Common/DataModel/vtkStaticPointLocator2D.cxx

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

  Program:   Visualization Toolkit
  Module:    vtkStaticPointLocator2D.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.

=========================================================================*/
#include "vtkStaticPointLocator2D.h"

#include "vtkCellArray.h"
#include "vtkIdList.h"
#include "vtkIntArray.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPoints.h"
#include "vtkPolyData.h"
#include "vtkBoundingBox.h"
#include "vtkBox.h"
#include "vtkLine.h"
#include "vtkPlane.h"
#include "vtkBoundingBox.h"
#include "vtkSMPTools.h"
#include "vtkSMPThreadLocalObject.h"

#include <vector>

vtkStandardNewMacro(vtkStaticPointLocator2D);

// There are stack-allocated bucket neighbor lists. This is the initial
// value. Too small and heap allocation kicks in.
#define VTK_INITIAL_BUCKET_SIZE 10000

#define Distance2BetweenPoints2D(p1,p2) \
   ( p1[0] - p2[0] ) * ( p1[0] - p2[0] ) + \
   ( p1[1] - p2[1] ) * ( p1[1] - p2[1] )

//-----------------------------------------------------------------------------
// The following code supports threaded point locator construction. The locator
// is assumed to be constructed once (i.e., it does not allow incremental point
// insertion). The algorithm proceeds in three steps:
// 1) All points are assigned a bucket index (combined i-j-k bucket location).
// The index is computed in parallel. This requires a one time allocation of an
// index array (which is also associated with the originating point ids).
// 2) vtkSMPTools::Sort() is used to sort the index array. Note that the sort
// carries along the point ids as well. This creates contiguous runs of points
// all resident in the same bucket.
// 3) The bucket offsets are updated to refer to the right entry location into
// the sorted point ids array. This enables quick access, and an indirect count
// of the number of points in each bucket.

// Believe it or not I had to change the name because MS Visual Studio was
// mistakenly linking the hidden, scoped classes (vtkNeighborBuckets) found
// in vtkPointLocator and vtkStaticPointLocator2D and causing weird faults.
struct NeighborBuckets2D;

//-----------------------------------------------------------------------------
// The bucketed points, including the sorted map. This is just a PIMPLd
// wrapper around the classes that do the real work.
struct vtkBucketList2D
{
  vtkStaticPointLocator2D *Locator; //locater
  vtkIdType NumPts; //the number of points to bucket
  vtkIdType NumBuckets;
  int BatchSize;

  // These are internal data members used for performance reasons
  vtkDataSet *DataSet;
  int Divisions[3];
  double Bounds[6];
  double H[3];
  double hX, hY;
  double fX, fY, bX, bY;
  vtkIdType xD, yD, zD;

  // Construction
  vtkBucketList2D(vtkStaticPointLocator2D *loc, vtkIdType numPts, int numBuckets)
  {
    this->Locator = loc;
    this->NumPts = numPts;
    this->NumBuckets = numBuckets;
    this->BatchSize = 10000; //building the offset array
    this->DataSet = loc->GetDataSet();

    // Setup internal data members for more efficient processing. Remember this is
    // a 2D locator so just processing (x,y) points.
    double spacing[3], bounds[6];
    loc->GetDivisions(this->Divisions);
    loc->GetSpacing(spacing);
    loc->GetBounds(bounds);
    this->hX = this->H[0] = spacing[0];
    this->hY = this->H[1] = spacing[1];
    this->fX = 1.0 / spacing[0];
    this->fY = 1.0 / spacing[1];
    this->bX = this->Bounds[0] = bounds[0];
    this->Bounds[1] = bounds[1];
    this->bY = this->Bounds[2] = bounds[2];
    this->Bounds[3] = bounds[3];
    this->xD = this->Divisions[0];
    this->yD = this->Divisions[1];
    this->zD = 1;
  }

  // Virtuals for templated subclasses
  virtual ~vtkBucketList2D() = default;
  virtual void BuildLocator() = 0;

  // place points in appropriate buckets
  void GetBucketNeighbors(NeighborBuckets2D* buckets,
                          const int ij[2], const int ndivs[2], int level);
  void GenerateFace(int face, int i, int j, int k,
                    vtkPoints *pts, vtkCellArray *polys);
  double Distance2ToBucket(const double x[3], const int nei[3]);
  double Distance2ToBounds(const double x[3], const double bounds[6]);

  //-----------------------------------------------------------------------------
  // Inlined for performance. These function invocations must be called after
  // BuildLocator() is invoked, otherwise the output is indeterminate.
  void GetBucketIndices(const double *x, int ij[2]) const
  {
    // Compute point index. Make sure it lies within range of locator.
    vtkIdType tmp0 = static_cast<vtkIdType>(((x[0] - bX) * fX));
    vtkIdType tmp1 = static_cast<vtkIdType>(((x[1] - bY) * fY));

    ij[0] = tmp0 < 0 ? 0 : (tmp0 >= xD ? xD-1 : tmp0);
    ij[1] = tmp1 < 0 ? 0 : (tmp1 >= yD ? yD-1 : tmp1);
  }

  //-----------------------------------------------------------------------------
  vtkIdType GetBucketIndex(const double *x) const
  {
    int ij[2];
    this->GetBucketIndices(x, ij);
    return ij[0] + ij[1]*xD;
  }
};

//-----------------------------------------------------------------------------
// Utility class to store an array of ij values
struct NeighborBuckets2D
{
  // Start with an array to avoid memory allocation overhead.
  // Initially, P will alias InitialBuffer, but could later
  // be assigned dynamically allocated memory.
  int InitialBuffer[VTK_INITIAL_BUCKET_SIZE*2];
  int *P;
  vtkIdType Count;
  vtkIdType MaxSize;

  NeighborBuckets2D()
  {
    this->P = this->InitialBuffer;
    this->Count = 0;
    this->MaxSize = VTK_INITIAL_BUCKET_SIZE;
  }

  ~NeighborBuckets2D()
  {
    this->Count = 0;
    if ( this->P != this->InitialBuffer )
    {
      delete[] this->P;
    }
  }

  int GetNumberOfNeighbors() { return this->Count; }
  void Reset() { this->Count = 0; }

  int *GetPoint(vtkIdType i)
  {
    return this->P + 2*i;
  }

  vtkIdType InsertNextBucket(const int x[2])
  {
    // Re-allocate if beyond the current max size.
    // (Increase by VTK_INITIAL_BUCKET_SIZE)
    int *tmp;
    vtkIdType offset=this->Count*2;

    if (this->Count >= this->MaxSize)
    {
      tmp = this->P;
      this->MaxSize *= 2;
      this->P = new int[this->MaxSize*2];

      memcpy(this->P, tmp, offset*sizeof(int));

      if ( tmp != this->InitialBuffer )
      {
        delete [] tmp;
      }
    }

    tmp = this->P + offset;
    *tmp++ = *x++;
    *tmp   = *x;
    this->Count++;
    return this->Count-1;
  }
};


//-----------------------------------------------------------------------------
//  Internal function to get bucket neighbors at specified level
//
void vtkBucketList2D::
GetBucketNeighbors(NeighborBuckets2D* buckets, const int ij[2],
                   const int ndivs[2], int level)
{
  int i, j, min, max, minLevel[2], maxLevel[2];
  int nei[2];

  //  Initialize
  //
  buckets->Reset();

  //  If at this bucket, just place into list
  //
  if ( level == 0 )
  {
    buckets->InsertNextBucket(ij);
    return;
  }

  //  Create permutations of the ij indices that are at the level
  //  required. If these are legal buckets, add to list for searching.
  //
  for ( i=0; i<2; i++ )
  {
    min = ij[i] - level;
    max = ij[i] + level;
    minLevel[i] = ( min > 0 ? min : 0);
    maxLevel[i] = ( max < (ndivs[i]-1) ? max : (ndivs[i]-1));
  }

  for ( i= minLevel[0]; i <= maxLevel[0]; i++ )
  {
    for ( j= minLevel[1]; j <= maxLevel[1]; j++ )
    {
      if (i == (ij[0] + level) || i == (ij[0] - level) ||
          j == (ij[1] + level) || j == (ij[1] - level) )
      {
        nei[0]=i; nei[1]=j;
        buckets->InsertNextBucket(nei);
      }
    }
  }
}

//-----------------------------------------------------------------------------
void vtkBucketList2D::
GenerateFace(int vtkNotUsed(face), int i, int j, int vtkNotUsed(k),
             vtkPoints *pts, vtkCellArray *polys)
{
  vtkIdType ids[4];
  double origin[3], x[3];

  // define first corner
  origin[0] = this->bX + i * this->hX;
  origin[1] = this->bY + j * this->hY;
  origin[2] = 0.0;
  ids[0] = pts->InsertNextPoint(origin);

  x[0] = origin[0];
  x[1] = origin[1] + this->hY;
  x[2] = origin[2];
  ids[1] = pts->InsertNextPoint(x);

  x[0] = origin[0];
  x[1] = origin[1] + this->hY;
  x[2] = origin[2];
  ids[2] = pts->InsertNextPoint(x);

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

  polys->InsertNextCell(4,ids);
}

//-----------------------------------------------------------------------------
// Calculate the distance between the point x to the bucket "nei".
//
// WARNING!!!!! Be very careful altering this routine.  Simple changes to this
// routine can make it 25% slower!!!!
//
double vtkBucketList2D::
Distance2ToBucket(const double x[3], const int nei[3])
{
  double bounds[6];

  bounds[0] =     nei[0]*this->hX + this->bX;
  bounds[1] = (nei[0]+1)*this->hX + this->bX;
  bounds[2] =     nei[1]*this->hY + this->bY;
  bounds[3] = (nei[1]+1)*this->hY + this->bY;
  bounds[4] = 0.0;
  bounds[5] = 0.0;

  return this->Distance2ToBounds(x, bounds);
}

//-----------------------------------------------------------------------------
// Calculate the distance between the point x and the specified bounds
//
// WARNING!!!!! Be very careful altering this routine.  Simple changes to this
// routine can make is 25% slower!!!!
double vtkBucketList2D::
Distance2ToBounds(const double x[3], const double bounds[6])
{
  double distance;
  double deltas[3];

  // Are we within the bounds?
  if (x[0] >= bounds[0] && x[0] <= bounds[1] &&
      x[1] >= bounds[2] && x[1] <= bounds[3])
  {
    return 0.0;
  }

  deltas[0] = deltas[1] = deltas[2] = 0.0;

  // dx
  //
  if (x[0] < bounds[0])
  {
    deltas[0] = bounds[0] - x[0];
  }
  else if (x[0] > bounds[1])
  {
    deltas[0] = x[0] - bounds[1];
  }

  // dy
  //
  if (x[1] < bounds[2])
  {
    deltas[1] = bounds[2] - x[1];
  }
  else if (x[1] > bounds[3])
  {
    deltas[1] = x[1] - bounds[3];
  }

  distance = vtkMath::Dot(deltas, deltas);
  return distance;
}

//-----------------------------------------------------------------------------
// The following tuple is what is sorted in the map. Note that it is templated
// because depending on the number of points / buckets to process we may want
// to use vtkIdType. Otherwise for performance reasons it's best to use an int
// (or other integral type). Typically sort() is 25-30% faster on smaller
// integral types, plus it takes a heck less memory (when vtkIdType is 64-bit
// and int is 32-bit).
template <typename TTuple>
struct LocatorTuple
{
  TTuple PtId; //originating point id
  TTuple Bucket; //i-j-k index into bucket space

  //Operator< used to support the subsequent sort operation.
  bool operator< (const LocatorTuple& tuple) const
    {return Bucket < tuple.Bucket;}
};


//-----------------------------------------------------------------------------
// This templated class manages the creation of the static locator
// structures. It also implements the operator() functors which are supplied
// to vtkSMPTools for threaded processesing.
template <typename TIds>
struct BucketList2D : public vtkBucketList2D
{
  // Okay the various ivars
  LocatorTuple<TIds> *Map; //the map to be sorted
  TIds               *Offsets; //offsets for each bucket into the map

  // Construction
  BucketList2D(vtkStaticPointLocator2D *loc, vtkIdType numPts, int numBuckets) :
    vtkBucketList2D(loc, numPts, numBuckets)
  {
    //one extra to simplify traversal
    this->Map = new LocatorTuple<TIds>[numPts+1];
    this->Map[numPts].Bucket = numBuckets;
    this->Offsets = new TIds[numBuckets+1];
    this->Offsets[numBuckets] = numPts;
  }

  // Release allocated memory
  ~BucketList2D() override
  {
    delete [] this->Map;
    delete [] this->Offsets;
  }

  // The number of point ids in a bucket is determined by computing the
  // difference between the offsets into the sorted points array.
  vtkIdType GetNumberOfIds(vtkIdType bucketNum)
  {
    return (this->Offsets[bucketNum+1] - this->Offsets[bucketNum]);
  }

  // Given a bucket number, return the point ids in that bucket.
  const LocatorTuple<TIds> *GetIds(vtkIdType bucketNum)
  {
    return this->Map + this->Offsets[bucketNum];
  }

  // Given a bucket number, return the point ids in that bucket.
  void GetIds(vtkIdType bucketNum, vtkIdList *bList)
  {
    const LocatorTuple<TIds> *ids = this->GetIds(bucketNum);
    vtkIdType numIds = this->GetNumberOfIds(bucketNum);
    bList->SetNumberOfIds(numIds);
    for (int i=0; i < numIds; i++)
    {
      bList->SetId(i,ids[i].PtId);
    }
  }

  // Templated implementations of the locator
  vtkIdType FindClosestPoint(const double x[3]);
  vtkIdType FindClosestPointWithinRadius(double radius, const double x[3],
                                         double inputDataLength, double& dist2);
  void FindClosestNPoints(int N, const double x[3], vtkIdList *result);
  void FindPointsWithinRadius(double R, const double x[3], vtkIdList *result);
  int IntersectWithLine(double a0[3], double a1[3], double tol, double& t,
                        double lineX[3], double ptX[3], vtkIdType &ptId);
  double FindCloseNBoundedPoints(int N, const double x[3], vtkIdList *result);

  void MergePoints(double tol, vtkIdType *pointMap);
  void GenerateRepresentation(int vtkNotUsed(level), vtkPolyData *pd);

  // Internal methods
  bool BucketIntersectsCircle(int i, int j, const double center[3], double R2);
  void GetOverlappingBuckets(NeighborBuckets2D* buckets, const double x[3],
                             const int ij[2], double dist, int level);
  void GetOverlappingBuckets(NeighborBuckets2D* buckets,const double x[3],
                             double dist, int prevMinLevel[2], int prevMaxLevel[2]);

  // Implicit point representation, slower path
  template <typename T>
  struct MapDataSet
  {
    BucketList2D<T> *BList;
    vtkDataSet *DataSet;

    MapDataSet(BucketList2D<T> *blist, vtkDataSet *ds) :
      BList(blist), DataSet(ds)
    {
    }

    void  operator()(vtkIdType ptId, vtkIdType end)
    {
      double p[3];
      LocatorTuple<T> *t = this->BList->Map + ptId;
      for ( ; ptId < end; ++ptId, ++t )
      {
        this->DataSet->GetPoint(ptId,p);
        t->PtId = ptId;
        t->Bucket = this->BList->GetBucketIndex(p);
      }//for all points in this batch
    }
  };

  // Explicit point representation (e.g., vtkPointSet), faster path
  template <typename T, typename TPts>
  struct MapPointsArray
  {
    BucketList2D<T> *BList;
    const TPts *Points;

    MapPointsArray(BucketList2D<T> *blist, const TPts *pts) :
      BList(blist), Points(pts)
    {
    }

    void  operator()(vtkIdType ptId, vtkIdType end)
    {
      double p[3];
      const TPts *x = this->Points + 3*ptId;
      LocatorTuple<T> *t = this->BList->Map + ptId;
      for ( ; ptId < end; ++ptId, x+=3, ++t )
      {
        p[0] = static_cast<double>(x[0]);
        p[1] = static_cast<double>(x[1]);
        t->PtId = ptId;
        t->Bucket = this->BList->GetBucketIndex(p);
      }//for all points in this batch
    }
  };

  // A clever way to build offsets in parallel. Basically each thread builds
  // offsets across a range of the sorted map. Recall that offsets are an
  // integral value referring to the locations of the sorted points that
  // reside in each bucket.
  template <typename T>
  struct MapOffsets
  {
    BucketList2D<T> *BList;
    vtkIdType NumPts;
    int NumBuckets;

    MapOffsets(BucketList2D<T> *blist) : BList(blist)
    {
        this->NumPts = this->BList->NumPts;
        this->NumBuckets = this->BList->NumBuckets;
    }

    // Traverse sorted points (i.e., tuples) and update bucket offsets.
    void  operator()(vtkIdType batch, vtkIdType batchEnd)
    {
      T *offsets = this->BList->Offsets;
      const LocatorTuple<T> *curPt =
        this->BList->Map + batch*this->BList->BatchSize;
      const LocatorTuple<T> *endBatchPt =
        this->BList->Map + batchEnd*this->BList->BatchSize;
      const LocatorTuple<T> *endPt =
        this->BList->Map + this->NumPts;
      const LocatorTuple<T> *prevPt;
      endBatchPt = ( endBatchPt > endPt ? endPt : endBatchPt );

      // Special case at the very beginning of the mapped points array.  If
      // the first point is in bucket# N, then all buckets up and including
      // N must refer to the first point.
      if ( curPt == this->BList->Map )
      {
        prevPt = this->BList->Map;
        std::fill_n(offsets, curPt->Bucket+1, 0); //point to the first points
      }//at the very beginning of the map (sorted points array)

      // We are entering this functor somewhere in the interior of the
      // mapped points array. All we need to do is point to the entry
      // position because we are interested only in prevPt->Bucket.
      else
      {
        prevPt = curPt;
      }//else in the middle of a batch

      // Okay we have a starting point for a bucket run. Now we can begin
      // filling in the offsets in this batch. A previous thread should
      // have/will have completed the previous and subsequent runs outside
      // of the [batch,batchEnd) range
      for ( curPt=prevPt; curPt < endBatchPt; )
      {
        for ( ; curPt->Bucket == prevPt->Bucket && curPt <= endBatchPt;
              ++curPt )
        {
          ; //advance
        }
        // Fill in any gaps in the offset array
        std::fill_n(offsets + prevPt->Bucket + 1,
                    curPt->Bucket - prevPt->Bucket,
                    curPt - this->BList->Map);
        prevPt = curPt;
      }//for all batches in this range
    }//operator()
  };

  // Merge points that are pecisely coincident. Operates in parallel on
  // locator buckets. Does not need to check neighbor buckets.
  template <typename T>
  struct MergePrecise
  {
    BucketList2D<T> *BList;
    vtkDataSet *DataSet;
    vtkIdType *MergeMap;

    MergePrecise(BucketList2D<T> *blist, vtkIdType *mergeMap) :
      BList(blist), MergeMap(mergeMap)
    {
      this->DataSet = blist->DataSet;
    }

    void  operator()(vtkIdType bucket, vtkIdType endBucket)
    {
      BucketList2D<T> *bList=this->BList;
      vtkIdType *mergeMap=this->MergeMap;
      int i, j;
      const LocatorTuple<TIds> *ids;
      double p[3], p2[3];
      vtkIdType ptId, ptId2, numIds;

      for ( ; bucket < endBucket; ++bucket )
      {
        if ( (numIds = bList->GetNumberOfIds(bucket)) > 0 )
        {
          ids = bList->GetIds(bucket);
          for (i=0; i < numIds; i++)
          {
            ptId = ids[i].PtId;
            if ( mergeMap[ptId] < 0 )
            {
              mergeMap[ptId] = ptId;
              this->DataSet->GetPoint(ptId, p);
              for (j=i+1; j < numIds; j++)
              {
                ptId2 = ids[j].PtId;
                if ( mergeMap[ptId2] < 0 )
                {
                  this->DataSet->GetPoint(ptId2, p2);
                  if ( p[0] == p2[0] && p[1] == p2[1] )
                  {
                    mergeMap[ptId2] = ptId;
                  }
                }
              }
            } //if point not yet visited
          }
        }
      }
    }
  };

  // Merge points that are coincident within a tolerance. Operates in
  // parallel on points. Needs to check neighbor buckets which slows it down
  // considerably. Note that merging is one direction: larger ids are merged
  // to lower.
  template <typename T>
  struct MergeClose
  {
    BucketList2D<T> *BList;
    vtkDataSet *DataSet;
    vtkIdType *MergeMap;
    double Tol;

    vtkSMPThreadLocalObject<vtkIdList> PIds;

    MergeClose(BucketList2D<T> *blist, double tol, vtkIdType *mergeMap) :
      BList(blist), MergeMap(mergeMap), Tol(tol)
    {
      this->DataSet = blist->DataSet;
    }

    // Just allocate a little bit of memory to get started.
    void Initialize()
    {
      vtkIdList*& pIds = this->PIds.Local();
      pIds->Allocate(128); //allocate some memory
    }

    void  operator()(vtkIdType ptId, vtkIdType endPtId)
    {
      BucketList2D<T> *bList=this->BList;
      vtkIdType *mergeMap=this->MergeMap;
      int i;
      double p[3];
      vtkIdType nearId, numIds;
      vtkIdList*& nearby = this->PIds.Local();

      for ( ; ptId < endPtId; ++ptId )
      {
        if ( mergeMap[ptId] < 0 )
        {
          mergeMap[ptId] = ptId;
          this->DataSet->GetPoint(ptId, p);
          bList->FindPointsWithinRadius(this->Tol, p, nearby);
          if ( (numIds = nearby->GetNumberOfIds()) > 0 )
          {
            for (i=0; i < numIds; i++)
            {
              nearId = nearby->GetId(i);
              if ( ptId < nearId &&
                   (mergeMap[nearId] < 0 || ptId < mergeMap[nearId]) )
              {
                mergeMap[nearId] = ptId;
              }
            }
          }
        }//if point not yet processed
      }//for all points in this batch
    }

    void Reduce()
    {}
  };

  // Build the map and other structures to support locator operations
  void BuildLocator() override
  {
    // Place each point in a bucket
    //
    vtkPointSet *ps=static_cast<vtkPointSet *>(this->DataSet);
    int mapped=0;
    if ( ps )
    {//map points array: explicit points representation
      int dataType = ps->GetPoints()->GetDataType();
      void *pts = ps->GetPoints()->GetVoidPointer(0);
      if ( dataType == VTK_FLOAT )
      {
        MapPointsArray<TIds,float> mapper(this,static_cast<float*>(pts));
        vtkSMPTools::For(0,this->NumPts, mapper);
        mapped = 1;
      }
      else if ( dataType == VTK_DOUBLE )
      {
        MapPointsArray<TIds,double> mapper(this,static_cast<double*>(pts));
        vtkSMPTools::For(0,this->NumPts, mapper);
        mapped = 1;
      }
    }

    if ( ! mapped )
    {//map dataset points: non-float points or implicit points representation
      MapDataSet<TIds> mapper(this,this->DataSet);
      vtkSMPTools::For(0,this->NumPts, mapper);
    }

    // Now gather the points into contiguous runs in buckets
    //
    vtkSMPTools::Sort(this->Map, this->Map + this->NumPts);

    // Build the offsets into the Map. The offsets are the positions of
    // each bucket into the sorted list. They mark the beginning of the
    // list of points in each bucket. Amazingly, this can be done in
    // parallel.
    //
    int numBatches = static_cast<int>(
      ceil(static_cast<double>(this->NumPts) / this->BatchSize));
    MapOffsets<TIds> offMapper(this);
    vtkSMPTools::For(0,numBatches, offMapper);
  }
};

//-----------------------------------------------------------------------------
// Given a position x, return the id of the point closest to it.
template <typename TIds> vtkIdType BucketList2D<TIds>::
FindClosestPoint(const double x[3])
{
  int i, j;
  double minDist2;
  double dist2 = VTK_DOUBLE_MAX;
  double pt[3];
  int closest, level;
  vtkIdType ptId, cno, numIds;
  int ij[2], *nei;
  NeighborBuckets2D buckets;
  const LocatorTuple<TIds> *ids;

  //  Find bucket point is in.
  //
  this->GetBucketIndices(x, ij);

  //  Need to search this bucket for the closest point.  If there are no
  //  points in this bucket, search 1st level neighbors, and so on, until
  //  closest point found.
  //
  for (closest=(-1),minDist2=VTK_DOUBLE_MAX,level=0; (closest == -1) &&
         (level < this->Divisions[0] || level < this->Divisions[1]); level++)
  {
    this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);

    for (i=0; i<buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      cno = nei[0] + nei[1]*this->xD;

      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        for (j=0; j < numIds; j++)
        {
          ptId = ids[j].PtId;
          this->DataSet->GetPoint(ptId, pt);
          if ( (dist2 = Distance2BetweenPoints2D(x,pt)) < minDist2 )
          {
            closest = ptId;
            minDist2 = dist2;
          }
        }
      }
    }
  }

  //
  // Because of the relative location of the points in the buckets, the
  // point found previously may not be the closest point. We have to
  // search those bucket neighbors that might also contain the point.
  //
  if ( minDist2 > 0.0 )
  {
    this->GetOverlappingBuckets (&buckets, x, ij, sqrt(minDist2), 0);
    for (i=0; i<buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      cno = nei[0] + nei[1]*this->xD;

      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        for (j=0; j < numIds; j++)
        {
          ptId = ids[j].PtId;
          this->DataSet->GetPoint(ptId, pt);
          if ( (dist2 = Distance2BetweenPoints2D(x,pt)) < minDist2 )
          {
            closest = ptId;
            minDist2 = dist2;
          }
        }//for each point
      }//if points in bucket
    }//for each overlapping bucket
  }//if not identical point

  return closest;
}

//-----------------------------------------------------------------------------
template <typename TIds> vtkIdType BucketList2D<TIds>::
FindClosestPointWithinRadius(double radius, const double x[3],
                             double inputDataLength, double& dist2)
{
  int i, j;
  double pt[3];
  vtkIdType ptId, closest = -1;
  int ij[2], *nei;
  double minDist2;

  double refinedRadius, radius2, refinedRadius2;
  double currentRadius;
  double distance2ToDataBounds, maxDistance;
  int ii, radiusLevels[2], radiusLevel, prevMinLevel[2], prevMaxLevel[2];
  NeighborBuckets2D buckets;
  const LocatorTuple<TIds> *ids;

  // Initialize
  dist2 = -1.0;
  radius2 = radius*radius;
  minDist2 = 1.01*radius2;   // something slightly bigger....

  vtkDataArray *pointData =
    static_cast<vtkPointSet *>(this->DataSet)->GetPoints()->GetData();

  //  Find the bucket the point is in.
  //
  this->GetBucketIndices(x, ij);

  // Start by searching the bucket that the point is in.
  //
  vtkIdType numIds;
  vtkIdType cno = ij[0] + ij[1]*this->xD;
  if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
  {
    ids = this->GetIds(cno);
    for (j=0; j < numIds; j++)
    {
      ptId = ids[j].PtId;
      pointData->GetTuple(ptId, pt);
      if ( (dist2 = Distance2BetweenPoints2D(x,pt)) < minDist2 )
      {
        closest = ptId;
        minDist2 = dist2;
      }
    }
  }

  // Now, search only those buckets that are within a radius. The radius used
  // is the smaller of sqrt(minDist2) and the radius that is passed in. To avoid
  // checking a large number of buckets unnecessarily, if the radius is
  // larger than the dimensions of a bucket, we search outward using a
  // simple heuristic of rings.  This heuristic ends up collecting inner
  // buckets multiple times, but this only happens in the case where these
  // buckets are empty, so they are discarded quickly.
  //
  if ( minDist2 < radius2 )
  {
    refinedRadius = sqrt(minDist2);
    refinedRadius2 = dist2;
  }
  else
  {
    refinedRadius = radius;
    refinedRadius2 = radius2;
  }

  if (inputDataLength != 0.0)
  {
    distance2ToDataBounds = this->Distance2ToBounds(x, this->Bounds);
    maxDistance = sqrt(distance2ToDataBounds) + inputDataLength;
    if (refinedRadius > maxDistance)
    {
      refinedRadius = maxDistance;
      refinedRadius2 = maxDistance*maxDistance;
    }
  }

  for (i = 0; i < 2; i++)
  {
    radiusLevels[i] = static_cast<int>(refinedRadius/this->H[i]);
    if (radiusLevels[i] > this->Divisions[i] / 2)
    {
      radiusLevels[i] = this->Divisions[i] / 2;
    }
  }

  radiusLevel = radiusLevels[0];
  radiusLevel = radiusLevels[1] > radiusLevel ? radiusLevels[1] : radiusLevel;
  if (radiusLevel == 0)
  {
    radiusLevel = 1;
  }

  // radius schedule increases the radius each iteration, this is currently
  // implemented by decreasing ii by 1 each iteration.  another alternative
  // is to double the radius each iteration, i.e. ii = ii >> 1
  // In practice, reducing ii by one has been found to be more efficient.
  prevMinLevel[0] = prevMaxLevel[0] = ij[0];
  prevMinLevel[1] = prevMaxLevel[1] = ij[1];
  for (ii=radiusLevel; ii >= 1; ii--)
  {
    currentRadius = refinedRadius; // used in if at bottom of this for loop

    // Build up a list of buckets that are arranged in rings
    this->GetOverlappingBuckets(&buckets, x, refinedRadius/ii, prevMinLevel,
                                prevMaxLevel);

    for (i=0; i<buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      // do we still need to test this bucket?
      if (this->Distance2ToBucket(x, nei) < refinedRadius2)
      {
        cno = nei[0] + nei[1]*this->xD;
        if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
        {
          ids = this->GetIds(cno);
          for (j=0; j < numIds; j++)
          {
            ptId = ids[j].PtId;
            pointData->GetTuple(ptId, pt);
            if ( (dist2 = Distance2BetweenPoints2D(x,pt)) < minDist2 )
            {
              closest = ptId;
              minDist2 = dist2;
              refinedRadius = sqrt(minDist2);
              refinedRadius2 = minDist2;
            }
          }//for each pt in bucket
        }//if ids
      }//if bucket is within the current best distance
    }//for each overlapping bucket

    // Don't want to check a smaller radius than we just checked so update
    // it appropriately
    if (refinedRadius < currentRadius && ii > 2) //always check ii==1
    {
      ii = static_cast<int>(static_cast<double>(ii)
                            * (refinedRadius / currentRadius)) + 1;
      if (ii < 2)
      {
        ii = 2;
      }
    }
  }//for each radius in the radius schedule

  if ((closest != -1) && (minDist2 <= radius2))
  {
    dist2 = minDist2;
  }
  else
  {
    closest = -1;
  }

  return closest;
}

namespace {
//-----------------------------------------------------------------------------
// Obtaining closest points requires sorting nearby points
struct IdTuple
{
  vtkIdType PtId;
  double    Dist2;

  IdTuple() : PtId(-1), Dist2(0.0) {}
  IdTuple(vtkIdType ptId, double dist2) : PtId(ptId), Dist2(dist2) {}

  bool operator< (const IdTuple& tuple) const
    {return Dist2 < tuple.Dist2;}
};

typedef std::vector<IdTuple> IdTupleType;
typedef std::vector<IdTuple>::iterator IdTupleIterator;

}

//-----------------------------------------------------------------------------
template <typename TIds> void BucketList2D<TIds>::
FindClosestNPoints(int N, const double x[3], vtkIdList *result)
{
  int i=0, j=0;
  double dist2;
  double pt[3];
  int level, maxLevel;
  vtkIdType ptId, cno, numIds;
  int ij[2], *nei;
  NeighborBuckets2D buckets;
  const LocatorTuple<TIds> *ids;

  //  Find the bucket the point is in.
  this->GetBucketIndices(x, ij);

  // Gather points keeping track of maximum radius in the first group of
  // points.
  level = 0;
  double maxDist2 = 0.0;
  IdTupleType sortedPts; sortedPts.reserve(128);

  // Start in the current bucket and expand out to grab the first N
  // points. Keep track of maximum distance.
  this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);
  while ( buckets.GetNumberOfNeighbors() > 0 )
  {
    for (i=0; i<buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      cno = nei[0] + nei[1]*this->xD;
      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        for (j=0; j < numIds; j++)
        {
          ptId = ids[j].PtId;
          this->DataSet->GetPoint(ptId, pt);
          dist2 = Distance2BetweenPoints2D(x,pt);
          if ( dist2 > maxDist2 )
          {
            maxDist2 = dist2;
          }
          sortedPts.emplace_back(IdTuple(ptId,dist2));
        }
        // As soon as N points found, jump out.
        if ( static_cast<int>(sortedPts.size()) >= N )
        {
          goto FOUND_N;
        }
      }//if points in bucket
    }//for unprocessed buckets

    level++;
    this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);
  }//while still not found N points

  // We've found N initial points (or exhausted all points). Now insert
  // additional points that are closer than this original sample.
  FOUND_N:
  if ( static_cast<int>(sortedPts.size()) >= N )
  {
    // If here, resume processing current buckets to identify additional
    // close points. Then go out one more level and do the same thing. Watch
    // boundary condition.
    int iStart = i;
    int jStart = j+1;
    maxLevel = level + 2; //finish current one plus one more level
    while ( level < maxLevel  )
    {
      for (i=iStart; i < buckets.GetNumberOfNeighbors(); i++)
      {
        nei = buckets.GetPoint(i);
        cno = nei[0] + nei[1]*this->xD;
        if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
        {
          ids = this->GetIds(cno);
          // Start where previous loop left off
          for (j=jStart; j < numIds; j++)
          {
            ptId = ids[j].PtId;
            this->DataSet->GetPoint(ptId, pt);
            dist2 = Distance2BetweenPoints2D(x,pt);
            if ( dist2 <= maxDist2 )
            {
              sortedPts.emplace_back(IdTuple(ptId,dist2));
            }
          }
          jStart = 0;
        }//if points in bucket
      }//for unprocessed buckets
      iStart = 0;

      level++;
      this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);
    }
  }

  // Now do the final sort to find N closest.
  std::sort(sortedPts.begin(), sortedPts.end());
  N = ( static_cast<int>(sortedPts.size()) < N ?
        static_cast<int>(sortedPts.size()) : N );

  // Copy result
  result->SetNumberOfIds(N);
  for (i=0; i < N; i++)
  {
    result->SetId(i,sortedPts.at(i).PtId);
  }
}

//-----------------------------------------------------------------------------
// The Radius defines a block of buckets which the sphere of radis R may
// touch.
template <typename TIds> void BucketList2D<TIds>::
FindPointsWithinRadius(double R, const double x[3], vtkIdList *result)
{
  double dist2;
  double pt[3];
  vtkIdType ptId, cno, numIds;
  double R2 = R*R;
  const LocatorTuple<TIds> *ids;
  double xMin[2], xMax[2];
  int i, j, ii, jOffset, ijMin[2], ijMax[2];

  // Determine the range of indices in each direction based on radius R
  xMin[0] = x[0] - R;
  xMin[1] = x[1] - R;
  xMax[0] = x[0] + R;
  xMax[1] = x[1] + R;

  //  Find the footprint in the locator
  this->GetBucketIndices(xMin, ijMin);
  this->GetBucketIndices(xMax, ijMax);

  // Clear out previous results
  result->Reset();

  // Add points within footprint and radius
  for ( j=ijMin[1]; j <= ijMax[1]; ++j)
  {
    jOffset = j*this->xD;
    for ( i=ijMin[0]; i <= ijMax[0]; ++i)
    {
      cno = i + jOffset;

      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        for (ii=0; ii < numIds; ii++)
        {
          ptId = ids[ii].PtId;
          this->DataSet->GetPoint(ptId, pt);
          dist2 = Distance2BetweenPoints2D(x,pt);
          if (dist2 <= R2)
          {
            result->InsertNextId(ptId);
          }
        }//for all points in bucket
      }//if points in bucket
    }//i-footprint
  }//j-footprint
}

//-----------------------------------------------------------------------------
// Find the point within tol of the finite line, and closest to the starting
// point of the line (i.e., min parametric coordinate t). This is specialized
// for 2D, so the line may either be parallel to the locator or not. If not,
// the locator plane is intersected and the closest point is found from the
// intersection point. Otherwise, the ray is traversed through the locator as
// described below.
//
// Note that we have to traverse more than just the buckets (aka bins)
// containing the line since the closest point could be in a neighboring
// bin. To keep the code simple here's the straightforward approach used in
// the code below. Imagine tracing a circle of radius tol along the finite
// line, and processing all bins (and of course the points in the bins) which
// intersect the circle. We use a typical ray tracing approach (see
// vtkStaticCellLocator for references) and update the current voxels/bins at
// boundaries, including intersecting the circle with neighboring bins. Since
// this simple approach may visit bins multiple times, we keep an array that
// marks whether the bin has been visited previously and skip it if we have.
template <typename TIds> int BucketList2D<TIds>::
IntersectWithLine(double a0[3], double a1[3], double tol, double& t,
                  double lineX[3], double ptX[3], vtkIdType &ptId)
{
  double *bounds = this->Bounds;
  int *ndivs = this->Divisions;
  double *h = this->H;
  double n[3]={0,0,1};

  // First check if this line is in a 2D plane or not. If not, intersect the
  // locator plane with the line and return closest point.
  if ( a0[2] != a1[2] ) //not in locator plane
  {
    double minPnt[3];
    vtkBoundingBox bbox(bounds);
    bbox.Inflate(tol,tol,0.0);
    bbox.GetMinPoint(minPnt);
    if ( vtkPlane::IntersectWithLine(a0,a1, n,minPnt, t,lineX) &&
         bbox.ContainsPoint(lineX) )
    {
      ptId = this->FindClosestPoint(lineX);
      if ( ptId < 0 )
      {
        return 0;
      }
      this->DataSet->GetPoint(ptId, ptX);
      return 1;
    }
    else
    {
      ptId = (-1);
      return 0;
    }
  }//line not in z-plane

  // If here then the ray is parallel to the z-plane. In this case, traversing the
  // pixels (i.e., buckets) in the locator is required.
  TIds ii, numPtsInBin;
  double x[3], xl[3], rayDir[3], xmin[3], xmax[3];
  int ij[2], ijMin[2], ijMax[2];
  int i, j, enterExitCount;
  vtkIdType idx, pId, bestPtId=(-1);
  double step[2], next[2], tMax[2], tDelta[2];
  double curPos[3], curT, tHit, tMin=VTK_FLOAT_MAX;
  double tol2 = tol*tol;
  unsigned char *bucketHasBeenVisited = nullptr;
  vtkMath::Subtract(a1,a0,rayDir);

  // Need to pad out bbox
  vtkBoundingBox bbox(bounds);
  bbox.Inflate(0.0,0.0,tol);
  bbox.GetBounds(bounds);

  if ( vtkBox::IntersectBox(bounds, a0, rayDir, curPos, curT) )
  {
    // Initialize intersection query array if necessary. This is done
    // locally to ensure thread safety.
    bucketHasBeenVisited = new unsigned char [ this->NumBuckets ];
    memset(bucketHasBeenVisited, 0, this->NumBuckets);

    // Get the i-j-k point of intersection and bin index. This is
    // clamped to the boundary of the locator.
    this->GetBucketIndices(curPos, ij);

    // Set up some parameters for traversing through bins
    step[0] = (rayDir[0] >= 0.0) ? 1.0 : -1.0;
    step[1] = (rayDir[1] >= 0.0) ? 1.0 : -1.0;

    // If the ray is going in the negative direction, then the next voxel boundary
    // is on the "-" direction so we stay in the current voxel.
    next[0] = bounds[0] + h[0]*(rayDir[0] >= 0.0 ? (ij[0] + step[0]) : ij[0]);
    next[1] = bounds[2] + h[1]*(rayDir[1] >= 0.0 ? (ij[1] + step[1]) : ij[1]);

    tMax[0] = (rayDir[0] != 0.0 ) ? (next[0] - curPos[0])/rayDir[0] : VTK_FLOAT_MAX;
    tMax[1] = (rayDir[1] != 0.0 ) ? (next[1] - curPos[1])/rayDir[1] : VTK_FLOAT_MAX;

    tDelta[0] = (rayDir[0] != 0.0) ? (h[0]/rayDir[0])*step[0] : VTK_FLOAT_MAX;
    tDelta[1] = (rayDir[1] != 0.0) ? (h[1]/rayDir[1])*step[1] : VTK_FLOAT_MAX;

    // Process current position including the bins in the sphere
    // footprint. Note there is a rare pathological case where the footprint
    // on voxel exit must also be considered.
    for ( bestPtId=(-1), enterExitCount=0; bestPtId < 0 || enterExitCount < 2; )
    {
      // Get the "footprint" of bins containing the sphere defined by the
      // current position and a radius of tol.
      xmin[0] = curPos[0] - tol;
      xmin[1] = curPos[1] - tol;
      xmax[0] = curPos[0] + tol;
      xmax[1] = curPos[1] + tol;
      this->GetBucketIndices(xmin,ijMin);
      this->GetBucketIndices(xmax,ijMax);

      // Start walking through the bins, find the best point of
      // intersection. Note that the ray may not penetrate all of the way
      // through the locator so may terminate when (t > 1.0).
      for (j=ijMin[1]; j <= ijMax[1]; ++j)
      {
        for (i=ijMin[0]; i <= ijMax[0]; ++i)
        {
          // Current bin index
          idx = i + j*ndivs[0];

          if ( !bucketHasBeenVisited[idx] )
          {
            bucketHasBeenVisited[idx] = 1;
            if ( (numPtsInBin=this->GetNumberOfIds(idx)) > 0 ) //there are some points here
              {
              const LocatorTuple<TIds> *ptIds = this->GetIds(idx);
              for (ii=0; ii < numPtsInBin; ii++)
              {
                pId = ptIds[ii].PtId;
                this->DataSet->GetPoint(pId, x);
                if ( vtkLine::DistanceToLine(x, a0, a1, tHit, xl) <= tol2 && t < tMin )
                {
                  tMin = t;
                  bestPtId = pId;
                }// point is within tolerance and closer
              }// over all points in bin
            }// if points in bin
          }//bucket not visited
        }//i bins
      }//j bins

      // Make sure to evaluate exit footprint as well. Must evaluate entrance
      // and exit of current voxel.
      if ( bestPtId >= 0 )
      {
        enterExitCount++;
      }

      // Advance to next pixel / bin
      if (tMax[0] < tMax[1])
      {
        ij[0] += static_cast<int>(step[0]);
        tMax[0] += tDelta[0];
        curT = tMax[0];
      }
      else
      {
        ij[1] += static_cast<int>(step[1]);
        tMax[1] += tDelta[1];
        curT = tMax[1];
      }

      // Check exit conditions
      if ( curT > 1.0 ||
           ij[0] < 0 || ij[0] >= ndivs[0] ||
           ij[1] < 0 || ij[1] >= ndivs[1] )
      {
        break;
      }
      else
      {
        curPos[0] = a0[0] + curT*rayDir[0];
        curPos[1] = a0[1] + curT*rayDir[1];
      }

    }// for looking for valid intersected point
  } // if (vtkBox::IntersectBox(...))

  // Clean up and get out
  delete [] bucketHasBeenVisited;

  // If a point has been intersected, recover the information and return.
  // This information could be cached....
  if (bestPtId >= 0)
  {
    // update the return information
    ptId = bestPtId;
    this->DataSet->GetPoint(ptId, ptX);
    vtkLine::DistanceToLine(ptX, a0, a1, t, lineX);

    return 1;
  }

  return 0;
}

//-----------------------------------------------------------------------------
template <typename TIds> double BucketList2D<TIds>::
FindCloseNBoundedPoints(int N, const double x[3], vtkIdList *result)
{
  int i, j;
  double dist2;
  double pt[3];
  int level;
  vtkIdType ptId, cno, numIds;
  int ij[2], *nei;
  NeighborBuckets2D buckets;
  const LocatorTuple<TIds> *ids;

  //  Find the bucket the point is in.
  this->GetBucketIndices(x, ij);

  // Gather points keeping track of maximum radius
  level = 0;
  double maxDist2 = 0.0;
  IdTupleType sortedPts; sortedPts.reserve(128);

  // Start in the current bucket and expand out to grab first N points. Keep
  // track of maximum distance.
  this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);
  while ( buckets.GetNumberOfNeighbors() > 0 )
  {
    // For all buckets in this level
    for (i=0; i<buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      cno = nei[0] + nei[1]*this->xD;
      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        for (j=0; j < numIds; j++)
        {
          ptId = ids[j].PtId;
          this->DataSet->GetPoint(ptId, pt);
          dist2 = Distance2BetweenPoints2D(x,pt);
          // accumulate first N points
          if ( static_cast<int>(sortedPts.size()) < N )
          {
            maxDist2 = ( dist2 > maxDist2 ? dist2 : maxDist2 );
            sortedPts.emplace_back(IdTuple(ptId,dist2));
          }
          else if ( dist2 <= maxDist2 )
          {
            sortedPts.emplace_back(IdTuple(ptId,dist2));
          }
        }
      }//if points in bucket
    }//for buckets in this level
    level++;
    // As soon as N points in this level found, jump out.
    if ( static_cast<int>(sortedPts.size()) >= N )
    {
      goto FOUND_N;
    }
    this->GetBucketNeighbors (&buckets, ij, this->Divisions, level);
  }//while still not found N points

  // We've found at least N initial points (or exhausted all points). Now insert
  // additional points that are closer than this original sample.
  FOUND_N:
  if ( static_cast<int>(sortedPts.size()) >= N )
  {
    // If here, check for any overlapping buckets we might have missed.
    this->GetOverlappingBuckets (&buckets, x, ij, sqrt(maxDist2), level-1);
    for (i=0; i < buckets.GetNumberOfNeighbors(); i++)
    {
      nei = buckets.GetPoint(i);
      cno = nei[0] + nei[1]*this->xD;
      if ( (numIds = this->GetNumberOfIds(cno)) > 0 )
      {
        ids = this->GetIds(cno);
        // Start where previous loop left off
        for (j=0; j < numIds; j++)
        {
          ptId = ids[j].PtId;
          this->DataSet->GetPoint(ptId, pt);
          dist2 = Distance2BetweenPoints2D(x,pt);
          if ( dist2 <= maxDist2 )
          {
            sortedPts.emplace_back(IdTuple(ptId,dist2));
          }
        }
      }//if points in bucket
    }//for unprocessed buckets
  }//if more than N points

  // Now do final sort and find N closest, and if there are points located at
  // the same distance as the Nth point, include them too.
  std::sort(sortedPts.begin(), sortedPts.end());
  if ( static_cast<int>(sortedPts.size()) <= N )
  {
    N = static_cast<int>(sortedPts.size());
  }
  else
  {
    maxDist2 = sortedPts.at(N-1).Dist2;
    while ( N < static_cast<int>(sortedPts.size()) &&
            sortedPts.at(N).Dist2 == maxDist2 )
    {
      N++;
    }
  }

  // Now copy result
  result->SetNumberOfIds(N);
  for (i=0; i < N; i++)
  {
    result->SetId(i,sortedPts.at(i).PtId);
  }

  return sqrt(maxDist2);
}

//-----------------------------------------------------------------------------
// Does the circle contain the bucket? Find the closest of the four points of
// the bucket and see if it is within R2.
template <typename TIds> bool BucketList2D<TIds>::
BucketIntersectsCircle(int i, int j, const double center[3], double R2)
{
  double delX = center[0] - (bX + static_cast<double>(i)*this->hX);
  double delY = center[1] - (bY + static_cast<double>(j)*this->hY);

  int quadrant = (delX > 0.0 ? 1 : 0);
  quadrant += (delY > 0.0 ? 2 : 0);

  switch (quadrant)
  {
    case 0:
      delX += this->hX;
      delY += this->hY;
      break;
    case 1:
      delY += this->hY;
      break;
    case 2:
      delX += this->hX;
      break;
    case 3:
      break;
  }

  return ( (delX*delX + delY*delY) <= R2 ? true : false);
}

//-----------------------------------------------------------------------------
// Merge points based on tolerance. Return a point map. There are two
// separate paths: when the tolerance is precisely 0.0, and when tol >
// 0.0. Both are executed in parallel, although the second uses a
// checkerboard approach to avoid write collisions.
template <typename TIds> void BucketList2D<TIds>::
MergePoints(double tol, vtkIdType *mergeMap)
{
  // First mark all points as uninitialized
  std::fill_n(mergeMap,this->NumPts,(-1));

  // If tol=0, then just process points bucket by bucket. Don't have to worry
  // about points in other buckets.
  if ( tol <= 0.0 )
  {
    MergePrecise<TIds> merge(this, mergeMap);
    vtkSMPTools::For(0,this->NumBuckets, merge);
  }

  // Merge within a tolerance. This is a greedy algorithm that can give
  // weird results since exactly which points to merge with is not an
  // obvious answer (without doing fancy clustering etc).
  else
  {
    MergeClose<TIds> merge(this, tol, mergeMap);
    vtkSMPTools::For(0,this->NumPts, merge);
  }
}

//-----------------------------------------------------------------------------
// Internal method to find those buckets that are within distance specified
// only those buckets outside of level radiuses of ij are returned
template <typename TIds> void BucketList2D<TIds>::
GetOverlappingBuckets(NeighborBuckets2D* buckets, const double x[3],
                      const int ij[2], double dist, int level)
{
  int i, j, nei[3], minLevel[2], maxLevel[2];
  double xMin[3], xMax[3];

  // Initialize
  buckets->Reset();

  // Determine the range of indices in each direction
  xMin[0] = x[0] - dist;
  xMin[1] = x[1] - dist;
  xMax[0] = x[0] + dist;
  xMax[1] = x[1] + dist;

  this->GetBucketIndices(xMin,minLevel);
  this->GetBucketIndices(xMax,maxLevel);

  for ( i= minLevel[0]; i <= maxLevel[0]; i++ )
  {
    for ( j= minLevel[1]; j <= maxLevel[1]; j++ )
    {
      if ( i < (ij[0]-level) || i > (ij[0]+level) ||
           j < (ij[1]-level) || j > (ij[1]+level) )
      {
        nei[0]=i; nei[1]=j;
        buckets->InsertNextBucket(nei);
      }
    }
  }
}

//-----------------------------------------------------------------------------
// Internal method to find those buckets that are within distance specified
// only those buckets outside of level radiuses of ij are returned
template <typename TIds> void BucketList2D<TIds>::
GetOverlappingBuckets(NeighborBuckets2D* buckets, const double x[3], double dist,
                      int prevMinLevel[2], int prevMaxLevel[2])
{
  int i, j, nei[3], minLevel[2], maxLevel[2];
  int jFactor;
  int jkSkipFlag;
  double xMin[2], xMax[2];

  // Initialize
  buckets->Reset();

  // Determine the range of indices in each direction
  xMin[0] = x[0] - dist;
  xMin[1] = x[1] - dist;
  xMax[0] = x[0] + dist;
  xMax[1] = x[1] + dist;

  this->GetBucketIndices(xMin,minLevel);
  this->GetBucketIndices(xMax,maxLevel);

  if (minLevel[0] == prevMinLevel[0] && maxLevel[0] == prevMaxLevel[0] &&
      minLevel[1] == prevMinLevel[1] && maxLevel[1] == prevMaxLevel[1] )
  {
    return;
  }

  for ( j= minLevel[1]; j <= maxLevel[1]; j++ )
  {
    if ( j >= prevMinLevel[1] && j <= prevMaxLevel[1])
    {
      jkSkipFlag = 1;
    }
    else
    {
      jkSkipFlag = 0;
    }
    jFactor = j * this->xD;
    for ( i= minLevel[0]; i <= maxLevel[0]; i++ )
    {
      if ( jkSkipFlag && i == prevMinLevel[0] )
      {
        i = prevMaxLevel[0];
        continue;
      }
      // if this bucket has any cells, add it to the list
      if ( this->GetNumberOfIds(i + jFactor ) > 0 )
      {
        nei[0]=i; nei[1]=j;
        buckets->InsertNextBucket(nei);
      }
    }
  }

  prevMinLevel[0] = minLevel[0];
  prevMinLevel[1] = minLevel[1];
  prevMaxLevel[0] = maxLevel[0];
  prevMaxLevel[1] = maxLevel[1];
}


//-----------------------------------------------------------------------------
// Build polygonal representation of locator. Create faces that separate
// inside/outside buckets, or separate inside/boundary of locator.
template <typename TIds> void BucketList2D<TIds>::
GenerateRepresentation(int vtkNotUsed(level), vtkPolyData *pd)
{
  vtkPoints *pts;
  vtkCellArray *polys;
  int ii, i, j, idx, inside;
  int offset[3]={0,0,0}, minusOffset[3]={0,0,0};

  pts = vtkPoints::New();
  pts->Allocate(5000);
  polys = vtkCellArray::New();
  polys->Allocate(10000);

  // loop over all buckets, creating appropriate faces
  for ( j=0; j < this->Divisions[1]; j++)
  {
    offset[1] = j * this->Divisions[0];
    minusOffset[1] = (j-1) * this->Divisions[0];
    for ( i=0; i < this->Divisions[0]; i++)
    {
      offset[0] = i;
      minusOffset[0] = i - 1;
      idx = offset[0] + offset[1];
      if ( this->GetNumberOfIds(idx) > 0 )
      {
        inside = 0;
      }
      else
      {
        inside = 1;
      }

      //check "negative" neighbors
      for (ii=0; ii < 3; ii++)
      {
        if ( minusOffset[ii] < 0 )
        {
          if ( inside )
          {
            this->GenerateFace(ii,i,j,0,pts,polys);
          }
        }
        else
        {
          if ( ii == 0 )
          {
            idx = minusOffset[0] + offset[1] + offset[2];
          }
          else if ( ii == 1 )
          {
            idx = offset[0] + minusOffset[1] + offset[2];
          }
          else
          {
            idx = offset[0] + offset[1] + minusOffset[2];
          }

          if ( (this->GetNumberOfIds(idx) > 0 && inside) ||
               (this->GetNumberOfIds(idx) > 0 && !inside) )
          {
            this->GenerateFace(ii,i,j,0,pts,polys);
          }
        }
        //those buckets on "positive" boundaries can generate faces specially
        if ( (i+1) >= this->Divisions[0] && inside )
        {
          this->GenerateFace(0,i+1,j,0,pts,polys);
        }
        if ( (j+1) >= this->Divisions[1] && inside )
        {
          this->GenerateFace(1,i,j+1,0,pts,polys);
        }

      }//over negative faces
    }//over i divisions
  }//over j divisions

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

//-----------------------------------------------------------------------------
// Here is the VTK class proper. It's implemented with the templated
// BucketList2D class.

//-----------------------------------------------------------------------------
// Construct with automatic computation of divisions, averaging
// 5 points per bucket.
vtkStaticPointLocator2D::vtkStaticPointLocator2D()
{
  this->NumberOfPointsPerBucket = 5;
  this->Divisions[0] = this->Divisions[1] = 50;
  this->H[0] = this->H[1] = 0.0;
  this->Buckets = nullptr;
  this->MaxNumberOfBuckets = VTK_INT_MAX;
  this->LargeIds = false;
}

//-----------------------------------------------------------------------------
vtkStaticPointLocator2D::~vtkStaticPointLocator2D()
{
  this->FreeSearchStructure();
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::Initialize()
{
  this->FreeSearchStructure();
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::FreeSearchStructure()
{
  if ( this->Buckets )
  {
    delete this->Buckets;
    this->Buckets = nullptr;
  }
}

//-----------------------------------------------------------------------------
//  Method to form subdivision of space based on the points provided and
//  subject to the constraints of levels and NumberOfPointsPerBucket.
//  The result is directly addressable and of uniform subdivision.
//
void vtkStaticPointLocator2D::BuildLocator()
{
  int ndivs[3];
  int i;
  vtkIdType numPts;

  if ( (this->Buckets != nullptr) && (this->BuildTime > this->MTime)
       && (this->BuildTime > this->DataSet->GetMTime()) )
  {
    return;
  }

  vtkDebugMacro( << "Hashing points..." );
  this->Level = 1; //only single lowest level - from superclass

  if ( !this->DataSet || (numPts = this->DataSet->GetNumberOfPoints()) < 1 )
  {
    vtkErrorMacro( << "No points to locate");
    return;
  }

  //  Make sure the appropriate data is available
  //
  if ( this->Buckets )
  {
    this->FreeSearchStructure();
  }

  // Size the root bucket.  Initialize bucket data structure, compute
  // level and divisions. The GetBounds() method below can be very slow;
  // hopefully it is cached or otherwise accelerated.
  //
  const double *bounds = this->DataSet->GetBounds();
  vtkIdType numBuckets = static_cast<vtkIdType>( static_cast<double>(numPts) /
                                                 static_cast<double>(this->NumberOfPointsPerBucket) );
  numBuckets = ( numBuckets > this->MaxNumberOfBuckets ? this->MaxNumberOfBuckets : numBuckets );

  vtkBoundingBox bbox(bounds);
  if ( this->Automatic )
  {
    bbox.ComputeDivisions(numBuckets, this->Bounds, ndivs);
  }
  else
  {
    bbox.Inflate(); //make sure non-zero volume
    bbox.GetBounds(this->Bounds);
    for (i=0; i<2; i++)
    {
      ndivs[i] = ( this->Divisions[i] < 1 ? 1 : this->Divisions[i] );
    }
  }

  this->Divisions[0] = ndivs[0];
  this->Divisions[1] = ndivs[1];
  this->NumberOfBuckets = numBuckets =
    static_cast<vtkIdType>(ndivs[0]) * static_cast<vtkIdType>(ndivs[1]);

  //  Compute width of bucket in three directions
  //
  for (i=0; i<2; i++)
  {
    this->H[i] = (this->Bounds[2*i+1] - this->Bounds[2*i]) / static_cast<double>(ndivs[i]);
  }

  // Instantiate the locator. The type is related to the maximum point id.
  // This is done for performance (e.g., the sort is faster) and significant
  // memory savings.
  //
  if ( numPts >= VTK_INT_MAX || numBuckets >= VTK_INT_MAX )
  {
    this->LargeIds = true;
    this->Buckets = new BucketList2D<vtkIdType>(this,numPts,numBuckets);
  }
  else
  {
    this->LargeIds = false;
    this->Buckets = new BucketList2D<int>(this,numPts,numBuckets);
  }

  // Actually construct the locator
  this->Buckets->BuildLocator();

  this->BuildTime.Modified();
}


//-----------------------------------------------------------------------------
// These methods satisfy the vtkStaticPointLocator2D API. The implementation is
// with the templated BucketList2D class. Note that a lot of the complexity here
// is due to the desire to use different id types (int versus vtkIdType) for the
// purposes of increasing speed and reducing memory.
//
// You're probably wondering why an if check (on LargeIds) is used to
// static_cast on BucketList2D<T> type, when virtual inheritance could be
// used. Benchmarking shows a small speed difference due to inlining, which
// the use of virtual methods short circuits.

//-----------------------------------------------------------------------------
// Given a position x, return the id of the point closest to it.
vtkIdType vtkStaticPointLocator2D::FindClosestPoint(const double x[3])
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return -1;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->FindClosestPoint(x);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->FindClosestPoint(x);
  }
}

//-----------------------------------------------------------------------------
vtkIdType vtkStaticPointLocator2D::
FindClosestPointWithinRadius(double radius, const double x[3],
                             double inputDataLength, double& dist2)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return -1;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      FindClosestPointWithinRadius(radius,x,inputDataLength,dist2);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      FindClosestPointWithinRadius(radius,x,inputDataLength,dist2);
  }
}

//-----------------------------------------------------------------------------
vtkIdType vtkStaticPointLocator2D::
FindClosestPointWithinRadius(double radius, const double x[3], double& dist2)
{
  return this->FindClosestPointWithinRadius(radius, x, this->DataSet->GetLength(),
                                            dist2);
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::
FindClosestNPoints(int N, const double x[3], vtkIdList *result)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      FindClosestNPoints(N,x,result);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      FindClosestNPoints(N,x,result);
  }
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::
FindPointsWithinRadius(double R, const double x[3], vtkIdList *result)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      FindPointsWithinRadius(R,x,result);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      FindPointsWithinRadius(R,x,result);
  }
}

//-----------------------------------------------------------------------------
// Find bounded points, approximately N, returning max radius Rmax. All
// points returned will be r <= Rmax.
double vtkStaticPointLocator2D::
FindCloseNBoundedPoints(int N, const double x[3], vtkIdList *result)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return 0.0;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      FindCloseNBoundedPoints(N,x,result);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      FindCloseNBoundedPoints(N,x,result);
  }
}

//-----------------------------------------------------------------------------
// This method traverses the locator along the defined ray, finding the
// closest point to a0 when projected onto the line (a0,a1) (i.e., min
// parametric coordinate t) and within the tolerance tol (measured in the
// world coordinate system).
int vtkStaticPointLocator2D::
IntersectWithLine(double a0[3], double a1[3], double tol, double& t,
                  double lineX[3], double ptX[3], vtkIdType &ptId)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return 0;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      IntersectWithLine(a0,a1,tol,t,lineX,ptX,ptId);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      IntersectWithLine(a0,a1,tol,t,lineX,ptX,ptId);
  }
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::
GenerateRepresentation(int level, vtkPolyData *pd)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      GenerateRepresentation(level,pd);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      GenerateRepresentation(level,pd);
  }
}

//-----------------------------------------------------------------------------
// Given a position x, return the id of the point closest to it.
vtkIdType vtkStaticPointLocator2D::
GetNumberOfPointsInBucket(vtkIdType bNum)
{
  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->
      GetNumberOfIds(bNum);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->
      GetNumberOfIds(bNum);
  }
}

//-----------------------------------------------------------------------------
// Given a position x, return the id of the point closest to it.
void vtkStaticPointLocator2D::
GetBucketIds(vtkIdType bNum, vtkIdList *bList)
{
  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->GetIds(bNum,bList);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->GetIds(bNum,bList);
  }
}

//-----------------------------------------------------------------------------
// Given a bucket, return the ids in the bucket.
void vtkStaticPointLocator2D::
MergePoints(double tol, vtkIdType *pointMap)
{
  this->BuildLocator(); // will subdivide if modified; otherwise returns
  if ( !this->Buckets )
  {
    return;
  }

  if ( this->LargeIds )
  {
    return static_cast<BucketList2D<vtkIdType>*>(this->Buckets)->MergePoints(tol,pointMap);
  }
  else
  {
    return static_cast<BucketList2D<int>*>(this->Buckets)->MergePoints(tol,pointMap);
  }
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::
GetBucketIndices(const double *x, int ij[2]) const
{
  this->Buckets->GetBucketIndices(x,ij);
}

//-----------------------------------------------------------------------------
vtkIdType vtkStaticPointLocator2D::
GetBucketIndex(const double *x) const
{
  return this->Buckets->GetBucketIndex(x);
}

//-----------------------------------------------------------------------------
void vtkStaticPointLocator2D::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os,indent);

  os << indent << "Number of Points Per Bucket: "
     << this->NumberOfPointsPerBucket << "\n";

  os << indent << "Divisions: (" << this->Divisions[0] << ", "
     << this->Divisions[1] << ")\n";

  os << indent << "Max Number Of Buckets: "
     << this->MaxNumberOfBuckets << "\n";

  os << indent << "Large IDs: " << this->LargeIds << "\n";
}