vtkVoronoiHull.h

Go to the documentation of this file.

// SPDX-FileCopyrightText: Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
// SPDX-License-Identifier: BSD-3-Clause
 
#ifndef vtkVoronoiHull_h
#define vtkVoronoiHull_h
 
#include "vtkDoubleArray.h"          // Support double points
#include "vtkFiltersMeshingModule.h" // For export macro
#include "vtkMath.h"                 // Euclidean norm
#include "vtkVoronoiCore.h"          // Enum: clip intersection status
 
#include <vector> // array support
 
VTK_ABI_NAMESPACE_BEGIN
 
class vtkPolyData;

enum class ProcessingStatus
{
  Deleted = 0,
  Valid = 1
};
 
//======= Define the convex polyhedron class used to produce Voronoi hulls.

struct VTKFILTERSMESHING_EXPORT vtkHullPoint
{
  double X[3];             // position
  double Val;              // evaluated value against a half-space clipping plane
  double R2;               // Voronoi petal radius
  int PtMap;               // renumber points that are actually used by valid faces
  int Faces[3];            // the three faces defining this point
  ProcessingStatus Status; // the status of the point
 
  // methods to define new point
  vtkHullPoint(double x, double y, double z)
    : X{ x, y, z }
    , Val(0)
    , R2(0.0)
    , PtMap(-1)
    , Faces{ -1, -1, -1 }
    , Status(ProcessingStatus::Valid)
  {
  }
  vtkHullPoint(double x[3])
    : X{ x[0], x[1], x[2] }
    , Val(0)
    , R2(0.0)
    , PtMap(-1)
    , Faces{ -1, -1, -1 }
    , Status(ProcessingStatus::Valid)
  {
  }
 
  // Replace a deleted point with a new point.
  void Replace(double x, double y, double z)
  {
    this->X[0] = x;
    this->X[1] = y;
    this->X[2] = z;
    this->Val = 0.0;
    this->R2 = 0.0;
    this->PtMap = (-1);
    this->Faces[0] = (-1);
    this->Faces[1] = (-1);
    this->Faces[2] = (-1);
    this->Status = ProcessingStatus::Valid;
  }
}; // vtkHullPoint

struct VTKFILTERSMESHING_EXPORT vtkHullFace
{
  vtkIdType NeiId;         // the neighboring generator point that produced this face
  int NumPts;              // the number of point ids defining this face
  int Points;              // the offset into FacePoints listing the point ids of this face
  int AllocSize;           // the number of slots allocated for the Points
  int InsertPos;           // the position to add a new point in the Points array
  ProcessingStatus Status; // the status of this face
 
  // Construct a polyhedron face
  vtkHullFace(vtkIdType neiId)
    : NeiId(neiId)
    , NumPts(0)
    , Points(-1)
    , AllocSize(0)
    , Status(ProcessingStatus::Valid)
  {
  }
 
  // Replace a deleted face with a new face. Allocated memory for point ids is
  // untouched.
  void Replace(vtkIdType neiPtId)
  {
    this->NeiId = neiPtId;
    this->Status = ProcessingStatus::Valid;
  }
}; // vtkHullFace

struct vtkHullEdgeTuple
{
  vtkIdType V0;       // min edge vertex id
  vtkIdType V1;       // max edge vertex id
  vtkIdType Id;       // point id of inserted point
  vtkIdType LoopIdx;  // order of the point around the new face.
  vtkIdType Faces[2]; // the two faces using the edge.
 
  vtkHullEdgeTuple(vtkIdType v0, vtkIdType v1)
    : V0(v0)
    , V1(v1)
    , Id(-1)
    , LoopIdx(-1)
    , Faces{ -1, -1 }
  {
    if (this->V0 > this->V1)
    {
      std::swap(this->V0, this->V1);
    }
  }
  bool operator==(const vtkHullEdgeTuple& et) const
  {
    return this->V0 == et.V0 && this->V1 == et.V1;
  }
  bool operator!=(const vtkHullEdgeTuple& et) const
  {
    return this->V0 != et.V0 || this->V1 != et.V1;
  }
  bool IsEdge(vtkIdType v0, vtkIdType v1) const
  {
    if (v0 < v1) // ordered properly
    {
      return (this->V0 == v0 && this->V1 == v1);
    }
    else // swap comparison required
    {
      return (this->V0 == v1 && this->V1 == v0);
    }
  }
}; // vtkHullEdgeTuple

class VTKFILTERSMESHING_EXPORT vtkVoronoiHull
{
public:
  using vtkHullPointsArray =
    std::vector<vtkHullPoint>; // the polyhedral points (and associated attributes)
  using vtkHullFacesArray = std::vector<vtkHullFace>; // a list of polyhedral faces
  using FacePointsArray = std::vector<int>;  // the list of points (by id) defining the faces
  using FaceScratchArray = std::vector<int>; // temporary face point ids array
  using InsertedEdgePointsArray = std::vector<vtkHullEdgeTuple>; // collect edge intersection points

  vtkVoronoiHull()
    : PtId(-1)
    , X{ 0, 0, 0 }
    , NumClips(0)
    , PruneTolerance(1.0e-13)
    , RecomputeCircumFlower(true)
    , RecomputePetals(true)
    , CircumFlower2(0.0)
    , MinRadius2(0.0)
    , MaxRadius2(0.0)
  {
    // Preallocate some space
    this->Points.reserve(256);
    this->Faces.reserve(256);
    this->FacePoints.reserve(2048);
    this->InProcessPoints.reserve(256);
    this->InProcessFaces.reserve(256);
    this->DeletedPoints.Reserve(256);
    this->DeletedFaces.Reserve(256);
 
    // Supporting data structures
    this->SortP.reserve(256);
    this->Petals = vtkSmartPointer<vtkDoubleArray>::New();
    this->Petals->SetNumberOfComponents(4); // x-y-z-R2
    this->Petals->Allocate(256);            // initial allocation
  }

  vtkVoronoiHull(const vtkVoronoiHull&)
    : PtId(-1)
    , X{ 0, 0, 0 }
    , NumClips(0)
    , PruneTolerance(1.0e-13)
    , RecomputeCircumFlower(true)
    , RecomputePetals(true)
    , CircumFlower2(0.0)
    , MinRadius2(0.0)
    , MaxRadius2(0.0)
  {
    // Preallocate some space
    this->Points.reserve(256);
    this->Faces.reserve(256);
    this->FacePoints.reserve(2048);
    this->InProcessPoints.reserve(256);
    this->InProcessFaces.reserve(256);
    this->DeletedPoints.Reserve(256);
    this->DeletedFaces.Reserve(256);
 
    // Each tile owns its own vtkDoubleArray
    this->SortP.reserve(256);
    this->Petals = vtkSmartPointer<vtkDoubleArray>::New();
    this->Petals->SetNumberOfComponents(4); // x-y-z-R2
    this->Petals->Allocate(256);            // initial allocation
  }
 
  vtkVoronoiHull& operator=(const vtkVoronoiHull&) { return *this; }

  void Initialize(vtkIdType genPtId, const double genPt[3], double bds[6]);

  ClipIntersectionStatus Clip(vtkIdType neiPtId, const double neiPt[3]);

  double GetCircumFlower2() { return this->CircumFlower2; }
  bool InCircumFlower(double r2) // radius**2 of point from generator
  {
    // Only recompute the circumflower if necessary; that is, when
    // a maximal point is eliminated by a polyhedral plane clip.
    if (this->RecomputeCircumFlower)
    {
      this->ComputeCircumFlower();
    }
    return (r2 <= this->CircumFlower2);
  }
  bool InFlower(const double x[3]);
  void UpdatePetals(double cf2);
  vtkDoubleArray* GetPetals()
  {
    if (this->RecomputePetals)
    {
      this->UpdatePetals(this->CircumFlower2);
    }
    return (this->Petals->GetNumberOfTuples() > 0 ? this->Petals : nullptr);
  }

  void MapPoints();

  void ProduceFacePolyData(vtkPolyData* pd, vtkHullFace* face);

  void ProducePolyData(vtkPolyData* pd);
 
  // Data members purposely left public for using classes to extract
  // information.
 
  // Information used to define the polyhedron- its generating point id and
  // position, plus region classification. Indicate whether degenerate faces
  // (i.e., those having ~zero area) can be deleted (i.e., pruned).
  vtkIdType PtId;        // Generating point id
  double X[3];           // Generating point position
  vtkIdType NumClips;    // The total number of clip operations since Initialize()
  double PruneTolerance; // Specify the prune tolerance
 
  // Support normal joggle in the case of degeneracies.
  vtkVoronoiRandom01Range Bumper;
  void BumpNormal(int bumpNum, double normal[3], double bumpNormal[3]);
  void BumpOrigin(int bumpNum, double origin[3], double bumpOrigin[3]);
 
  // These data members represent the constructed polyhedron.
  vtkIdType NumPts;          // The number of valid points in the points array
  vtkHullPointsArray Points; // Array of points defining this polyhedron
  vtkIdType NumFaces;        // The number of valid faces in the faces array
  vtkHullFacesArray Faces;   // A list of faces forming this polyhedron

  struct DeletionStack
  {
    std::vector<int> Stack;
    DeletionStack() { this->Stack.reserve(256); }
    void Push(int id) { this->Stack.emplace_back(id); }
    int Pop()
    {
      vtkIdType id = this->Stack.back();
      this->Stack.pop_back();
      return id;
    }
    bool IsEmpty() { return (this->Stack.empty()); }
    void Clear() { this->Stack.clear(); }
    void Reserve(int sze) { this->Stack.reserve(sze); }
  }; // DeletionStack


  struct FaceOperation
  {
    std::function<void(vtkVoronoiHull& hull, int, int, int)> Function;
    int FaceId;
    int StartIdx;
    int NumKeptPts;
 
    // Constructor
    FaceOperation(int faceId)
      : FaceId(faceId)
    {
    }
 
    // Support std::find()
    bool operator==(int faceId) const { return (this->FaceId == faceId); }
  };

  struct FaceProcessingArray : public std::vector<FaceOperation>
  {
    bool AddFace(vtkVoronoiHull* hull, int faceId)
    {
      if (std::find(this->begin(), this->end(), faceId) == this->end())
      {
        FaceOperation& faceOp = this->emplace_back(faceId);
        int numInts = hull->EvaluateFace(hull->GetFace(faceId), faceOp.StartIdx, faceOp.NumKeptPts);
        if (numInts <= 0)
        {
          faceOp.Function = &vtkVoronoiHull::DeleteFace;
        }
        else if (numInts == 2)
        {
          faceOp.Function = &vtkVoronoiHull::RebuildFace;
        }
        else
        {
          return false;
        }
      }
      return true; // successfully added the face for processing
    }
  };

  struct PointProcessingArray : public std::vector<int>
  {
    // Add a non-degenerate point, and connected faces, for
    // processing.
    bool AddPoint(vtkVoronoiHull* hull, vtkHullPoint& point, int ptId)
    {
      this->emplace_back(ptId);
      if (hull->InProcessFaces.AddFace(hull, point.Faces[0]) &&
        hull->InProcessFaces.AddFace(hull, point.Faces[1]) &&
        hull->InProcessFaces.AddFace(hull, point.Faces[2]))
      {
        return true;
      }
      else
      {
        return false;
      }
    }
  };

  vtkIdType AddNewPoint(double x, double y, double z);
  vtkIdType AddNewPoint(double x[3]) { return this->AddNewPoint(x[0], x[1], x[2]); }
  void DeletePoint(vtkIdType ptId);
  void SetPointFaces(vtkIdType pId, vtkIdType f0, vtkIdType f1, vtkIdType f2);

  int AddNewFace(vtkIdType npts, vtkIdType neiPtId);
  vtkHullFace* GetFace(int faceId) { return &(this->Faces[faceId]); }
  void AddFacePoint(vtkHullFace* face, vtkIdType ptId)
  {
    this->FacePoints[face->Points + face->InsertPos++] = ptId;
  }

  void AddNthFacePoint(vtkHullFace* face, int idx, vtkIdType ptId)
  {
    this->FacePoints[face->Points + idx] = ptId;
  }

  int GetFacePoint(vtkHullFace* face, int ptNum) { return this->FacePoints[face->Points + ptNum]; }

  void RebuildFacePoints(vtkHullFace* face, FaceScratchArray& idsBuffer);

  int EvaluateFace(vtkHullFace* face, int& startIdx, int& numKeptPts);

  void DeleteFace(int faceId, int vtkNotUsed(startIdx), int vtkNotUsed(numKeptPts));

  void RebuildFace(int faceId, int startIdx, int numKeptPts);

  int IntersectFaceEdge(int faceId, int p0, int p1);

  void AllocatePointIds(int npts, vtkHullFace& face);
 
protected:
  FacePointsArray FacePoints;  // Point ids used to define faces
  int MIN_POINTIDS_ALLOC = 10; // Minimum buffer allocation for face point ids
 
  // Keep track of deleted points and faces so their memory can be reused. This acts as a
  // sort of poor person's memory pool.
  DeletionStack DeletedPoints;
  DeletionStack DeletedFaces;
 
  // Used to process and track faces and points affected by a plane clip operation.
  PointProcessingArray InProcessPoints;       // Points affected by current clip operation
  FaceProcessingArray InProcessFaces;         // Faces affected by current clip operation
  InsertedEdgePointsArray InsertedEdgePoints; // New points generated on intersected edges
  FaceScratchArray FaceIdsBuffer; // An internal buffer used to rebuild faces after clipping
 
  // Indicate whether the Voronoi circumflower needs recomputing, and
  // keep track of the current circumflower and related information.
  void ComputeCircumFlower();
  bool RecomputeCircumFlower;
  bool RecomputePetals;
  double CircumFlower2;
  double MinRadius2;
  double MaxRadius2;
  std::vector<vtkHullPoint*> SortP;       // Points sorted on radius**2
  vtkSmartPointer<vtkDoubleArray> Petals; // Flower petals w/ radii > shell radius
 
  // Internal methods for processing clip operations of various types.
  void Clear()
  {
    this->NumPts = 0;
    this->Points.clear();
    this->NumFaces = 0;
    this->Faces.clear();
    this->FacePoints.clear();
    this->DeletedPoints.Clear();
    this->DeletedFaces.Clear();
  }

  ClipIntersectionStatus IntersectWithPlane(double origin[3], double normal[3], vtkIdType neiPtId);
}; // vtkVoronoiHull
 
// In the following, inlined methods for performance
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::SetPointFaces(vtkIdType pId, vtkIdType f0, vtkIdType f1, vtkIdType f2)
{
  this->Points[pId].Faces[0] = f0;
  this->Points[pId].Faces[1] = f1;
  this->Points[pId].Faces[2] = f2;
}
 
//------------------------------------------------------------------------------
inline vtkIdType vtkVoronoiHull::AddNewPoint(double x, double y, double z)
{
  vtkIdType id;
  // If there are no empty slots in the points array, then allocate a new point.
  if (this->DeletedPoints.IsEmpty())
  {
    id = this->Points.size();
    this->Points.emplace_back(x, y, z);
    this->Points.back().R2 = vtkMath::Distance2BetweenPoints(this->Points.back().X, this->X);
  }
  else // otherwise, replace a previously deleted point and reuse its memory.
  {
    id = this->DeletedPoints.Pop();
    this->Points[id].Replace(x, y, z);
    this->Points[id].R2 = vtkMath::Distance2BetweenPoints(this->Points[id].X, this->X);
  }
 
  this->NumPts++;
  return id;
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::DeletePoint(vtkIdType ptId)
{
  // The circumflower may need recomputing if this point is an extreme point.
  if ((4 * this->Points[ptId].R2) >= this->CircumFlower2)
  {
    this->RecomputeCircumFlower = true;
  }
 
  this->DeletedPoints.Push(ptId);
  this->Points[ptId].Status = ProcessingStatus::Deleted;
  this->NumPts--;
}
 
//------------------------------------------------------------------------------
inline int vtkVoronoiHull::AddNewFace(vtkIdType npts, vtkIdType neiPtId)
{
  vtkIdType id;
  // If there are no empty slots in the faces array, than allocate a new face.
  if (this->DeletedFaces.IsEmpty())
  {
    id = this->Faces.size();
    this->Faces.emplace_back(neiPtId);
    this->AllocatePointIds(npts, this->Faces.back());
  }
  else
  {
    id = this->DeletedFaces.Pop();
    this->Faces[id].Replace(neiPtId);
    this->AllocatePointIds(npts, this->Faces[id]);
  }
 
  this->NumFaces++;
  return id;
}
 
//------------------------------------------------------------------------------
inline int vtkVoronoiHull::EvaluateFace(vtkHullFace* face, int& startIdx, int& numKeptPts)
{
  startIdx = numKeptPts = 0;
  int npts = face->NumPts, numEdgeInts = 0;
  int ip, p0, p1;
  double val0, val1;
 
  for (int i = 0; i < npts; ++i)
  {
    p0 = this->GetFacePoint(face, i);
    ip = ((i + 1) == npts ? 0 : (i + 1));
    p1 = this->GetFacePoint(face, ip);
 
    val0 = this->Points[p0].Val;
    val1 = this->Points[p1].Val;
 
    if (val0 <= 0.0)
    {
      numKeptPts++;
    }
 
    if (val0 > 0 && val1 <= 0)
    {
      numEdgeInts++;
      startIdx = i;
    }
    else if (val0 <= 0 && val1 > 0)
    {
      numEdgeInts++;
    }
  }
 
  return numEdgeInts;
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::AllocatePointIds(int npts, vtkHullFace& face)
{
  face.NumPts = npts;
  face.InsertPos = 0;
 
  // See if allocation is necessary. Otherwise use previous.
  if (npts > face.AllocSize)
  {
    int size = (npts > MIN_POINTIDS_ALLOC ? npts : MIN_POINTIDS_ALLOC);
    vtkIdType offset = this->FacePoints.size();
    this->FacePoints.insert(this->FacePoints.end(), size, (-1));
    face.AllocSize = size;
    face.Points = offset;
  }
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::RebuildFacePoints(vtkHullFace* face, FaceScratchArray& idsBuffer)
{
  // Make sure space has been allocated for rebuilt point ids.
  int npts = static_cast<int>(idsBuffer.size());
  if (npts > face->AllocSize)
  {
    // Need to realloc space for point ids.
    this->AllocatePointIds(npts, *face);
  }
 
  // Copy buffer into face point ids.
  for (face->InsertPos = 0; face->InsertPos < npts; ++face->InsertPos)
  {
    this->FacePoints[face->Points + face->InsertPos] = idsBuffer[face->InsertPos];
  }
  face->NumPts = npts;
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::DeleteFace(int faceId, int, int)
{
  this->DeletedFaces.Push(faceId);
  this->Faces[faceId].Status = ProcessingStatus::Deleted;
  this->NumFaces--;
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::ComputeCircumFlower()
{
  // Compute the circumflower, and compute some info about
  // the flower radii.
  this->MinRadius2 = VTK_FLOAT_MAX;
  this->MaxRadius2 = VTK_FLOAT_MIN;
 
  // Determine the circumflower and minimal sphere radius by
  // checking against each of the flower petals.
  for (const auto& pt : this->Points)
  {
    if (pt.Status == ProcessingStatus::Valid)
    {
      this->MinRadius2 = std::min(pt.R2, this->MinRadius2);
      this->MaxRadius2 = std::max(pt.R2, this->MaxRadius2);
    }
  }
  this->CircumFlower2 = (4.0 * this->MaxRadius2); // (2*(max petal radius))**2
  this->RecomputeCircumFlower = false;            // circumflower is up to date
}
 
//------------------------------------------------------------------------------
inline bool vtkVoronoiHull::InFlower(const double x[3])
{
  // Check against the flower petals
  for (const auto& pt : this->Points)
  {
    if (pt.Status == ProcessingStatus::Valid)
    {
      double r2 = vtkMath::Distance2BetweenPoints(x, pt.X);
      if (r2 <= pt.R2)
      {
        return true;
      }
    }
  } // for all valid points
  // Point not in the flower since it's not in any petals
  return false;
}
 
//------------------------------------------------------------------------------
inline void vtkVoronoiHull::MapPoints()
{
  // Renumber the output points. Note that associated Faces should use the
  // PtMap id to ensure the the point connectivity ids are contiguous.
  vtkIdType id = 0;
  for (auto& pitr : this->Points)
  {
    if (pitr.Status == ProcessingStatus::Valid)
    {
      pitr.PtMap = id++;
    }
  }
}
 
//------------------------------------------------------------------------------
// Update the flower petals which are passed off to the locator.
// Only petals which exend past the minimal radius of the shell
// request are added to the list of petals. It is presumed that
// UpdateCircumFlower() has been invoked previously.
inline void vtkVoronoiHull::UpdatePetals(double cf2)
{
  // If the radii of the flower spheres (petals) is highly variable (which
  // occurs when the spacing of points is highly variable), then there is
  // likely a lot of empty search space. Only add flower petals which extend
  // past the outer shell request boundary. These petals are used to further
  // limit the point search space.
  this->Petals->Reset();
  this->RecomputePetals = false; // petals will be updated in the following
 
  constexpr double SphereRatio = 2.0, SphereRatio2 = SphereRatio * SphereRatio;
  if (this->MinRadius2 > 0 && ((this->MaxRadius2 / this->MinRadius2) < SphereRatio2))
  {
    return; // it's not worth using the petals
  }
 
  // Empirically determined
  constexpr double LargeSphereRatio = 0.25;
  int maxLargeSpheres = LargeSphereRatio * this->NumPts;
 
  this->SortP.clear();
  double minR2 = VTK_FLOAT_MAX, maxR2 = VTK_FLOAT_MIN;
  for (auto& pt : this->Points)
  {
    if (pt.Status == ProcessingStatus::Valid)
    {
      // (2*R)**2 >= shell request radius**2
      if ((4 * pt.R2) >= cf2)
      {
        minR2 = std::min(pt.R2, minR2);
        maxR2 = std::max(pt.R2, maxR2);
        this->SortP.emplace_back(&pt);
      }
    }
  }
 
  if (static_cast<int>(this->SortP.size()) > maxLargeSpheres || (maxR2 / minR2) < SphereRatio2)
  {
    return; // it's not worth using the petals
  }
  else // sort from large spheres to small
  {
    std::sort(this->SortP.begin(), this->SortP.end(),
      [](const vtkHullPoint* p0, const vtkHullPoint* p1) { return (p0->R2 > p1->R2); });
    for (auto& pt : this->SortP)
    {
      this->Petals->InsertNextTuple4(pt->X[0], pt->X[1], pt->X[2], pt->R2);
    }
  } // it's worth using large sphere culling
} // UpdatePetals
 
VTK_ABI_NAMESPACE_END
#endif
// VTK-HeaderTest-Exclude: vtkVoronoiHull.h