was for some other dataset.  So
  // we zero out those fields.

  vtkKdTree::ZeroNumberOfPoints(this->Top);
   
  return 0;
}
//----------------------------------------------------------------------------
void vtkKdTree::ZeroNumberOfPoints(vtkKdNode *kd)
{
  kd->SetNumberOfPoints(0);

  if (kd->GetLeft())
    {
    vtkKdTree::ZeroNumberOfPoints(kd->GetLeft());
    vtkKdTree::ZeroNumberOfPoints(kd->GetRight());
    }
}
//----------------------------------------------------------------------------
void vtkKdTree::SetNewBounds(double *bounds)
{
  vtkKdNode *kd = this->Top;

  if (!kd)
    {
    return;
    }

  int fixDimLeft[6], fixDimRight[6];
  int go=0;

  double kdb[6];
  kd->GetBounds(kdb);

  for (int i=0; i<3; i++)
    {
    int min = 2*i;
    int max = 2*i + 1;

    fixDimLeft[min] = fixDimRight[min] = 0;
    fixDimLeft[max] = fixDimRight[max] = 0;

    if (kdb[min] > bounds[min])
      {
      kdb[min] = bounds[min];
      go = fixDimLeft[min] = fixDimRight[min] = 1;
      }
    if (kdb[max] < bounds[max])
      {
      kdb[max] = bounds[max];
      go = fixDimLeft[max] = fixDimRight[max] = 1;
      }
    }

  if (go)
    {
    kd->SetBounds(kdb[0],kdb[1],kdb[2],kdb[3],kdb[4],kdb[5]);

    if (kd->GetLeft())
      {
      int cutDim = kd->GetDim() * 2;

      fixDimLeft[cutDim + 1] = 0;
      vtkKdTree::_SetNewBounds(kd->GetLeft(), bounds, fixDimLeft);
  
      fixDimRight[cutDim] = 0;
      vtkKdTree::_SetNewBounds(kd->GetRight(), bounds, fixDimRight);
      }
    }
}
//----------------------------------------------------------------------------
void vtkKdTree::_SetNewBounds(vtkKdNode *kd, double *b, int *fixDim)
{
  int go=0;
  int fixDimLeft[6], fixDimRight[6];

  double kdb[6];
  kd->GetBounds(kdb);

  for (int i=0; i<6; i++)
    {
    if (fixDim[i])
      {
      kdb[i] = b[i]; 
      go = 1;
      }
    fixDimLeft[i] = fixDim[i];
    fixDimRight[i] = fixDim[i];
    }

  if (go)
    {
    kd->SetBounds(kdb[0],kdb[1],kdb[2],kdb[3],kdb[4],kdb[5]);

    if (kd->GetLeft())
      {
      int cutDim = kd->GetDim() * 2;

      fixDimLeft[cutDim + 1] = 0;
      vtkKdTree::_SetNewBounds(kd->GetLeft(), b, fixDimLeft);
    
      fixDimRight[cutDim] = 0;
      vtkKdTree::_SetNewBounds(kd->GetRight(), b, fixDimRight);
      }
    }
}
//----------------------------------------------------------------------------
vtkKdNode *vtkKdTree::CopyTree(vtkKdNode *kd)
{
  vtkKdNode *top = vtkKdNode::New();
  vtkKdTree::CopyKdNode(top, kd);
  vtkKdTree::CopyChildNodes(top, kd);

  return top;
}
//----------------------------------------------------------------------------
void vtkKdTree::CopyChildNodes(vtkKdNode *to, vtkKdNode *from)
{   
  if (from->GetLeft())
    {
    vtkKdNode *left = vtkKdNode::New();
    vtkKdNode *right = vtkKdNode::New();
    
    vtkKdTree::CopyKdNode(left, from->GetLeft());
    vtkKdTree::CopyKdNode(right, from->GetRight());
  
    to->AddChildNodes(left, right);
    
    vtkKdTree::CopyChildNodes(to->GetLeft(), from->GetLeft());
    vtkKdTree::CopyChildNodes(to->GetRight(), from->GetRight());
    }
}
//----------------------------------------------------------------------------
void vtkKdTree::CopyKdNode(vtkKdNode *to, vtkKdNode *from)
{
  to->SetMinBounds(from->GetMinBounds());
  to->SetMaxBounds(from->GetMaxBounds());
  to->SetMinDataBounds(from->GetMinDataBounds());
  to->SetMaxDataBounds(from->GetMaxDataBounds());
  to->SetID(from->GetID());
  to->SetMinID(from->GetMinID());
  to->SetMaxID(from->GetMaxID());
  to->SetNumberOfPoints(from->GetNumberOfPoints());
  to->SetDim(from->GetDim());
}

//----------------------------------------------------------------------------
int vtkKdTree::ComputeLevel(vtkKdNode *kd)
{
  if (!kd)
    {
    return 0;
    }
  
  int iam = 1;

  if (kd->GetLeft() != NULL)
    {
     int depth1 = vtkKdTree::ComputeLevel(kd->GetLeft());
     int depth2 = vtkKdTree::ComputeLevel(kd->GetRight());

     if (depth1 > depth2) 
       {
       iam += depth1;
       }
     else
       {
       iam += depth2;
       }
    }
  return iam;
}
//----------------------------------------------------------------------------
void vtkKdTree::SetDataBoundsToSpatialBounds(vtkKdNode *kd)
{
  kd->SetMinDataBounds(kd->GetMinBounds());
  kd->SetMaxDataBounds(kd->GetMaxBounds());

  if (kd->GetLeft())
    {
    vtkKdTree::SetDataBoundsToSpatialBounds(kd->GetLeft());
    vtkKdTree::SetDataBoundsToSpatialBounds(kd->GetRight());
    }
}
//----------------------------------------------------------------------------
int vtkKdTree::SelectCutDirection(vtkKdNode *kd)
{
  int dim=0, i;

  int xdir = 1 << vtkKdTree::XDIM;
  int ydir = 1 << vtkKdTree::YDIM;
  int zdir = 1 << vtkKdTree::ZDIM;

  // determine direction in which to divide this region

  if (this->ValidDirections == xdir)
    {
    dim = vtkKdTree::XDIM;
    }
  else if (this->ValidDirections == ydir)
    {
    dim = vtkKdTree::YDIM;
    }
  else if (this->ValidDirections == zdir)
    {
    dim = vtkKdTree::ZDIM;
    }
  else
    {
    // divide in the longest direction, for more compact regions

    double diff[3], dataBounds[6], maxdiff;
    kd->GetDataBounds(dataBounds);

    for (i=0; i<3; i++)
      { 
      diff[i] = dataBounds[i*2+1] - dataBounds[i*2];
      }

    maxdiff = -1.0;

    if ((this->ValidDirections & xdir) && (diff[vtkKdTree::XDIM] > maxdiff))
      {
      dim = vtkKdTree::XDIM;
      maxdiff = diff[vtkKdTree::XDIM];
      }

    if ((this->ValidDirections & ydir) && (diff[vtkKdTree::YDIM] > maxdiff))
      {
      dim = vtkKdTree::YDIM;
      maxdiff = diff[vtkKdTree::YDIM];
      }

    if ((this->ValidDirections & zdir) && (diff[vtkKdTree::ZDIM] > maxdiff))
      {
      dim = vtkKdTree::ZDIM;
      }
    }
  return dim;
}
//----------------------------------------------------------------------------
int vtkKdTree::DivideTest(int size, int level)
{
  if (level >= this->MaxLevel) return 0;

  int minCells = this->GetMinCells();

  if (minCells && (minCells > (size/2))) return 0;
 
  int nRegionsNow  = 1 << level;
  int nRegionsNext = nRegionsNow << 1;

  if (this->NumberOfRegionsOrLess && (nRegionsNext > this->NumberOfRegionsOrLess)) return 0;
  if (this->NumberOfRegionsOrMore && (nRegionsNow >= this->NumberOfRegionsOrMore)) return 0;

  return 1;
}
//----------------------------------------------------------------------------
int vtkKdTree::DivideRegion(vtkKdNode *kd, float *c1, int *ids, int level)
{
  int ok = this->DivideTest(kd->GetNumberOfPoints(), level);

  if (!ok)
    {
    return 0;
    }

  int maxdim = this->SelectCutDirection(kd);

  kd->SetDim(maxdim);

  int dim1 = maxdim;   // best cut direction
  int dim2 = -1;       // other valid cut directions
  int dim3 = -1;

  int otherDirections = this->ValidDirections ^ (1 << maxdim);

  if (otherDirections)
    {
    int x = otherDirections & (1 << vtkKdTree::XDIM);
    int y = otherDirections & (1 << vtkKdTree::YDIM);
    int z = otherDirections & (1 << vtkKdTree::ZDIM);

    if (x)
      {
      dim2 = vtkKdTree::XDIM;

      if (y)
        {
        dim3 = vtkKdTree::YDIM;
        }
      else if (z)
        {
        dim3 = vtkKdTree::ZDIM;
        }
      }
    else if (y)
      {
      dim2 = vtkKdTree::YDIM;

      if (z)
        {
        dim3 = vtkKdTree::ZDIM;
        }
      }
    else if (z)
      {
      dim2 = vtkKdTree::ZDIM;
      }
    }

  this->DoMedianFind(kd, c1, ids, dim1, dim2, dim3);

  if (kd->GetLeft() == NULL)
    {
    return 0;   // unable to divide region further
    }

  int nleft = kd->GetLeft()->GetNumberOfPoints();

  int *leftIds  = ids;
  int *rightIds = ids ? ids + nleft : NULL;
  
  this->DivideRegion(kd->GetLeft(), c1, leftIds, level + 1);
  
  this->DivideRegion(kd->GetRight(), c1 + nleft*3, rightIds, level + 1);
  
  return 0;
}

//----------------------------------------------------------------------------
// Rearrange the point array.  Try dim1 first.  If there's a problem
// go to dim2, then dim3.
//
void vtkKdTree::DoMedianFind(vtkKdNode *kd, float *c1, int *ids,
                             int dim1, int dim2, int dim3)
{
  double coord;
  int dim;
  int midpt;

  int npoints = kd->GetNumberOfPoints();

  int dims[3];

  dims[0] = dim1; dims[1] = dim2; dims[2] = dim3;

  for (dim = 0; dim < 3; dim++)
    {
    if (dims[dim] < 0) 
      {
      break;
      }

    midpt = vtkKdTree::Select(dims[dim], c1, ids, npoints, coord);

    if (midpt == 0) 
      {
      continue;    // fatal
      }

    kd->SetDim(dims[dim]);

    vtkKdTree::AddNewRegions(kd, c1, midpt, dims[dim], coord);

    break;   // division is fine
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::AddNewRegions(vtkKdNode *kd, float *c1, int midpt, int dim, double coord)
{
  vtkKdNode *left = vtkKdNode::New();
  vtkKdNode *right = vtkKdNode::New();

  int npoints = kd->GetNumberOfPoints();

  int nleft = midpt;
  int nright = npoints - midpt;

  kd->AddChildNodes(left, right);

  double bounds[6];
  kd->GetBounds(bounds);

  left->SetBounds(
     bounds[0], ((dim == vtkKdTree::XDIM) ? coord : bounds[1]),
     bounds[2], ((dim == vtkKdTree::YDIM) ? coord : bounds[3]),
     bounds[4], ((dim == vtkKdTree::ZDIM) ? coord : bounds[5]));
  
  left->SetNumberOfPoints(nleft);
  
  right->SetBounds(
     ((dim == vtkKdTree::XDIM) ? coord : bounds[0]), bounds[1],
     ((dim == vtkKdTree::YDIM) ? coord : bounds[2]), bounds[3],
     ((dim == vtkKdTree::ZDIM) ? coord : bounds[4]), bounds[5]); 
  
  right->SetNumberOfPoints(nright);
  
  left->SetDataBounds(c1);
  right->SetDataBounds(c1 + nleft*3);
}
// Use Floyd & Rivest (1975) to find the median:
// Given an array X with element indices ranging from L to R, and
// a K such that L <= K <= R, rearrange the elements such that
// X[K] contains the ith sorted element,  where i = K - L + 1, and
// all the elements X[j], j < k satisfy X[j] < X[K], and all the
// elements X[j], j > k satisfy X[j] >= X[K].

#define Exchange(array, ids, x, y) \
  {                                 \
  float temp[3];                    \
  temp[0]        = array[3*x];      \
  temp[1]        = array[3*x + 1];  \
  temp[2]        = array[3*x + 2];  \
  array[3*x]     = array[3*y];      \
  array[3*x + 1] = array[3*y + 1];  \
  array[3*x + 2] = array[3*y + 2];  \
  array[3*y]     = temp[0];         \
  array[3*y + 1] = temp[1];         \
  array[3*y + 2] = temp[2];         \
  if (ids)                          \
    {                               \
    vtkIdType tempid = ids[x];      \
    ids[x]           = ids[y];      \
    ids[y]           = tempid;      \
    }                               \
}

#define sign(x) ((x<0) ? (-1) : (1))
#ifndef max
#define max(x,y) ((x>y) ? (x) : (y))
#endif
#ifndef min
#define min(x,y) ((x<y) ? (x) : (y))
#endif

//----------------------------------------------------------------------------
int vtkKdTree::Select(int dim, float *c1, int *ids, int nvals, double &coord)
{
  int left = 0;
  int mid = nvals / 2;
  int right = nvals -1;

  vtkKdTree::_Select(dim, c1, ids, left, right, mid);

  // We need to be careful in the case where the "mid"
  // value is repeated several times in the array.  We
  // want to roll the dividing index (mid) back to the
  // first occurence in the array, so that there is no
  // ambiguity about which spatial region a given point
  // belongs in.
  //
  // The array has been rearranged (in _Select) like this:
  //
  // All values c1[n], left <= n < mid, satisfy c1[n] <= c1[mid]
  // All values c1[n], mid < n <= right, satisfy c1[n] >= c1[mid]
  //
  // In addition, by careful construction, there is a J <= mid
  // such that
  //
  // All values c1[n], n < J, satisfy c1[n] < c1[mid] STRICTLY
  // All values c1[n], J <= n <= mid, satisfy c1[n] = c1[mid]
  // All values c1[n], mid < n <= right , satisfy c1[n] >= c1[mid]
  //
  // We need to roll back the "mid" value to the "J".  This
  // means our spatial regions are less balanced, but there
  // is no ambiguity regarding which region a point belongs in.

  int midValIndex = mid*3 + dim;

  while ((mid > left) && (c1[midValIndex-3] == c1[midValIndex]))
    {
    mid--;
    midValIndex -= 3;
    }

  if (mid == left)
    {
    return mid;     // failed to divide region
    }

  float leftMax = vtkKdTree::FindMaxLeftHalf(dim, c1, mid);

  coord=(static_cast<double>(c1[midValIndex])
         +static_cast<double>(leftMax))/2.0;

  return mid;
}

//----------------------------------------------------------------------------
float vtkKdTree::FindMaxLeftHalf(int dim, float *c1, int K)
{
  int i;

  float *Xcomponent = c1 + dim;
  float max = Xcomponent[0];

  for (i=3; i<K*3; i+=3)
    {
    if (Xcomponent[i] > max) 
      {
      max = Xcomponent[i];
      }
    }
  return max;
}

//----------------------------------------------------------------------------
// Note: The indices (L, R, X) into the point array should be vtkIdTypes rather
// than ints, but this change causes the k-d tree build time to double.
// _Select is the heart of this build, called for every sub-interval that
// is to be reordered.  We will leave these as ints now.

void vtkKdTree::_Select(int dim, float *X, int *ids, 
                        int L, int R, int K)
{
  int N, I, J, S, SD, LL, RR;
  float Z, T;
  int manyTValues=0;

  while (R > L)
    {
    if ( R - L > 600)
      {
      // "Recurse on a sample of size S to get an estimate for the
      // (K-L+1)-th smallest element into X[K], biased slightly so
      // that the (K-L+1)-th element is expected to lie in the
      // smaller set after partitioning"

      N = R - L + 1;
      I = K - L + 1;
      Z = static_cast<float>(log(static_cast<float>(N)));
      S = static_cast<int>(.5 * exp(2*Z/3));
      SD = static_cast<int>(.5 * sqrt(Z*S*static_cast<float>(N-S)/N) * sign(I - N/2));
      LL = max(L, K - static_cast<int>(I*static_cast<float>(S)/N) + SD);
      RR = min(R, K + static_cast<int>((N-I)*static_cast<float>(S)/N) + SD);
      _Select(dim, X, ids, LL, RR, K);
      }

    float *Xcomponent = X + dim;   // x, y or z component

    T = Xcomponent[K*3];

    // "the following code partitions X[L:R] about T."

    I = L;
    J = R;

    Exchange(X, ids, L, K);

    if (Xcomponent[R*3] >= T) 
      {
      if (Xcomponent[R*3] == T) manyTValues++;
      Exchange(X, ids, R, L);
      }
    while (I < J)
      {
      Exchange(X, ids, I, J);

      while (Xcomponent[(++I)*3] < T)
        {
        ;
        }

      while ((J>L) && (Xcomponent[(--J)*3] >= T))
        {
        if (!manyTValues && (J>L) && (Xcomponent[J*3] == T))
          {
          manyTValues = 1;
          }
        }
      }

    if (Xcomponent[L*3] == T)
      {
      Exchange(X, ids, L, J);
      }
    else
      {
      J++;
      Exchange(X, ids, J, R);
      }

    if ((J < K) && manyTValues)
      {
      // Select has a worst case - when many of the same values
      // are repeated in an array.  It is bad enough that it is
      // worth detecting and optimizing for.  Here we're taking the
      // interval of values that are >= T, and rearranging it into
      // an interval of values = T followed by those > T.

      I = J;
      J = R+1;

      while (I < J)
        {
        while ((++I < J) && (Xcomponent[I*3] == T))
          {
          ;
          }
        if (I == J) break;

        while ((--J > I) && (Xcomponent[J*3] > T))
          {
          ;
          }
        if (J == I) break;

        Exchange(X, ids, I, J);
        }

      // I and J are at the first array element that is > T
      // If K is within the sequence of T's, we're done, else
      // move the new [L,R] interval to the sequence of values
      // that are strictly greater than T.

      if (K < J)
        {
        J = K;
        }
      else
        {
        J = J-1;
        }
      }

    // "now adjust L,R so they surround the subset containing
    // the (K-L+1)-th smallest element"

    if (J <= K) 
      {
      L = J + 1;
      }
    if (K <= J) 
      {
      R = J - 1;
      }
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::SelfRegister(vtkKdNode *kd)
{
  if (kd->GetLeft() == NULL)
    {
    this->RegionList[kd->GetID()] = kd; 
    }
  else
    {
    this->SelfRegister(kd->GetLeft());
    this->SelfRegister(kd->GetRight());
    }

  return;
}

//----------------------------------------------------------------------------
int vtkKdTree::SelfOrder(int startId, vtkKdNode *kd)
{
  int nextId;

  if (kd->GetLeft() == NULL)
    {
    kd->SetID(startId);
    kd->SetMaxID(startId);
    kd->SetMinID(startId);

    nextId = startId + 1;
    }
  else
    {
    kd->SetID(-1);
    nextId = vtkKdTree::SelfOrder(startId, kd->GetLeft());
    nextId = vtkKdTree::SelfOrder(nextId, kd->GetRight());

    kd->SetMinID(startId);
    kd->SetMaxID(nextId - 1);
    }

  return nextId;
}

void vtkKdTree::BuildRegionList()
{
  if (this->Top == NULL) 
    {
    return;
    }

  this->NumberOfRegions = vtkKdTree::SelfOrder(0, this->Top);
  
  this->RegionList = new vtkKdNode * [this->NumberOfRegions];

  this->SelfRegister(this->Top);
}

//----------------------------------------------------------------------------
// K-d tree from points, for finding duplicate and near-by points
//
void vtkKdTree::BuildLocatorFromPoints(vtkPointSet *pointset)
{
  this->BuildLocatorFromPoints(pointset->GetPoints());
}

void vtkKdTree::BuildLocatorFromPoints(vtkPoints *ptArray)
{
  this->BuildLocatorFromPoints(&ptArray, 1);
}

//----------------------------------------------------------------------------
void vtkKdTree::BuildLocatorFromPoints(vtkPoints **ptArrays, int numPtArrays) 
{
  int ptId;
  int i;

  int totalNumPoints = 0;

  for (i = 0; i < numPtArrays; i++)
    {
    totalNumPoints += ptArrays[i]->GetNumberOfPoints();
    }

  if (totalNumPoints < 1)
    {
    vtkErrorMacro(<< "vtkKdTree::BuildLocatorFromPoints - no points");
    return;
    }

  if (totalNumPoints >= VTK_INT_MAX)
    {
     // The heart of the k-d tree build is the recursive median find in
     // _Select.  It rearranges point IDs along with points themselves.
     // When point IDs are stored in an "int" instead of a vtkIdType, 
     // performance doubles.  So we store point IDs in an "int" during
     // the calculation.  This will need to be rewritten if true 64 bit
     // IDs are required.

     vtkErrorMacro(<<
    "BuildLocatorFromPoints - intentional 64 bit error - time to rewrite code");
     return;
    }

  vtkDebugMacro( << "Creating Kdtree" );
  
  if ((this->Timing) && (this->TimerLog == NULL) )
    {
    this->TimerLog = vtkTimerLog::New();
    }

  TIMER("Set up to build k-d tree");

  this->FreeSearchStructure();
  this->ClearLastBuildCache();

  // Fix bounds - (1) push out a little if flat 
  // (2) pull back the x, y and z lower bounds a little bit so that
  // points are clearly "inside" the spatial region.  Point p is
  // "inside" region r = [r1, r2] if r1 < p <= r2.

  double bounds[6], diff[3];

  ptArrays[0]->GetBounds(bounds);

  for (i=1; i<numPtArrays; i++)
    {
    double tmpbounds[6];
    ptArrays[i]->GetBounds(tmpbounds);

    if (tmpbounds[0] < bounds[0]) 
      {
      bounds[0] = tmpbounds[0];
      }
    if (tmpbounds[2] < bounds[2]) 
      {
      bounds[2] = tmpbounds[2];
      }
    if (tmpbounds[4] < bounds[4]) 
      {
      bounds[4] = tmpbounds[4];
      }
    if (tmpbounds[1] > bounds[1]) 
      {
      bounds[1] = tmpbounds[1];
      }
    if (tmpbounds[3] > bounds[3]) 
      {
      bounds[3] = tmpbounds[3];
      }
    if (tmpbounds[5] > bounds[5]) 
      {
      bounds[5] = tmpbounds[5];
      }
    }

  this->MaxWidth = 0.0; 

  for (i=0; i<3; i++)
    {
    diff[i] = bounds[2*i+1] - bounds[2*i];
    this->MaxWidth = static_cast<float>
      ((diff[i] > this->MaxWidth) ? diff[i] : this->MaxWidth);
    }

  this->FudgeFactor = this->MaxWidth * 10e-6;

  double aLittle = this->MaxWidth * 10e-2;

  for (i=0; i<3; i++)
    {
    if (diff[i] < aLittle)         // case (1) above
      {
      double temp = bounds[2*i];
      bounds[2*i]   = bounds[2*i+1] - aLittle;
      bounds[2*i+1] = temp + aLittle;
      }
    else                           // case (2) above
      {
      bounds[2*i] -= this->FudgeFactor;
      }
    }

  // root node of k-d tree - it's the whole space
   
  vtkKdNode *kd = this->Top = vtkKdNode::New();

  kd->SetBounds(bounds[0], bounds[1], 
                bounds[2], bounds[3], 
                bounds[4], bounds[5]);

  kd->SetNumberOfPoints(totalNumPoints);

  kd->SetDataBounds(bounds[0], bounds[1],
                    bounds[2], bounds[3],
                    bounds[4], bounds[5]); 


  this->LocatorIds = new int [totalNumPoints];
  this->LocatorPoints = new float [3 * totalNumPoints];

  if ( !this->LocatorPoints || !this->LocatorIds)
    {
    this->FreeSearchStructure();
    vtkErrorMacro(<< "vtkKdTree::BuildLocatorFromPoints - memory allocation");
    return;
    }

  int *ptIds = this->LocatorIds;
  float *points = this->LocatorPoints;

  for (i=0, ptId = 0; i<numPtArrays; i++)
    {
    int npoints = ptArrays[i]->GetNumberOfPoints();
    int nvals = npoints * 3;

    int pointArrayType = ptArrays[i]->GetDataType();

    if (pointArrayType == VTK_FLOAT)
      {
      vtkDataArray *da = ptArrays[i]->GetData();
      vtkFloatArray *fa = vtkFloatArray::SafeDownCast(da);
      memcpy(points + ptId, fa->GetPointer(0), sizeof(float) * nvals );
      ptId += nvals;
      }
    else
      {
      // Hopefully point arrays are usually floats.  This conversion will
      // really slow things down.

      for (vtkIdType ii=0; ii<npoints; ii++)
        {
        double *pt = ptArrays[i]->GetPoint(ii);
        
        points[ptId++] = static_cast<float>(pt[0]);
        points[ptId++] = static_cast<float>(pt[1]);
        points[ptId++] = static_cast<float>(pt[2]);
        }
      }
    }

  for (ptId=0; ptId<totalNumPoints; ptId++)
    {
    // _Select dominates DivideRegion algorithm, operating on
    // ints is much fast than operating on long longs

    ptIds[ptId] = ptId;
    }

  TIMERDONE("Set up to build k-d tree");

  TIMER("Build tree");

  this->DivideRegion(kd, points, ptIds, 0);

  this->SetActualLevel();
  this->BuildRegionList();

  // Create a location array for the points of each region

  this->LocatorRegionLocation = new int [this->NumberOfRegions];

  int idx = 0;

  for (int reg = 0; reg < this->NumberOfRegions; reg++)
    {
    this->LocatorRegionLocation[reg] = idx;

    idx += this->RegionList[reg]->GetNumberOfPoints();
    }

  this->NumberOfLocatorPoints = idx;

  this->SetCalculator(this->Top);

  TIMERDONE("Build tree");
}

//----------------------------------------------------------------------------
// Query functions subsequent to BuildLocatorFromPoints,
// relating to duplicate and nearby points
//
vtkIdTypeArray *vtkKdTree::BuildMapForDuplicatePoints(float tolerance = 0.0)
{
  int i;

  if ((tolerance < 0.0) || (tolerance >= this->MaxWidth))
    {
    vtkWarningMacro(<< "vtkKdTree::BuildMapForDuplicatePoints - invalid tolerance");
    tolerance = this->MaxWidth;
    }

  TIMER("Find duplicate points");

  int *idCount = new int [this->NumberOfRegions];
  int **uniqueFound = new int * [this->NumberOfRegions];

  if (!idCount || !uniqueFound)
    {
    if (idCount) 
      {
      delete [] idCount;
      }
    if (uniqueFound) 
      {
      delete [] uniqueFound;
      }

    vtkErrorMacro(<< "vtkKdTree::BuildMapForDuplicatePoints memory allocation");
    return NULL;
    }

  memset(idCount, 0, sizeof(int) * this->NumberOfRegions);

  for (i=0; i<this->NumberOfRegions; i++)
    {
    uniqueFound[i] = new int [this->RegionList[i]->GetNumberOfPoints()];
 
    if (!uniqueFound[i])
      {
      delete [] idCount;
      for (int j=0; j<i; j++) delete [] uniqueFound[j];
      delete [] uniqueFound;
      vtkErrorMacro(<< "vtkKdTree::BuildMapForDuplicatePoints memory allocation");
      return NULL;
      }
    }

  float tolerance2 = tolerance * tolerance;

  vtkIdTypeArray *uniqueIds = vtkIdTypeArray::New();
  uniqueIds->SetNumberOfValues(this->NumberOfLocatorPoints);

  int idx = 0;
  int nextRegionId = 0;
  float *point = this->LocatorPoints;

  while (idx < this->NumberOfLocatorPoints)
    {
    // first point we have in this region

    int currentId = this->LocatorIds[idx];

    int regionId = this->GetRegionContainingPoint(point[0],point[1],point[2]);

    if ((regionId == -1) || (regionId != nextRegionId))
      {
      delete [] idCount;
      for (i=0; i<this->NumberOfRegions; i++) delete [] uniqueFound[i];
      delete [] uniqueFound;
      uniqueIds->Delete();
      vtkErrorMacro(<< "vtkKdTree::BuildMapForDuplicatePoints corrupt k-d tree");
      return NULL; 
      }

    int duplicateFound = -1;

    if ((tolerance > 0.0) && (regionId > 0))
      {
      duplicateFound = this->SearchNeighborsForDuplicate(regionId, point, 
                               uniqueFound, idCount, tolerance, tolerance2);
      }

    if (duplicateFound >= 0)
      {
      uniqueIds->SetValue(currentId, this->LocatorIds[duplicateFound]);
      }
    else
      {
      uniqueFound[regionId][idCount[regionId]++] = idx;
      uniqueIds->SetValue(currentId, currentId);
      }

    // test the other points in this region

    int numRegionPoints = this->RegionList[regionId]->GetNumberOfPoints();

    int secondIdx = idx + 1;
    int nextFirstIdx = idx + numRegionPoints;

    for (int idx2 = secondIdx ; idx2 < nextFirstIdx; idx2++)
      {
      point += 3;
      currentId = this->LocatorIds[idx2];

      duplicateFound = this->SearchRegionForDuplicate(point,
                            uniqueFound[regionId], idCount[regionId], tolerance2);

      if ((tolerance > 0.0) && (duplicateFound < 0) && (regionId > 0)) 
        {
        duplicateFound =  this->SearchNeighborsForDuplicate(regionId, point, 
                                     uniqueFound, idCount, tolerance, tolerance2);
        }

      if (duplicateFound >= 0)
        {
        uniqueIds->SetValue(currentId, this->LocatorIds[duplicateFound]);
        }
      else
        {
        uniqueFound[regionId][idCount[regionId]++] = idx2;
        uniqueIds->SetValue(currentId, currentId);
        }
      }

    idx = nextFirstIdx;
    point += 3;
    nextRegionId++;
    }

  for (i=0; i<this->NumberOfRegions; i++)
    {
    delete [] uniqueFound[i];
    }
  delete [] uniqueFound;
  delete [] idCount;

  TIMERDONE("Find duplicate points");

  return uniqueIds;
}

//----------------------------------------------------------------------------
int vtkKdTree::SearchRegionForDuplicate(float *point, int *pointsSoFar, 
                                        int len, float tolerance2)
{
  int duplicateFound = -1;
  int id;

  for (id=0; id < len; id++)
    {
    int otherId = pointsSoFar[id];
  
    float *otherPoint = this->LocatorPoints + (otherId * 3);
  
    float distance2 = vtkMath::Distance2BetweenPoints(point, otherPoint);
  
    if (distance2 <= tolerance2)
      {
      duplicateFound = otherId;
      break;
      }
    }
  return duplicateFound;
}

//----------------------------------------------------------------------------
int vtkKdTree::SearchNeighborsForDuplicate(int regionId, float *point,
                                    int **pointsSoFar, int *len, 
                                    float tolerance, float tolerance2)
{
  int duplicateFound = -1;

  float dist2 = 
    this->RegionList[regionId]->GetDistance2ToInnerBoundary(point[0],point[1],point[2]);

  if (dist2 >= tolerance2)
    {
    // There are no other regions with data that are within the
    // tolerance distance of this point.

    return duplicateFound;
    }

  // Find all regions that are within the tolerance distance of the point

  int *regionIds = new int [this->NumberOfRegions];

  this->BSPCalculator->ComputeIntersectionsUsingDataBoundsOn();

#ifdef USE_SPHERE

  // Find all regions which intersect a sphere around the point
  // with radius equal to tolerance.  Compute the intersection using
  // the bounds of data within regions, not the bounds of the region.

  int nRegions = 
    this->BSPCalculator->IntersectsSphere2(regionIds, this->NumberOfRegions,
                                     point[0], point[1], point[2], tolerance2);
#else

  // Technically, we want all regions that intersect a sphere around the
  // point. But this takes much longer to compute than a box.  We'll compute
  // all regions that intersect a box.  We may occasionally get a region
  // we don't need, but that's OK.

  double box[6];
  box[0] = point[0] - tolerance; box[1] = point[0] + tolerance;
  box[2] = point[1] - tolerance; box[3] = point[1] + tolerance;
  box[4] = point[2] - tolerance; box[5] = point[2] + tolerance;

  int nRegions = this->BSPCalculator->IntersectsBox(regionIds, this->NumberOfRegions, box);

#endif

  this->BSPCalculator->ComputeIntersectionsUsingDataBoundsOff();

  for (int reg=0; reg < nRegions; reg++)
    {
    if ((regionIds[reg] == regionId)  || (len[reg] == 0) )
      {
      continue;
      }

    duplicateFound = this->SearchRegionForDuplicate(point,  pointsSoFar[reg], 
                                                  len[reg], tolerance2);

    if (duplicateFound) 
      {
      break;
      }
    }

  delete [] regionIds;

  return duplicateFound;
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindPoint(double x[3])
{
  return this->FindPoint(x[0], x[1], x[2]);
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindPoint(double x, double y, double z)
{
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindPoint - must build locator first");
    return -1;
    }

  int regionId = this->GetRegionContainingPoint(x, y, z);

  if (regionId == -1)
    {
    return -1;
    }

  int idx = this->LocatorRegionLocation[regionId];

  vtkIdType ptId = -1;

  float *point = this->LocatorPoints + (idx * 3);

  float fx = static_cast<float>(x);
  float fy = static_cast<float>(y);
  float fz = static_cast<float>(z);

  for (int i=0; i < this->RegionList[regionId]->GetNumberOfPoints(); i++)
    {
    if ( (point[0] == fx) && (point[1] == fy) && (point[2] == fz))
      {
      ptId = static_cast<vtkIdType>(this->LocatorIds[idx + i]);
      break;
      } 

    point += 3;
    }

  return ptId;
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindClosestPoint(double x[3], double &dist2)
{
  vtkIdType id = this->FindClosestPoint(x[0], x[1], x[2], dist2);

  return id;
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindClosestPoint(double x, double y, double z, double &dist2)
{
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindClosestPoint: must build locator first");
    return -1;
    }

  double minDistance2 = 0.0;

  int closeId=-1, newCloseId=-1;  
  double newDistance2 = 4 * this->MaxWidth * this->MaxWidth;

  int regionId = this->GetRegionContainingPoint(x, y, z);

  if (regionId < 0)
    {
    // This point is not inside the space divided by the k-d tree.
    // Find the point on the boundary that is closest to it.

    double pt[3];
    this->Top->GetDistance2ToBoundary(x, y, z, pt, 1);

    double *min = this->Top->GetMinBounds();
    double *max = this->Top->GetMaxBounds();

    // GetDistance2ToBoundary will sometimes return a point *just*
    // *barely* outside the bounds of the region.  Move that point to
    // just barely *inside* instead.

    if (pt[0] <= min[0]) 
      {
      pt[0] = min[0] + this->FudgeFactor;
      }
    if (pt[1] <= min[1]) 
      {
      pt[1] = min[1] + this->FudgeFactor;
      }
    if (pt[2] <= min[2]) 
      {
      pt[2] = min[2] + this->FudgeFactor;
      }
    if (pt[0] >= max[0]) 
      {
      pt[0] = max[0] - this->FudgeFactor;
      }
    if (pt[1] >= max[1])
      {
      pt[1] = max[1] - this->FudgeFactor;
      }
    if (pt[2] >= max[2]) 
      {
      pt[2] = max[2] - this->FudgeFactor;
      }

    regionId = this->GetRegionContainingPoint(pt[0], pt[1], pt[2]);

    closeId = this->_FindClosestPointInRegion(regionId,
                                              x, y, z,
                                              minDistance2);

    // Check to see if neighboring regions have a closer point

    newCloseId = 
      this->FindClosestPointInSphere(x, y, z,
                                     sqrt(minDistance2),    // radius
                                     regionId,        // skip this region
                                     newDistance2);   // distance to closest point
    
    }
  else     // Point is inside a k-d tree region
    {
    closeId = 
      this->_FindClosestPointInRegion(regionId, x, y, z, minDistance2);
  
    if (minDistance2 > 0.0)
      {
      float dist2ToBoundary =
        this->RegionList[regionId]->GetDistance2ToInnerBoundary(x, y, z);
  
      if (dist2ToBoundary < minDistance2)
        {
        // The closest point may be in a neighboring region

        newCloseId = this->FindClosestPointInSphere(x, y, z,
                                                    sqrt(minDistance2),   // radius
                                                    regionId,       // skip this region
                                                    newDistance2);
        }
      }
    }

  if (newDistance2 < minDistance2 && newCloseId != -1)
    {
    closeId = newCloseId;
    minDistance2 = newDistance2;
    }

  vtkIdType closePointId = static_cast<vtkIdType>(this->LocatorIds[closeId]);

  dist2 = minDistance2;

  return closePointId;
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindClosestPointWithinRadius(
  double radius, const double x[3], double& dist2)
{
  int localCloseId = 
    this->FindClosestPointInSphere(x[0], x[1], x[2], radius, -1, dist2);
  if(localCloseId >= 0)
    {
    return static_cast<vtkIdType>(this->LocatorIds[localCloseId]);
    }
  return -1;
}


//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindClosestPointInRegion(int regionId, double *x, double &dist2)
{
  return this->FindClosestPointInRegion(regionId, x[0], x[1], x[2], dist2);
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::FindClosestPointInRegion(int regionId, 
                                              double x, double y, 
                                              double z, double &dist2)
{
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindClosestPointInRegion - must build locator first");
    return -1;
    }
  int localId = this->_FindClosestPointInRegion(regionId, x, y, z, dist2);

  vtkIdType originalId = -1;

  if (localId >= 0)
    {
    originalId = static_cast<vtkIdType>(this->LocatorIds[localId]);
    }

  return originalId;
}

//----------------------------------------------------------------------------
int vtkKdTree::_FindClosestPointInRegion(int regionId, 
                                     double x, double y, double z, double &dist2)
{
  int minId=0;

  double minDistance2 = 4 * this->MaxWidth * this->MaxWidth;

  int idx = this->LocatorRegionLocation[regionId];

  float *candidate = this->LocatorPoints + (idx * 3);

  int numPoints = this->RegionList[regionId]->GetNumberOfPoints();
  for (int i=0; i < numPoints; i++)
    {
    double dx = (x - candidate[0]) * (x - candidate[0]);

    if (dx < minDistance2)
      {
      double dxy = dx + ((y - candidate[1]) * (y - candidate[1]));

      if (dxy < minDistance2)
        {
        double dxyz = dxy + ((z - candidate[2]) * (z - candidate[2]));

        if (dxyz < minDistance2)
          {
          minId = idx + i;
          minDistance2 = dxyz;

          if (dxyz == 0.0) 
            {
            break;
            }
          }
        }
      }

    candidate += 3;
    }

  dist2 = minDistance2;

  return minId;
}

//----------------------------------------------------------------------------
int vtkKdTree::FindClosestPointInSphere(double x, double y, double z, 
                                        double radius, int skipRegion,
                                        double &dist2)
{
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindClosestPointInSphere - must build locator first");
    return -1;
    }
  int *regionIds = new int [this->NumberOfRegions];

  this->BSPCalculator->ComputeIntersectionsUsingDataBoundsOn();

  int nRegions = 
    this->BSPCalculator->IntersectsSphere2(regionIds, this->NumberOfRegions, x, y, z, radius*radius);

  this->BSPCalculator->ComputeIntersectionsUsingDataBoundsOff();

  double minDistance2 = 4 * this->MaxWidth * this->MaxWidth;
  int localCloseId = -1;

  bool recheck = 0; // used to flag that we should recheck the distance
  for (int reg=0; reg < nRegions; reg++)
    {
    if (regionIds[reg] == skipRegion) 
      {
      continue;
      }

    int neighbor = regionIds[reg];

    // recheck that the bin is closer than the current minimum distance
    if(!recheck || this->RegionList[neighbor]->GetDistance2ToBoundary(x, y, z, 1) < minDistance2)
      {
      double newDistance2;
      int newLocalCloseId = this->_FindClosestPointInRegion(neighbor,
                                                            x, y, z, newDistance2);
      
      if (newDistance2 < minDistance2 && newDistance2 <= radius*radius)
        {
        minDistance2 = newDistance2;
        localCloseId = newLocalCloseId;
        recheck = 1; // changed the minimum distance so mark to check subsequent bins
        }
      }
    }
  
  delete [] regionIds;

  dist2 = minDistance2;
  return localCloseId;
}

//----------------------------------------------------------------------------
void vtkKdTree::FindPointsWithinRadius(double R, const double x[3], 
                                       vtkIdList* result)
{
  result->Reset();
  // don't forget to square the radius
  this->FindPointsWithinRadius(this->Top, R*R, x, result);
}

//----------------------------------------------------------------------------
void vtkKdTree::FindPointsWithinRadius(vtkKdNode* node, double R2, 
                                       const double x[3], 
                                       vtkIdList* result)

{
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindPointsWithinRadius - must build locator first");
    return;
    }

  double b[6];
  node->GetBounds(b);

  double mindist2 = 0; // distance to closest vertex of BB
  double maxdist2 = 0; // distance to furthest vertex of BB
  // x-dir
  if(x[0] < b[0])
    {
    mindist2 = (b[0]-x[0])*(b[0]-x[0]);
    maxdist2 = (b[1]-x[0])*(b[1]-x[0]);
    }
  else if(x[0] > b[1])
    {
    mindist2 = (b[1]-x[0])*(b[1]-x[0]);
    maxdist2 = (b[0]-x[0])*(b[0]-x[0]);
    }
  else if((b[1]-x[0]) > (x[0]-b[0]))
    {
    maxdist2 = (b[1]-x[0])*(b[1]-x[0]);    
    }
  else
    {
    maxdist2 = (b[0]-x[0])*(b[0]-x[0]);
    }
  // y-dir
  if(x[1] < b[2])
    {
    mindist2 += (b[2]-x[1])*(b[2]-x[1]);
    maxdist2 += (b[3]-x[1])*(b[3]-x[1]);
    }
  else if(x[1] > b[3])
    {
    mindist2 += (b[3]-x[1])*(b[3]-x[1]);
    maxdist2 += (b[2]-x[1])*(b[2]-x[1]);
    }
  else if((b[3]-x[1]) > (x[1]-b[2]))
    {
    maxdist2 += (b[3]-x[1])*(b[3]-x[1]);
    }
  else
    {
    maxdist2 += (b[2]-x[1])*(b[2]-x[1]);
    }
  // z-dir
  if(x[2] < b[4])
    {
    mindist2 += (b[4]-x[2])*(b[4]-x[2]);
    maxdist2 += (b[5]-x[2])*(b[5]-x[2]);
    }
  else if(x[2] > b[5])
    {
    mindist2 += (b[5]-x[2])*(b[5]-x[2]);
    maxdist2 += (b[4]-x[2])*(b[4]-x[2]);
    }
  else if((b[5]-x[2]) > (x[2]-b[4]))
    {
    maxdist2 += (b[5]-x[2])*(b[5]-x[2]);
    }
  else
    {
    maxdist2 += (x[2]-b[4])*(x[2]-b[4]);
    }

  if(mindist2 > R2)
    {
    // non-intersecting
    return;
    }

  if(maxdist2 <= R2)
    {
    // sphere contains BB
    this->AddAllPointsInRegion(node, result);
    return;
    }

  // partial intersection of sphere & BB
  if (node->GetLeft() == NULL)
    {
    int regionID = node->GetID();
    int regionLoc = this->LocatorRegionLocation[regionID];
    float* pt = this->LocatorPoints + (regionLoc * 3);
    vtkIdType numPoints = this->RegionList[regionID]->GetNumberOfPoints();
    for (vtkIdType i = 0; i < numPoints; i++)
      {
      double dist2 = (pt[0]-x[0])*(pt[0]-x[0])+
        (pt[1]-x[1])*(pt[1]-x[1])+(pt[2]-x[2])*(pt[2]-x[2]);
      if(dist2 <= R2)
        {
        vtkIdType ptId = static_cast<vtkIdType>(this->LocatorIds[regionLoc + i]);
        result->InsertNextId(ptId);
        }
      pt += 3;
      }
    }
  else
    {
    this->FindPointsWithinRadius(node->GetLeft(), R2, x, result);
    this->FindPointsWithinRadius(node->GetRight(), R2, x, result);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::FindClosestNPoints(int N, const double x[3],
                                   vtkIdList* result)
{
  result->Reset();
  if(N<=0)
    {
    return;
    }
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindClosestNPoints - must build locator first");
    return;
    }

  int numTotalPoints = this->Top->GetNumberOfPoints();
  if(numTotalPoints < N)
    {
    vtkWarningMacro("Number of requested points is greater than total number of points in KdTree");
    N = numTotalPoints;
    }
  result->SetNumberOfIds(N);

  // now we want to go about finding a region that contains at least N points 
  // but not many more -- hopefully the region contains X as well but we 
  // can't depend on that
  vtkKdNode* node = this->Top;
  vtkKdNode* startingNode = 0;
  if(!node->ContainsPoint(x[0], x[1], x[2], 0))
    {
    // point is not in the region
    int numPoints = node->GetNumberOfPoints();
    vtkKdNode* prevNode = node;
    while(node->GetLeft() && numPoints > N)
      {
      prevNode = node;
      double leftDist2 = node->GetLeft()->GetDistance2ToBoundary(x[0], x[1], x[2], 1);
      double rightDist2 = node->GetRight()->GetDistance2ToBoundary(x[0], x[1], x[2], 1);
      if(leftDist2 < rightDist2)
        {
        node = node->GetLeft();
        }
      else
        {
        node = node->GetRight();
        }
      numPoints = node->GetNumberOfPoints();
      }
    if(numPoints < N)
      {
      startingNode = prevNode;
      }
    else
      {
      startingNode = node;
      }
    }
  else
    {
    int numPoints = node->GetNumberOfPoints();
    vtkKdNode* prevNode = node;
    while(node->GetLeft() && numPoints > N)
      {
      prevNode = node;
      if(node->GetLeft()->ContainsPoint(x[0], x[1], x[2], 0))
        {
        node = node->GetLeft();
        }
      else
        {
        node = node->GetRight();      
        }
      numPoints = node->GetNumberOfPoints();
      }
    if(numPoints < N)
      {
      startingNode = prevNode;
      }
    else
      {
      startingNode = node;
      }
    }

  // now that we have a starting region, go through its points
  // and order them
  int regionId = startingNode->GetID();
  int numPoints = startingNode->GetNumberOfPoints();
  int where;
  if(regionId >= 0)
    {
    where = this->LocatorRegionLocation[regionId];
    }
  else
    {
    vtkKdNode* left = startingNode->GetLeft();
    vtkKdNode* next = left->GetLeft();
    while(next)
      {
      left = next;
      next = next->GetLeft();
      }
    int leftRegionId = left->GetID();
    where = this->LocatorRegionLocation[leftRegionId];
    }
  int *ids = this->LocatorIds + where;
  float* pt = this->LocatorPoints + (where*3);
  float xfloat[3] = {x[0], x[1], x[2]};
  OrderPoints orderedPoints(N);
  for (int i=0; i<numPoints; i++)
    {
    float dist2 = vtkMath::Distance2BetweenPoints(xfloat, pt);
    orderedPoints.InsertPoint(dist2, ids[i]);
    pt += 3;
    }

  // to finish up we have to check other regions for 
  // closer points
  float LargestDist2 = orderedPoints.GetLargestDist2();
  double delta[3] = {0,0,0};
  double bounds[6];
  node = this->Top;
  vtkstd::queue<vtkKdNode*> nodesToBeSearched;
  nodesToBeSearched.push(node);
  while(!nodesToBeSearched.empty())
    {
    node = nodesToBeSearched.front();
    nodesToBeSearched.pop();
    if(node == startingNode)
      {
      continue;
      }
    vtkKdNode* left = node->GetLeft();
    if(left)
      {
      left->GetDataBounds(bounds);
      if(vtkMath::PointIsWithinBounds(const_cast<double*>(x), bounds, delta) == 1 ||
         left->GetDistance2ToBoundary(x[0], x[1], x[2], 1) < LargestDist2)
        {
        nodesToBeSearched.push(left);
        }
      node->GetRight()->GetDataBounds(bounds);
      if(vtkMath::PointIsWithinBounds(const_cast<double*>(x), bounds, delta) == 1 ||
         node->GetRight()->GetDistance2ToBoundary(x[0], x[1], x[2], 1) < LargestDist2)
        {
        nodesToBeSearched.push(node->GetRight());
        }
      }
    else if(node->GetDistance2ToBoundary(x[0], x[1], x[2], 1) < LargestDist2)
      {
      regionId = node->GetID();
      numPoints = node->GetNumberOfPoints();
      where = this->LocatorRegionLocation[regionId];
      ids = this->LocatorIds + where;
      pt = this->LocatorPoints + (where*3);
      for (int i=0; i<numPoints; i++)
        {
        float dist2 = vtkMath::Distance2BetweenPoints(xfloat, pt);
        orderedPoints.InsertPoint(dist2, ids[i]);
        pt += 3;
        }
      LargestDist2 = orderedPoints.GetLargestDist2();
      }
    }
  orderedPoints.GetSortedIds(result);
}
                                   

//----------------------------------------------------------------------------
vtkIdTypeArray *vtkKdTree::GetPointsInRegion(int regionId)
{
  if ( (regionId < 0) || (regionId >= this->NumberOfRegions))
    {
    vtkErrorMacro(<< "vtkKdTree::GetPointsInRegion invalid region ID");
    return NULL;
    }

  if (!this->LocatorIds)
    {
    vtkErrorMacro(<< "vtkKdTree::GetPointsInRegion build locator first");
    return NULL;
    }

  int numPoints = this->RegionList[regionId]->GetNumberOfPoints();
  int where = this->LocatorRegionLocation[regionId];

  vtkIdTypeArray *ptIds = vtkIdTypeArray::New();
  ptIds->SetNumberOfValues(numPoints);

  int *ids = this->LocatorIds + where;

  for (int i=0; i<numPoints; i++)
    {
    ptIds->SetValue(i, ids[i]);
    }

  return ptIds;
}

//----------------------------------------------------------------------------
// Code to save state/time of last k-d tree build, and to
// determine if a data set's geometry has changed since the
// last build. 
//
void vtkKdTree::InvalidateGeometry()
{
  // Remove observers to data sets.
  for (int i = 0; i < this->LastNumDataSets; i++)
    {
    this->LastInputDataSets[i]
      ->RemoveObserver(this->LastDataSetObserverTags[i]);
    }

  this->LastNumDataSets = 0;
}

//-----------------------------------------------------------------------------
void vtkKdTree::ClearLastBuildCache()
{
  this->InvalidateGeometry();

  if (this->LastDataCacheSize > 0)
    {
    delete [] this->LastInputDataSets;
    delete [] this->LastDataSetObserverTags;
    delete [] this->LastDataSetType;
    delete [] this->LastInputDataInfo;
    delete [] this->LastBounds;
    delete [] this->LastNumCells;
    delete [] this->LastNumPoints;
    this->LastDataCacheSize = 0;
    }
  this->LastNumDataSets = 0;
  this->LastInputDataSets = NULL;
  this->LastDataSetObserverTags = NULL;
  this->LastDataSetType = NULL;
  this->LastInputDataInfo = NULL;
  this->LastBounds        = NULL;
  this->LastNumPoints     = NULL;
  this->LastNumCells      = NULL;
}

//----------------------------------------------------------------------------
void vtkKdTree::UpdateBuildTime()
{
  this->BuildTime.Modified();

  // Save enough information so that next time we execute,
  // we can determine whether input geometry has changed.

  this->InvalidateGeometry();

  int numDataSets = this->GetNumberOfDataSets();
  if (numDataSets > this->LastDataCacheSize)
    {
    this->ClearLastBuildCache();

    this->LastInputDataSets = new vtkDataSet * [numDataSets];
    this->LastDataSetObserverTags = new unsigned long [numDataSets];
    this->LastDataSetType = new int [numDataSets];
    this->LastInputDataInfo = new double [9 * numDataSets];
    this->LastBounds = new double [6 * numDataSets];
    this->LastNumPoints = new vtkIdType [numDataSets];
    this->LastNumCells = new vtkIdType [numDataSets];
    this->LastDataCacheSize = numDataSets;
    }

  this->LastNumDataSets = numDataSets;

  int nextds = 0;

  vtkCollectionSimpleIterator cookie;
  this->DataSets->InitTraversal(cookie);
  for (vtkDataSet *in = this->DataSets->GetNextDataSet(cookie);
       in != NULL; in = this->DataSets->GetNextDataSet(cookie))
    {
    if (nextds >= numDataSets)
      {
      vtkErrorMacro(<< "vtkKdTree::UpdateBuildTime corrupt counts");
      return;
      }

    vtkCallbackCommand *cbc = vtkCallbackCommand::New();
    cbc->SetCallback(LastInputDeletedCallback);
    cbc->SetClientData(this);
    this->LastDataSetObserverTags[nextds]
      = in->AddObserver(vtkCommand::DeleteEvent, cbc);
    cbc->Delete();

    this->LastInputDataSets[nextds] = in;

    this->LastNumPoints[nextds] = in->GetNumberOfPoints();
    this->LastNumCells[nextds] = in->GetNumberOfCells();

    in->GetBounds(this->LastBounds + 6*nextds);
  
    int type = this->LastDataSetType[nextds] = in->GetDataObjectType();

    if ((type == VTK_IMAGE_DATA) || (type == VTK_UNIFORM_GRID))
      {
      double origin[3], spacing[3];
      int dims[3];
  
      if (type == VTK_IMAGE_DATA)
        {
        vtkImageData *id = vtkImageData::SafeDownCast(in);
        id->GetDimensions(dims);
        id->GetOrigin(origin);
        id->GetSpacing(spacing);
        }
      else
        {
        vtkUniformGrid *ug = vtkUniformGrid::SafeDownCast(in);
        ug->GetDimensions(dims);
        ug->GetOrigin(origin);
        ug->GetSpacing(spacing);
        }
  
      this->SetInputDataInfo(nextds, dims, origin, spacing);
      }

    nextds++;
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::SetInputDataInfo(int i, int dims[3], double origin[3], 
                                 double spacing[3])
{
  int idx = 9*i;
  this->LastInputDataInfo[idx++] = static_cast<double>(dims[0]);
  this->LastInputDataInfo[idx++] = static_cast<double>(dims[1]);
  this->LastInputDataInfo[idx++] = static_cast<double>(dims[2]);
  this->LastInputDataInfo[idx++] = origin[0];
  this->LastInputDataInfo[idx++] = origin[1];
  this->LastInputDataInfo[idx++] = origin[2];
  this->LastInputDataInfo[idx++] = spacing[0];
  this->LastInputDataInfo[idx++] = spacing[1];
  this->LastInputDataInfo[idx++] = spacing[2];
}

//----------------------------------------------------------------------------
int vtkKdTree::CheckInputDataInfo(int i, int dims[3], double origin[3], 
                                  double spacing[3])
{
  int sameValues = 1;
  int idx = 9*i; 

  if ((dims[0] != static_cast<int>(this->LastInputDataInfo[idx])) ||
      (dims[1] != static_cast<int>(this->LastInputDataInfo[idx+1])) ||
      (dims[2] != static_cast<int>(this->LastInputDataInfo[idx+2])) ||
      (origin[0] != this->LastInputDataInfo[idx+3]) ||
      (origin[1] != this->LastInputDataInfo[idx+4]) ||
      (origin[2] != this->LastInputDataInfo[idx+5]) ||
      (spacing[0] != this->LastInputDataInfo[idx+6]) ||
      (spacing[1] != this->LastInputDataInfo[idx+7]) ||
      (spacing[2] != this->LastInputDataInfo[idx+8]) ) 
    {
    sameValues = 0;
    }

  return sameValues;
}

//----------------------------------------------------------------------------
int vtkKdTree::NewGeometry()
{
  if (this->GetNumberOfDataSets() != this->LastNumDataSets)
    {
    return 1;
    }

  vtkDataSet **tmp = new vtkDataSet * [this->GetNumberOfDataSets()];
  for (int i=0; i < this->GetNumberOfDataSets(); i++)
    {
    tmp[i] = this->GetDataSet(i);
    }

  int itsNew = this->NewGeometry(tmp, this->GetNumberOfDataSets());

  delete [] tmp;

  return itsNew;
}
int vtkKdTree::NewGeometry(vtkDataSet **sets, int numSets)
{
  int newGeometry = 0;
#if 0
  vtkPointSet *ps = NULL;
#endif
  vtkRectilinearGrid *rg = NULL;
  vtkImageData *id = NULL;
  vtkUniformGrid *ug = NULL;
  int same=0;
  int dims[3];
  double origin[3], spacing[3];

  if (numSets != this->LastNumDataSets)
    {
    return 1;
    }

  for (int i=0; i<numSets; i++)
    {
    vtkDataSet *in = this->LastInputDataSets[i];
    int type = in->GetDataObjectType();
  
    if (type != this->LastDataSetType[i])
      {
      newGeometry = 1;
      break;
      }
  
    switch (type)
      {
      case VTK_POLY_DATA:
      case VTK_UNSTRUCTURED_GRID:
      case VTK_STRUCTURED_GRID:
  #if 0
        // For now, vtkPExodusReader creates a whole new
        // vtkUnstructuredGrid, even when just changing
        // field arrays.  So we'll just check bounds.
        ps = vtkPointSet::SafeDownCast(in);
        if (ps->GetPoints()->GetMTime() > this->BuildTime)
          {
          newGeometry = 1;
          }
  #else
        if ((sets[i]->GetNumberOfPoints() != this->LastNumPoints[i]) || 
            (sets[i]->GetNumberOfCells() != this->LastNumCells[i]) )
          {
          newGeometry = 1;
          }
        else
          {
          double b[6];
          sets[i]->GetBounds(b);
          double *lastb = this->LastBounds + 6*i;
  
          for (int dim=0; dim<6; dim++)
            {
            if (*lastb++ != b[dim])
              {
              newGeometry = 1;
              break;
              }
            }
          }
  #endif
        break;
      
      case VTK_RECTILINEAR_GRID:
  
        rg = vtkRectilinearGrid::SafeDownCast(in);
        if ((rg->GetXCoordinates()->GetMTime() > this->BuildTime) ||
            (rg->GetYCoordinates()->GetMTime() > this->BuildTime) ||
            (rg->GetZCoordinates()->GetMTime() > this->BuildTime) )
          {
          newGeometry = 1;
          }
        break;
  
      case VTK_IMAGE_DATA:
      case VTK_STRUCTURED_POINTS:
      
        id = vtkImageData::SafeDownCast(in);
  
        id->GetDimensions(dims);
        id->GetOrigin(origin);
        id->GetSpacing(spacing);
  
        same = this->CheckInputDataInfo(i, dims, origin, spacing);
  
        if (!same)
          {
          newGeometry = 1;
          }
  
        break;
  
      case VTK_UNIFORM_GRID:
  
        ug = vtkUniformGrid::SafeDownCast(in);
  
        ug->GetDimensions(dims);
        ug->GetOrigin(origin);
        ug->GetSpacing(spacing);
  
        same = this->CheckInputDataInfo(i, dims, origin, spacing);
        
        if (!same)
          {
          newGeometry = 1;
          }
        else if (ug->GetPointVisibilityArray()->GetMTime() > 
                 this->BuildTime)
          {
          newGeometry = 1;
          }
        else if (ug->GetCellVisibilityArray()->GetMTime() > 
                 this->BuildTime)
          {
          newGeometry = 1;
          }
        break;
  
      default:
        vtkWarningMacro(<< 
          "vtkKdTree::NewGeometry: unanticipated type");
  
        newGeometry = 1;
      }
    if (newGeometry) 
      {
      break;
      }
    }

  return newGeometry;
}

//----------------------------------------------------------------------------
void vtkKdTree::__printTree(vtkKdNode *kd, int depth, int v)
{
  if (v) 
    { 
    kd->PrintVerboseNode(depth);
    }
  else   
    { 
    kd->PrintNode(depth);
    }

  if (kd->GetLeft()) 
    { 
    vtkKdTree::__printTree(kd->GetLeft(), depth+1, v);
    }
  if (kd->GetRight()) 
    { 
    vtkKdTree::__printTree(kd->GetRight(), depth+1, v);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::_printTree(int v)
{
  vtkKdTree::__printTree(this->Top, 0, v);
}

//----------------------------------------------------------------------------
void vtkKdTree::PrintRegion(int id)
{
  this->RegionList[id]->PrintNode(0);
}

//----------------------------------------------------------------------------
void vtkKdTree::PrintTree()
{   
  _printTree(0);
}  

//----------------------------------------------------------------------------
void vtkKdTree::PrintVerboseTree()
{      
  _printTree(1);
}          

//----------------------------------------------------------------------------
void vtkKdTree::FreeSearchStructure()
{
  if (this->Top) 
    {
    vtkKdTree::DeleteAllDescendants(this->Top);
    this->Top->Delete();
    this->Top = NULL;
    }
  if (this->RegionList)
    {
    delete [] this->RegionList;
    this->RegionList = NULL;
    } 

  this->NumberOfRegions = 0;
  this->SetActualLevel();

  this->DeleteCellLists();

  if (this->CellRegionList)
    {
    delete [] this->CellRegionList;
    this->CellRegionList = NULL;
    }

  if (this->LocatorPoints)
    {
    delete [] this->LocatorPoints;
    this->LocatorPoints = NULL;
    }

  if (this->LocatorIds)
    {
    delete [] this->LocatorIds;
    this->LocatorIds = NULL;
    }

  if (this->LocatorRegionLocation)
    {
    delete [] this->LocatorRegionLocation;
    this->LocatorRegionLocation = NULL;
    }
}

//----------------------------------------------------------------------------
// build PolyData representation of all spacial regions------------
//
void vtkKdTree::GenerateRepresentation(int level, vtkPolyData *pd)
{
  if (this->GenerateRepresentationUsingDataBounds)
    {
    this->GenerateRepresentationDataBounds(level, pd);
    }
  else
    {
    this->GenerateRepresentationWholeSpace(level, pd);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::GenerateRepresentationWholeSpace(int level, vtkPolyData *pd)
{
  int i;

  vtkPoints *pts;
  vtkCellArray *polys;

  if ( this->Top == NULL )
    {
    vtkErrorMacro(<<"vtkKdTree::GenerateRepresentation empty tree");
    return;
    }

  if ((level < 0) || (level > this->Level)) 
    {
    level = this->Level;
    }

  int npoints = 0;
  int npolys  = 0;

  for (i=0 ; i < level; i++)
    {
    int levelPolys = 1 << (i-1);
    npoints += (4 * levelPolys);
    npolys += levelPolys;
    }

  pts = vtkPoints::New();
  pts->Allocate(npoints); 
  polys = vtkCellArray::New();
  polys->Allocate(npolys);

  // level 0 bounding box

  vtkIdType ids[8];
  vtkIdType idList[4];
  double     x[3];
  vtkKdNode    *kd    = this->Top;

  double *min = kd->GetMinBounds();
  double *max = kd->GetMaxBounds();

  x[0]  = min[0]; x[1]  = max[1]; x[2]  = min[2];
  ids[0] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = max[1]; x[2]  = min[2];
  ids[1] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = max[1]; x[2]  = max[2];
  ids[2] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = max[1]; x[2]  = max[2];
  ids[3] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = min[1]; x[2]  = min[2];
  ids[4] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = min[1]; x[2]  = min[2];
  ids[5] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = min[1]; x[2]  = max[2];
  ids[6] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = min[1]; x[2]  = max[2];
  ids[7] = pts->InsertNextPoint(x);

  idList[0] = ids[0]; idList[1] = ids[1]; idList[2] = ids[2]; idList[3] = ids[3];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[1]; idList[1] = ids[5]; idList[2] = ids[6]; idList[3] = ids[2];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[5]; idList[1] = ids[4]; idList[2] = ids[7]; idList[3] = ids[6];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[4]; idList[1] = ids[0]; idList[2] = ids[3]; idList[3] = ids[7];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[3]; idList[1] = ids[2]; idList[2] = ids[6]; idList[3] = ids[7];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[1]; idList[1] = ids[0]; idList[2] = ids[4]; idList[3] = ids[5];
  polys->InsertNextCell(4, idList);

  if (kd->GetLeft() && (level > 0))
    {
    this->_generateRepresentationWholeSpace(kd, pts, polys, level-1);
    }

  pd->SetPoints(pts);
  pts->Delete();
  pd->SetPolys(polys);
  polys->Delete();
  pd->Squeeze();
}

//----------------------------------------------------------------------------
void vtkKdTree::_generateRepresentationWholeSpace(vtkKdNode *kd, 
                                        vtkPoints *pts, 
                                        vtkCellArray *polys, 
                                        int level)
{
  int i;
  double p[4][3];
  vtkIdType ids[4];

  if ((level < 0) || (kd->GetLeft() == NULL)) 
    {
    return;
    }

  double *min = kd->GetMinBounds();
  double *max = kd->GetMaxBounds();  
  double *leftmax = kd->GetLeft()->GetMaxBounds();

  // splitting plane

  switch (kd->GetDim())
    {
    case XDIM:

      p[0][0] = leftmax[0]; p[0][1] = max[1]; p[0][2] = max[2];
      p[1][0] = leftmax[0]; p[1][1] = max[1]; p[1][2] = min[2];
      p[2][0] = leftmax[0]; p[2][1] = min[1]; p[2][2] = min[2];
      p[3][0] = leftmax[0]; p[3][1] = min[1]; p[3][2] = max[2];

      break;

    case YDIM:

      p[0][0] = min[0]; p[0][1] = leftmax[1]; p[0][2] = max[2];
      p[1][0] = min[0]; p[1][1] = leftmax[1]; p[1][2] = min[2];
      p[2][0] = max[0]; p[2][1] = leftmax[1]; p[2][2] = min[2];
      p[3][0] = max[0]; p[3][1] = leftmax[1]; p[3][2] = max[2];

      break;

    case ZDIM:

      p[0][0] = min[0]; p[0][1] = min[1]; p[0][2] = leftmax[2];
      p[1][0] = min[0]; p[1][1] = max[1]; p[1][2] = leftmax[2];
      p[2][0] = max[0]; p[2][1] = max[1]; p[2][2] = leftmax[2];
      p[3][0] = max[0]; p[3][1] = min[1]; p[3][2] = leftmax[2];

      break;
    }


  for (i=0; i<4; i++) ids[i] = pts->InsertNextPoint(p[i]);

  polys->InsertNextCell(4, ids);

  this->_generateRepresentationWholeSpace(kd->GetLeft(), pts, polys, level-1);
  this->_generateRepresentationWholeSpace(kd->GetRight(), pts, polys, level-1);
}

//----------------------------------------------------------------------------
void vtkKdTree::GenerateRepresentationDataBounds(int level, vtkPolyData *pd)
{
  int i;
  vtkPoints *pts;
  vtkCellArray *polys;

  if ( this->Top == NULL )
    {
    vtkErrorMacro(<<"vtkKdTree::GenerateRepresentation no tree");
    return;
    }

  if ((level < 0) || (level > this->Level)) 
    {
    level = this->Level;
    }

  int npoints = 0;
  int npolys  = 0;

  for (i=0; i < level; i++)
    {
    int levelBoxes= 1 << i;
    npoints += (8 * levelBoxes);
    npolys += (6 * levelBoxes);
    }

  pts = vtkPoints::New();
  pts->Allocate(npoints); 
  polys = vtkCellArray::New();
  polys->Allocate(npolys);

  _generateRepresentationDataBounds(this->Top, pts, polys, level);

  pd->SetPoints(pts);
  pts->Delete();
  pd->SetPolys(polys);
  polys->Delete();
  pd->Squeeze();
}

//----------------------------------------------------------------------------
void vtkKdTree::_generateRepresentationDataBounds(vtkKdNode *kd, vtkPoints *pts,
                     vtkCellArray *polys, int level)
{
  if (level > 0)
    {
      if (kd->GetLeft())
        {
        _generateRepresentationDataBounds(kd->GetLeft(), pts, polys, level-1);
        _generateRepresentationDataBounds(kd->GetRight(), pts, polys, level-1);
        }

      return;
    }
  vtkKdTree::AddPolys(kd, pts, polys);
}

//----------------------------------------------------------------------------
// PolyData rep. of all spacial regions, shrunk to data bounds-------
//
void vtkKdTree::AddPolys(vtkKdNode *kd, vtkPoints *pts, vtkCellArray *polys)
{
  vtkIdType ids[8];
  vtkIdType idList[4];
  double     x[3];

  double *min;
  double *max;

  if (this->GenerateRepresentationUsingDataBounds)
    {
    min = kd->GetMinDataBounds();
    max = kd->GetMaxDataBounds();
    }
  else
    {
    min = kd->GetMinBounds();
    max = kd->GetMaxBounds();
    }

  x[0]  = min[0]; x[1]  = max[1]; x[2]  = min[2];
  ids[0] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = max[1]; x[2]  = min[2];
  ids[1] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = max[1]; x[2]  = max[2];
  ids[2] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = max[1]; x[2]  = max[2];
  ids[3] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = min[1]; x[2]  = min[2];
  ids[4] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = min[1]; x[2]  = min[2];
  ids[5] = pts->InsertNextPoint(x);

  x[0]  = max[0]; x[1]  = min[1]; x[2]  = max[2];
  ids[6] = pts->InsertNextPoint(x);

  x[0]  = min[0]; x[1]  = min[1]; x[2]  = max[2];
  ids[7] = pts->InsertNextPoint(x);

  idList[0] = ids[0]; idList[1] = ids[1]; idList[2] = ids[2]; idList[3] = ids[3];
  polys->InsertNextCell(4, idList);
  
  idList[0] = ids[1]; idList[1] = ids[5]; idList[2] = ids[6]; idList[3] = ids[2];
  polys->InsertNextCell(4, idList);
  
  idList[0] = ids[5]; idList[1] = ids[4]; idList[2] = ids[7]; idList[3] = ids[6];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[4]; idList[1] = ids[0]; idList[2] = ids[3]; idList[3] = ids[7];
  polys->InsertNextCell(4, idList);
  
  idList[0] = ids[3]; idList[1] = ids[2]; idList[2] = ids[6]; idList[3] = ids[7];
  polys->InsertNextCell(4, idList);

  idList[0] = ids[1]; idList[1] = ids[0]; idList[2] = ids[4]; idList[3] = ids[5];
  polys->InsertNextCell(4, idList);
}

//----------------------------------------------------------------------------
// PolyData representation of a list of spacial regions------------
//
void vtkKdTree::GenerateRepresentation(int *regions, int len, vtkPolyData *pd)
{
  int i;
  vtkPoints *pts;
  vtkCellArray *polys;

  if ( this->Top == NULL )
    {
    vtkErrorMacro(<<"vtkKdTree::GenerateRepresentation no tree");
    return;
    }

  int npoints = 8 * len;
  int npolys  = 6 * len;

  pts = vtkPoints::New();
  pts->Allocate(npoints); 
  polys = vtkCellArray::New();
  polys->Allocate(npolys);

  for (i=0; i<len; i++)
    {
    if ((regions[i] < 0) || (regions[i] >= this->NumberOfRegions)) 
      {
      break;
      }

    vtkKdTree::AddPolys(this->RegionList[regions[i]], pts, polys);
    }

  pd->SetPoints(pts);
  pts->Delete();
  pd->SetPolys(polys);
  polys->Delete();
  pd->Squeeze();
}

//----------------------------------------------------------------------------
//  Cell ID lists
//
#define SORTLIST(l, lsize) vtkstd::sort(l, l + lsize)

#define REMOVEDUPLICATES(l, lsize, newsize) \
{                                     \
int ii,jj;                            \
for (ii=0, jj=0; ii<lsize; ii++)      \
  {                                   \
  if ((ii > 0) && (l[ii] == l[jj-1])) \
    {         \
    continue; \
    }         \
  if (jj != ii)    \
    {              \
    l[jj] = l[ii]; \
    }              \
  jj++;            \
}                  \
newsize = jj;      \
}

//----------------------------------------------------------------------------
int vtkKdTree::FoundId(vtkIntArray *idArray, int id)
{
  // This is a simple linear search, because I think it is rare that
  // an id array would be provided, and if one is it should be small.

  int found = 0;
  int len = idArray->GetNumberOfTuples();
  int *ids = idArray->GetPointer(0);

  for (int i=0; i<len; i++)
    {
    if (ids[i] == id)
      {
      found = 1;
      }
    }
    
  return found;
}

//----------------------------------------------------------------------------
int vtkKdTree::findRegion(vtkKdNode *node, float x, float y, float z)
{
  return vtkKdTree::findRegion(node,static_cast<double>(x),static_cast<double>(y),static_cast<double>(z));
}

//----------------------------------------------------------------------------
int vtkKdTree::findRegion(vtkKdNode *node, double x, double y, double z)
{
  int regionId;

  if (!node->ContainsPoint(x, y, z, 0))
    {
    return -1;
    }

  if (node->GetLeft() == NULL)
    {
    regionId = node->GetID();
    }
  else
    {
    regionId = vtkKdTree::findRegion(node->GetLeft(), x, y, z);

    if (regionId < 0)
      {
      regionId = vtkKdTree::findRegion(node->GetRight(), x, y, z);
      }
    }

  return regionId;
}

//----------------------------------------------------------------------------
void vtkKdTree::CreateCellLists()
{
  this->CreateCellLists(static_cast<int *>(NULL), 0);
  return;
}

//----------------------------------------------------------------------------
void vtkKdTree::CreateCellLists(int *regionList, int listSize)
{
  this->CreateCellLists(this->GetDataSet(), regionList, listSize);
  return;
}

//----------------------------------------------------------------------------
void vtkKdTree::CreateCellLists(int dataSetIndex, int *regionList, int listSize)
{
  vtkDataSet *dataSet = this->GetDataSet(dataSetIndex);
  if (!dataSet)
    {
    vtkErrorMacro(<<"vtkKdTree::CreateCellLists invalid data set");
    return;
    }

  this->CreateCellLists(dataSet, regionList, listSize);
  return;
}

//----------------------------------------------------------------------------
void vtkKdTree::CreateCellLists(vtkDataSet *set, int *regionList, int listSize)
{
  int i, AllRegions;

  if ( this->GetDataSetIndex(set) < 0)
    {
    vtkErrorMacro(<<"vtkKdTree::CreateCellLists invalid data set");
    return;
    }

  vtkKdTree::_cellList *list = &this->CellList;

  if (list->nRegions > 0)
    {
    this->DeleteCellLists();
    }

  list->emptyList = vtkIdList::New();

  list->dataSet = set;

  if ((regionList == NULL) || (listSize == 0)) 
    {
    list->nRegions = this->NumberOfRegions;    // all regions
    }
  else 
    {
    list->regionIds = new int [listSize];
  
    if (!list->regionIds)
      {
      vtkErrorMacro(<<"vtkKdTree::CreateCellLists memory allocation");
      return;
      }

    memcpy(list->regionIds, regionList, sizeof(int) * listSize);
    SORTLIST(list->regionIds, listSize);
    REMOVEDUPLICATES(list->regionIds, listSize, list->nRegions);
  
    if (list->nRegions == this->NumberOfRegions)
      {
      delete [] list->regionIds;
      list->regionIds = NULL;
      }
    }

  if (list->nRegions == this->NumberOfRegions)
    {
    AllRegions = 1;
    }
  else
    {
    AllRegions = 0; 
    } 
    
  int *idlist = NULL;
  int idListLen = 0;
  
  if (this->IncludeRegionBoundaryCells)
    {
    list->boundaryCells = new vtkIdList * [list->nRegions];

    if (!list->boundaryCells)
      {
      vtkErrorMacro(<<"vtkKdTree::CreateCellLists memory allocation");
      return;
      }
    
    for (i=0; i<list->nRegions; i++)
      {
      list->boundaryCells[i] = vtkIdList::New();
      }
    idListLen = this->NumberOfRegions;
    
    idlist = new int [idListLen];
    }
  
  int *listptr = NULL;
    
  if (!AllRegions)
    {
    listptr = new int [this->NumberOfRegions];

    if (!listptr)
      {
      vtkErrorMacro(<<"vtkKdTree::CreateCellLists memory allocation");
      return;
      }

    for (i=0; i<this->NumberOfRegions; i++)
      {
      listptr[i] = -1;
      }
    }

  list->cells = new vtkIdList * [list->nRegions];

  if (!list->cells)
    {
    vtkErrorMacro(<<"vtkKdTree::CreateCellLists memory allocation");
    return;
    }

  for (i = 0; i < list->nRegions; i++)
    {
    list->cells[i] = vtkIdList::New();

    if (listptr) 
      {
      listptr[list->regionIds[i]] = i;
      }
    }

  // acquire a list in cell Id order of the region Id each
  // cell centroid falls in

  int *regList = this->CellRegionList;

  if (regList == NULL)
    {
    regList = this->AllGetRegionContainingCell();
    }

  int setNum = this->GetDataSetIndex(set);

  if (setNum > 0)
    {
    int ncells = this->GetDataSetsNumberOfCells(0,setNum-1);
    regList += ncells;
    }

  int nCells = set->GetNumberOfCells();

  for (int cellId=0; cellId<nCells; cellId++)
    {
    if (this->IncludeRegionBoundaryCells)
      {
      // Find all regions the cell intersects, including
      // the region the cell centroid lies in.
      // This can be an expensive calculation, intersections
      // of a convex region with axis aligned boxes.

      int nRegions = 
        this->BSPCalculator->IntersectsCell(idlist, idListLen, 
          set->GetCell(cellId), regList[cellId]);
      
      if (nRegions == 1)
        {
        int idx = (listptr) ? listptr[idlist[0]] : idlist[0];
      
        if (idx >= 0) 
          {
          list->cells[idx]->InsertNextId(cellId);
          }
        }
      else
        {
        for (int r=0; r < nRegions; r++)
          {
          int regionId = idlist[r];
    
          int idx = (listptr) ? listptr[regionId] : regionId;

          if (idx < 0) 
            {
            continue;
            }

          if (regionId == regList[cellId])
            {
            list->cells[idx]->InsertNextId(cellId);
            }
          else
            {
            list->boundaryCells[idx]->InsertNextId(cellId);
            }         
          }
        }
      }
    else 
      {
      // just find the region the cell centroid lies in - easy

      int regionId = regList[cellId];
    
      int idx = (listptr) ? listptr[regionId] : regionId;
  
      if (idx >= 0) 
        {
        list->cells[idx]->InsertNextId(cellId);
        }
      } 
    }

  if (listptr)
    {
    delete [] listptr;
    } 
  if (idlist)
    {
    delete [] idlist;
    }   
}     

//----------------------------------------------------------------------------
vtkIdList * vtkKdTree::GetList(int regionId, vtkIdList **which)
{
  int i;
  struct _cellList *list = &this->CellList;
  vtkIdList *cellIds = NULL;

  if (which && (list->nRegions == this->NumberOfRegions))
    {
    cellIds = which[regionId];
    }
  else if (which)
    {
    for (i=0; i< list->nRegions; i++)
      {
      if (list->regionIds[i] == regionId)
        {
        cellIds = which[i];
        break;
        }
      }
    }
  else
    {
    cellIds = list->emptyList; 
    }

  return cellIds;
}

//----------------------------------------------------------------------------
vtkIdList * vtkKdTree::GetCellList(int regionID)
{
  return this->GetList(regionID, this->CellList.cells);
}

//----------------------------------------------------------------------------
vtkIdList * vtkKdTree::GetBoundaryCellList(int regionID)
{
  return this->GetList(regionID, this->CellList.boundaryCells);
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::GetCellLists(vtkIntArray *regions,
          int setIndex, vtkIdList *inRegionCells, vtkIdList *onBoundaryCells)
{
  vtkDataSet *set = this->GetDataSet(setIndex);
  if (!set)
    {
    vtkErrorMacro(<<"vtkKdTree::GetCellLists no such data set");
    return 0;
    }
  return this->GetCellLists(regions, set, 
                            inRegionCells, onBoundaryCells);
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::GetCellLists(vtkIntArray *regions,
          vtkIdList *inRegionCells, vtkIdList *onBoundaryCells)
{
  return this->GetCellLists(regions, this->GetDataSet(), 
                            inRegionCells, onBoundaryCells);
}

//----------------------------------------------------------------------------
vtkIdType vtkKdTree::GetCellLists(vtkIntArray *regions, vtkDataSet *set,
          vtkIdList *inRegionCells, vtkIdList *onBoundaryCells)
{
  int reg, regionId;
  vtkIdType cell, cellId, numCells;
  vtkIdList *cellIds;

  vtkIdType totalCells = 0;

  if ( (inRegionCells == NULL) && (onBoundaryCells == NULL))
    {
    return totalCells;
    }

  int nregions = regions->GetNumberOfTuples();

  if (nregions == 0)
    {
    return totalCells;
    }

  // Do I have cell lists for all these regions?  If not, build cell
  // lists for all regions for this data set.

  int rebuild = 0;

  if (this->CellList.dataSet != set)
    {
    rebuild = 1;
    }
  else if (nregions > this->CellList.nRegions)
    {
    rebuild = 1;
    }
  else if ((onBoundaryCells != NULL) && (this->CellList.boundaryCells == NULL))
    {
    rebuild = 1;
    }
  else if (this->CellList.nRegions < this->NumberOfRegions)
    {
    // these two lists should generally be "short"

    int *haveIds = this->CellList.regionIds;

    for (int wantReg=0; wantReg < nregions; wantReg++)
      {
      int wantRegion = regions->GetValue(wantReg);
      int gotId = 0;

      for (int haveReg=0; haveReg < this->CellList.nRegions; haveReg++)
        {
        if (haveIds[haveReg] == wantRegion)
          {
          gotId = 1;
          break;
          }
        }
      if (!gotId)
        {
        rebuild = 1;
        break;
        }
      }
    }

  if (rebuild)
    {
    if (onBoundaryCells != NULL)
      {
      this->IncludeRegionBoundaryCellsOn();
      }
    this->CreateCellLists(set, NULL, 0);  // for all regions
    }

  // OK, we have cell lists for these regions.  Make lists of region
  // cells and boundary cells.

  int CheckSet = (onBoundaryCells && (nregions > 1));

  vtkstd::set<vtkIdType> ids;
  vtkstd::pair<vtkstd::set<vtkIdType>::iterator, bool> idRec;

  vtkIdType totalRegionCells = 0;
  vtkIdType totalBoundaryCells = 0;

  vtkIdList **inRegionList = new vtkIdList * [nregions];

  // First the cell IDs with centroid in the regions

  for (reg = 0; reg < nregions; reg++)
    {
    regionId = regions->GetValue(reg);

    inRegionList[reg] = this->GetCellList(regionId);

    totalRegionCells += inRegionList[reg]->GetNumberOfIds();
    }

  if (inRegionCells)
    {
    inRegionCells->Initialize();
    inRegionCells->SetNumberOfIds(totalRegionCells);
    }
        
  int nextCell = 0;
          
  for (reg = 0; reg <  nregions; reg++)
    {     
    cellIds = inRegionList[reg];
      
    numCells = cellIds->GetNumberOfIds();
        
    for (cell = 0; cell < numCells; cell++)
      { 
      if (inRegionCells)
        {
        inRegionCells->SetId(nextCell++, cellIds->GetId(cell));
        }
      
      if (CheckSet)
        {
        // We have to save the ids, so we don't include
        // them as boundary cells.  A cell in one region
        // may be a boundary cell of another region.
      
        ids.insert(cellIds->GetId(cell));
        }
      }
    }
  
  delete [] inRegionList;
  
  if (onBoundaryCells == NULL)
    {
    return totalRegionCells;
    }
  
  // Now the list of all cells on the boundary of the regions,
  // which do not have their centroid in one of the regions

  onBoundaryCells->Initialize();
    
  for (reg = 0; reg < nregions; reg++)
    {
    regionId = regions->GetValue(reg);

    cellIds = this->GetBoundaryCellList(regionId);
    
    numCells = cellIds->GetNumberOfIds();
  
    for (cell = 0; cell < numCells; cell++)
      {
      cellId = cellIds->GetId(cell);
    
      if (CheckSet)
        {
        // if we already included this cell because it is within 
        // one of the regions, or on the boundary of another, skip it

        idRec = ids.insert(cellId);

        if (idRec.second == 0) 
          {
          continue;
          }
        }

      onBoundaryCells->InsertNextId(cellId);
      totalBoundaryCells++;
      }

    totalCells += totalBoundaryCells;
    }

  return totalCells;
}

//----------------------------------------------------------------------------
int vtkKdTree::GetRegionContainingCell(vtkIdType cellID)
{
  return this->GetRegionContainingCell(this->GetDataSet(), cellID);
}

//----------------------------------------------------------------------------
int vtkKdTree::GetRegionContainingCell(int setIndex, vtkIdType cellID)
{
  vtkDataSet *set = this->GetDataSet(setIndex);
  if (!set)
    {
    vtkErrorMacro(<<"vtkKdTree::GetRegionContainingCell no such data set");
    return -1;
    }
  return this->GetRegionContainingCell(set, cellID);
}

//----------------------------------------------------------------------------
int vtkKdTree::GetRegionContainingCell(vtkDataSet *set, vtkIdType cellID)
{
  int regionID = -1;

  if ( this->GetDataSetIndex(set) < 0)
    {
    vtkErrorMacro(<<"vtkKdTree::GetRegionContainingCell no such data set");
    return -1;
    }
  if ( (cellID < 0) || (cellID >= set->GetNumberOfCells()))
    {
    vtkErrorMacro(<<"vtkKdTree::GetRegionContainingCell bad cell ID");
    return -1;
    }
  
  if (this->CellRegionList)
    {
    if (set == this->GetDataSet())        // 99.99999% of the time
      {
      return this->CellRegionList[cellID];
      }
    
    int setNum = this->GetDataSetIndex(set);
    
    int offset = this->GetDataSetsNumberOfCells(0, setNum-1);
    
    return this->CellRegionList[offset + cellID];
    }
  
  float center[3];
  
  this->ComputeCellCenter(set, cellID, center);
  
  regionID = this->GetRegionContainingPoint(center[0], center[1], center[2]);
  
  return regionID;
}

//----------------------------------------------------------------------------
int *vtkKdTree::AllGetRegionContainingCell()
{ 
  if (this->CellRegionList)
    {
    return this->CellRegionList;
    }
  this->CellRegionList = new int [this->GetNumberOfCells()];
  
  if (!this->CellRegionList)
    {
    vtkErrorMacro(<<"vtkKdTree::AllGetRegionContainingCell memory allocation");
    return NULL;
    }
  
  int *listPtr = this->CellRegionList;

  vtkCollectionSimpleIterator cookie;
  this->DataSets->InitTraversal(cookie);
  for (vtkDataSet *iset = this->DataSets->GetNextDataSet(cookie);
       iset != NULL; iset = this->DataSets->GetNextDataSet(cookie))
    {
    int setCells = iset->GetNumberOfCells();
    
    float *centers = this->ComputeCellCenters(iset);
    
    float *pt = centers;

    for (int cellId = 0; cellId < setCells; cellId++)
      {
      listPtr[cellId] =
        this->GetRegionContainingPoint(pt[0], pt[1], pt[2]);

      pt += 3;
      }

    listPtr += setCells;

    delete [] centers;
    }

  return this->CellRegionList;
}

//----------------------------------------------------------------------------
int vtkKdTree::GetRegionContainingPoint(double x, double y, double z)
{
  return vtkKdTree::findRegion(this->Top, x, y, z);
}
//----------------------------------------------------------------------------
int vtkKdTree::MinimalNumberOfConvexSubRegions(vtkIntArray *regionIdList,
                                               double **convexSubRegions)
{
  int nids = 0;

  if ((regionIdList == NULL) ||
      ((nids = regionIdList->GetNumberOfTuples()) == 0))
    {
    vtkErrorMacro(<< 
      "vtkKdTree::MinimalNumberOfConvexSubRegions no regions specified");
    return 0;
    }

  int i;
  int *ids = regionIdList->GetPointer(0);

  if (nids == 1)
    {
    if ( (ids[0] < 0) || (ids[0] >= this->NumberOfRegions))
      {
      vtkErrorMacro(<< 
        "vtkKdTree::MinimalNumberOfConvexSubRegions bad region ID");
      return 0;
      }

    double *bounds = new double [6];

    this->RegionList[ids[0]]->GetBounds(bounds);

    *convexSubRegions = bounds;

    return 1;
    }

  // create a sorted list of unique region Ids

  vtkstd::set<int> idSet;
  vtkstd::set<int>::iterator it;

  for (i=0; i<nids; i++)
    {
    idSet.insert(ids[i]);
    }

  int nUniqueIds = static_cast<int>(idSet.size());

  int *idList = new int [nUniqueIds];
      
  for (i=0, it = idSet.begin(); it != idSet.end(); ++it, ++i)
    { 
    idList[i] = *it;
    }

  vtkKdNode **regions = new vtkKdNode * [nUniqueIds];

  int nregions = vtkKdTree::__ConvexSubRegions(idList, nUniqueIds, this->Top, regions);
    
  double *bounds = new double [nregions * 6];

  for (i=0; i<nregions; i++) 
    {
    regions[i]->GetBounds(bounds + (i*6));
    }

  *convexSubRegions = bounds;
    
  delete [] idList;
  delete [] regions;

  return nregions; 
}
//----------------------------------------------------------------------------
int vtkKdTree::__ConvexSubRegions(int *ids, int len, vtkKdNode *tree, vtkKdNode **nodes)
{
  int nregions = tree->GetMaxID() - tree->GetMinID() + 1;

  if (nregions == len)
    {
    *nodes = tree;
    return 1;
    }

  if (tree->GetLeft() == NULL)
    {
    return 0;
    }

  int min = ids[0];
  int max = ids[len-1];

  int leftMax = tree->GetLeft()->GetMaxID();
  int rightMin = tree->GetRight()->GetMinID();

  if (max <= leftMax)
    {
    return vtkKdTree::__ConvexSubRegions(ids, len, tree->GetLeft(), nodes);
    }
  else if (min >= rightMin)
    {
    return vtkKdTree::__ConvexSubRegions(ids, len, tree->GetRight(), nodes);
    }
  else
    {
    int leftIds = 1;

    for (int i=1; i<len-1; i++)
      {
      if (ids[i] <= leftMax)
        {
        leftIds++;
        }
      else
        {
        break;
        }
      }

    int numNodesLeft =
      vtkKdTree::__ConvexSubRegions(ids, leftIds, tree->GetLeft(), nodes);

    
    int numNodesRight =
      vtkKdTree::__ConvexSubRegions(ids + leftIds, len - leftIds,
                               tree->GetRight(), nodes + numNodesLeft);
    
    return (numNodesLeft + numNodesRight);                                               
    }
}

//-----------------------------------------------------------------------------
#ifndef VTK_LEGACY_REMOVE

int vtkKdTree::DepthOrderRegions(vtkIntArray *regionIds,
                                 double *directionOfProjection,
                                 vtkIntArray *orderedList)
{   
  VTK_LEGACY_REPLACED_BODY(vtkKdTree::DepthOrderRegions, "VTK 5.2",
                           vtkKdTree::ViewOrderRegionsInDirection);
  return this->ViewOrderRegionsInDirection(regionIds, directionOfProjection,
                                           orderedList);
}

int vtkKdTree::DepthOrderAllRegions(double *directionOfProjection,
                                    vtkIntArray *orderedList)
{   
  VTK_LEGACY_REPLACED_BODY(vtkKdTree::DepthOrderAllRegions, "VTK 5.2",
                           vtkKdTree::ViewOrderAllRegionsInDirection);
  return this->ViewOrderAllRegionsInDirection(directionOfProjection,
                                              orderedList);
}

#endif //VTK_LEGACY_REMOVE

//----------------------------------------------------------------------------
int vtkKdTree::ViewOrderRegionsInDirection(
                                          vtkIntArray *regionIds,
                                          const double directionOfProjection[3],
                                          vtkIntArray *orderedList)
{
  int i;
        
  vtkIntArray *IdsOfInterest = NULL;
      
  if (regionIds && (regionIds->GetNumberOfTuples() > 0))
    {   
    // Created sorted list of unique ids
      
    vtkstd::set<int> ids;
    vtkstd::set<int>::iterator it;
    int nids = regionIds->GetNumberOfTuples();

    for (i=0; i<nids; i++)
      {
      ids.insert(regionIds->GetValue(i));
      }

    if (ids.size() < static_cast<unsigned int>(this->NumberOfRegions))
      {
      IdsOfInterest = vtkIntArray::New();
      IdsOfInterest->SetNumberOfValues(ids.size());

      for (it = ids.begin(), i=0; it != ids.end(); ++it, ++i)
        {
        IdsOfInterest->SetValue(i, *it);
        }
      }
    }

  int size = this->_ViewOrderRegionsInDirection(IdsOfInterest, 
                                                directionOfProjection,
                                                orderedList);

  if (IdsOfInterest)
    {
    IdsOfInterest->Delete();
    }

  return size;
}

//----------------------------------------------------------------------------
int vtkKdTree::ViewOrderAllRegionsInDirection(
                                          const double directionOfProjection[3],
                                          vtkIntArray *orderedList)
{
  return this->_ViewOrderRegionsInDirection(NULL, directionOfProjection,
                                            orderedList);
}     

//----------------------------------------------------------------------------
int vtkKdTree::ViewOrderRegionsFromPosition(vtkIntArray *regionIds,
                                            const double cameraPosition[3],
                                            vtkIntArray *orderedList)
{
  int i;
        
  vtkIntArray *IdsOfInterest = NULL;
      
  if (regionIds && (regionIds->GetNumberOfTuples() > 0))
    {   
    // Created sorted list of unique ids
      
    vtkstd::set<int> ids;
    vtkstd::set<int>::iterator it;
    int nids = regionIds->GetNumberOfTuples();

    for (i=0; i<nids; i++)
      {
      ids.insert(regionIds->GetValue(i));
      }

    if (ids.size() < static_cast<unsigned int>(this->NumberOfRegions))
      {
      IdsOfInterest = vtkIntArray::New();
      IdsOfInterest->SetNumberOfValues(ids.size());

      for (it = ids.begin(), i=0; it != ids.end(); ++it, ++i)
        {
        IdsOfInterest->SetValue(i, *it);
        }
      }
    }

  int size = this->_ViewOrderRegionsFromPosition(IdsOfInterest, 
                                                 cameraPosition,
                                                 orderedList);

  if (IdsOfInterest)
    {
    IdsOfInterest->Delete();
    }

  return size;
}

//----------------------------------------------------------------------------
int vtkKdTree::ViewOrderAllRegionsFromPosition(const double cameraPosition[3],
                                               vtkIntArray *orderedList)
{
  return this->_ViewOrderRegionsFromPosition(NULL, cameraPosition, orderedList);
}

//----------------------------------------------------------------------------
int vtkKdTree::_ViewOrderRegionsInDirection(vtkIntArray *IdsOfInterest,
                                            const double dir[3],
                                            vtkIntArray *orderedList)
{
  int nextId = 0;
      
  int numValues = (IdsOfInterest ? IdsOfInterest->GetNumberOfTuples() :
                                   this->NumberOfRegions);
    
  orderedList->Initialize();
  orderedList->SetNumberOfValues(numValues);

  int size = vtkKdTree::__ViewOrderRegionsInDirection(this->Top, orderedList,
                                                      IdsOfInterest, dir,
                                                      nextId);
  if (size < 0)
    {
    vtkErrorMacro(<<"vtkKdTree::DepthOrderRegions k-d tree structure is corrupt");
    orderedList->Initialize();
    return 0;
    }

  return size;
}
//----------------------------------------------------------------------------
int vtkKdTree::__ViewOrderRegionsInDirection(vtkKdNode *node,
                                             vtkIntArray *list,
                                             vtkIntArray *IdsOfInterest,
                                             const double dir[3], int nextId)
{
  if (node->GetLeft() == NULL)
    {
    if (!IdsOfInterest || vtkKdTree::FoundId(IdsOfInterest, node->GetID()))
      {
      list->SetValue(nextId, node->GetID());
      nextId = nextId+1;
      }

      return nextId;
    }

  int cutPlane = node->GetDim();

  if ((cutPlane < 0) || (cutPlane > 2))
    {
    return -1;
    }

  double closest = dir[cutPlane] * -1;

  vtkKdNode *closeNode = (closest < 0) ? node->GetLeft() : node->GetRight();
  vtkKdNode *farNode  = (closest >= 0) ? node->GetLeft() : node->GetRight();
    
  int nextNextId = vtkKdTree::__ViewOrderRegionsInDirection(closeNode, list,
                                                            IdsOfInterest, dir,
                                                            nextId);
                                   
  if (nextNextId == -1)
    {
    return -1;
    }
      
  nextNextId = vtkKdTree::__ViewOrderRegionsInDirection(farNode, list,
                                                        IdsOfInterest, dir,
                                                        nextNextId);
      
  return nextNextId;
}     

//----------------------------------------------------------------------------
int vtkKdTree::_ViewOrderRegionsFromPosition(vtkIntArray *IdsOfInterest,
                                             const double pos[3],
                                             vtkIntArray *orderedList)
{
  int nextId = 0;
      
  int numValues = (IdsOfInterest ? IdsOfInterest->GetNumberOfTuples() :
                                   this->NumberOfRegions);
    
  orderedList->Initialize();
  orderedList->SetNumberOfValues(numValues);

  int size = vtkKdTree::__ViewOrderRegionsFromPosition(this->Top, orderedList,
                                                       IdsOfInterest, pos,
                                                       nextId);
  if (size < 0)
    {
    vtkErrorMacro(<<"vtkKdTree::DepthOrderRegions k-d tree structure is corrupt");
    orderedList->Initialize();
    return 0;
    }

  return size;
}
//----------------------------------------------------------------------------
int vtkKdTree::__ViewOrderRegionsFromPosition(vtkKdNode *node,
                                              vtkIntArray *list,
                                              vtkIntArray *IdsOfInterest,
                                              const double pos[3], int nextId)
{
  if (node->GetLeft() == NULL)
    {
    if (!IdsOfInterest || vtkKdTree::FoundId(IdsOfInterest, node->GetID()))
      {
      list->SetValue(nextId, node->GetID());
      nextId = nextId+1;
      }

      return nextId;
    }

  int cutPlane = node->GetDim();

  if ((cutPlane < 0) || (cutPlane > 2))
    {
    return -1;
    }

  double closest = pos[cutPlane] - node->GetDivisionPosition();

  vtkKdNode *closeNode = (closest < 0) ? node->GetLeft() : node->GetRight();
  vtkKdNode *farNode  = (closest >= 0) ? node->GetLeft() : node->GetRight();
    
  int nextNextId = vtkKdTree::__ViewOrderRegionsFromPosition(closeNode, list,
                                                             IdsOfInterest, pos,
                                                             nextId);
                                   
  if (nextNextId == -1)
    {
    return -1;
    }
      
  nextNextId = vtkKdTree::__ViewOrderRegionsFromPosition(farNode, list,
                                                         IdsOfInterest, pos,
                                                         nextNextId);
      
  return nextNextId;
}     

//----------------------------------------------------------------------------
// These requests change the boundaries of the k-d tree, so must
// update the MTime.
//
void vtkKdTree::NewPartitioningRequest(int req)
{
  if (req != this->ValidDirections)
    {
    this->Modified();
    this->ValidDirections = req;
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitXPartitioning()
{
  this->NewPartitioningRequest((1 << vtkKdTree::YDIM) | (1 << vtkKdTree::ZDIM));
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitYPartitioning()
{
  this->NewPartitioningRequest((1 << vtkKdTree::ZDIM) | (1 << vtkKdTree::XDIM));
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitZPartitioning()
{
  this->NewPartitioningRequest((1 << vtkKdTree::XDIM) | (1 << vtkKdTree::YDIM));
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitXYPartitioning()
{   
  this->NewPartitioningRequest((1 << vtkKdTree::ZDIM));
}      

//----------------------------------------------------------------------------
void vtkKdTree::OmitYZPartitioning()
{         
  this->NewPartitioningRequest((1 << vtkKdTree::XDIM));
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitZXPartitioning()
{
  this->NewPartitioningRequest((1 << vtkKdTree::YDIM));
}

//----------------------------------------------------------------------------
void vtkKdTree::OmitNoPartitioning()
{
  int req = ((1 << vtkKdTree::XDIM)|(1 << vtkKdTree::YDIM)|(1 << vtkKdTree::ZDIM));
  this->NewPartitioningRequest(req);
}

//---------------------------------------------------------------------------
void vtkKdTree::PrintTiming(ostream& os, vtkIndent )
{
  vtkTimerLog::DumpLogWithIndents(&os, 0.0f);
}

//---------------------------------------------------------------------------
void vtkKdTree::ReportReferences(vtkGarbageCollector *collector)
{
  this->Superclass::ReportReferences(collector);

  vtkGarbageCollectorReport(collector, this->DataSets, "DataSets");
}

//----------------------------------------------------------------------------
void vtkKdTree::UpdateProgress(double amt)
{
  this->Progress = amt;
  this->InvokeEvent(vtkCommand::ProgressEvent,static_cast<void *>(&amt));
}

//----------------------------------------------------------------------------
void vtkKdTree::UpdateSubOperationProgress(double amt)
{
  this->UpdateProgress(this->ProgressOffset + this->ProgressScale*amt);
}

//----------------------------------------------------------------------------
void vtkKdTree::FindPointsInArea(double* area, vtkIdTypeArray* ids, bool clearArray)
{
  if (clearArray)
    {
    ids->Reset();
    }
  if (!this->LocatorPoints)
    {
    vtkErrorMacro(<< "vtkKdTree::FindPointsInArea - must build locator first");
    return;
    }
  this->FindPointsInArea(this->Top, area, ids);
}

//----------------------------------------------------------------------------
void vtkKdTree::FindPointsInArea(vtkKdNode* node, double* area, vtkIdTypeArray* ids)
{
  double b[6];
  node->GetBounds(b);

  if (b[0] > area[1] || b[1] < area[0] ||
    b[2] > area[3] || b[3] < area[2] ||
    b[4] > area[5] || b[5] < area[4])
    {
    return;
    }

  bool contains = false;
  if (area[0] <= b[0] && b[1] <= area[1] &&
    area[2] <= b[2] && b[3] <= area[3] &&
    area[4] <= b[4] && b[5] <= area[5])
    {
    contains = true;
    }

  if (contains)
    {
    this->AddAllPointsInRegion(node, ids);
    }
  else // intersects
    {
    if (node->GetLeft() == NULL)
      {
      int regionID = node->GetID();
      int regionLoc = this->LocatorRegionLocation[regionID];
      float* pt = this->LocatorPoints + (regionLoc * 3);
      vtkIdType numPoints = this->RegionList[regionID]->GetNumberOfPoints();
      for (vtkIdType i = 0; i < numPoints; i++)
        {
        if (area[0] <= pt[0] && pt[0] <= area[1] &&
          area[2] <= pt[1] && pt[1] <= area[3] &&
          area[4] <= pt[2] && pt[2] <= area[5])
          {
          vtkIdType ptId = static_cast<vtkIdType>(this->LocatorIds[regionLoc + i]);
          ids->InsertNextValue(ptId);
          }
        pt += 3;
        }
      }
    else
      {
      this->FindPointsInArea(node->GetLeft(), area, ids);
      this->FindPointsInArea(node->GetRight(), area, ids);
      }
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::AddAllPointsInRegion(vtkKdNode* node, vtkIdTypeArray* ids)
{
  if (node->GetLeft() == NULL)
    {
    int regionID = node->GetID();
    int regionLoc = this->LocatorRegionLocation[regionID];
    vtkIdType numPoints = this->RegionList[regionID]->GetNumberOfPoints();
    for (vtkIdType i = 0; i < numPoints; i++)
      {
      vtkIdType ptId = static_cast<vtkIdType>(this->LocatorIds[regionLoc + i]);
      ids->InsertNextValue(ptId);
      }
    }
  else
    {
    this->AddAllPointsInRegion(node->GetLeft(), ids);
    this->AddAllPointsInRegion(node->GetRight(), ids);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::AddAllPointsInRegion(vtkKdNode* node, vtkIdList* ids)
{
  if (node->GetLeft() == NULL)
    {
    int regionID = node->GetID();
    int regionLoc = this->LocatorRegionLocation[regionID];
    vtkIdType numPoints = this->RegionList[regionID]->GetNumberOfPoints();
    for (vtkIdType i = 0; i < numPoints; i++)
      {
      vtkIdType ptId = static_cast<vtkIdType>(this->LocatorIds[regionLoc + i]);
      ids->InsertNextId(ptId);
      }
    }
  else
    {
    this->AddAllPointsInRegion(node->GetLeft(), ids);
    this->AddAllPointsInRegion(node->GetRight(), ids);
    }
}

//----------------------------------------------------------------------------
void vtkKdTree::PrintSelf(ostream& os, vtkIndent indent)
{ 
  this->Superclass::PrintSelf(os,indent);

  os << indent << "ValidDirections: " << this->ValidDirections << endl;
  os << indent << "MinCells: " << this->MinCells << endl;
  os << indent << "NumberOfRegionsOrLess: " << this->NumberOfRegionsOrLess << endl;
  os << indent << "NumberOfRegionsOrMore: " << this->NumberOfRegionsOrMore << endl;

  os << indent << "NumberOfRegions: " << this->NumberOfRegions << endl;

  os << indent << "DataSets: " << this->DataSets << endl;

  os << indent << "Top: " << this->Top << endl;
  os << indent << "RegionList: " << this->RegionList << endl;

  os << indent << "Timing: " << this->Timing << endl;
  os << indent << "TimerLog: " << this->TimerLog << endl;

  os << indent << "IncludeRegionBoundaryCells: ";
        os << this->IncludeRegionBoundaryCells << endl;
  os << indent << "GenerateRepresentationUsingDataBounds: ";
        os<< this->GenerateRepresentationUsingDataBounds << endl;

  if (this->CellList.nRegions > 0)
    {
    os << indent << "CellList.dataSet " << this->CellList.dataSet << endl;
    os << indent << "CellList.regionIds " << this->CellList.regionIds << endl;
    os << indent << "CellList.nRegions " << this->CellList.nRegions << endl;
    os << indent << "CellList.cells " << this->CellList.cells << endl;
    os << indent << "CellList.boundaryCells " << this->CellList.boundaryCells << endl;
    }
  os << indent << "CellRegionList: " << this->CellRegionList << endl;

  os << indent << "LocatorPoints: " << this->LocatorPoints << endl;
  os << indent << "NumberOfLocatorPoints: " << this->NumberOfLocatorPoints << endl;
  os << indent << "LocatorIds: " << this->LocatorIds << endl;
  os << indent << "LocatorRegionLocation: " << this->LocatorRegionLocation << endl;

  os << indent << "FudgeFactor: " << this->FudgeFactor << endl;
  os << indent << "MaxWidth: " << this->MaxWidth << endl;

  os << indent << "Cuts: ";
  if( this->Cuts )
  {
    this->Cuts->PrintSelf(os << endl, indent.GetNextIndent() );
  }
  else
  {
    os << "(none)" << endl;
  }
  os << indent << "Progress: " << this->Progress << endl;
}