ExplicitTriangulation.h

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#pragma once
 
// base code includes
#include <AbstractTriangulation.h>
#include <CellArray.h>
#include <FlatJaggedArray.h>
 
#include <memory>
 
namespace ttk {
 
  class ExplicitTriangulation final : public AbstractTriangulation {
 
  public:
    ExplicitTriangulation();
 
    ~ExplicitTriangulation() override;
 
    ExplicitTriangulation(const ExplicitTriangulation &) = default;
    ExplicitTriangulation(ExplicitTriangulation &&) = default;
    ExplicitTriangulation &operator=(const ExplicitTriangulation &) = default;
    ExplicitTriangulation &operator=(ExplicitTriangulation &&) = default;
 
    int clear();
 
    size_t footprint(size_t size = 0) const;
 
    inline int getCellEdgeInternal(const SimplexId &cellId,
                                   const int &localEdgeId,
                                   SimplexId &edgeId) const override {
 
#ifndef TTK_ENABLE_KAMIKAZE
      if((cellId < 0) || (cellId >= (SimplexId)tetraEdgeList_.size()))
        return -1;
      if((localEdgeId < 0)
         || (localEdgeId >= (SimplexId)tetraEdgeList_[cellId].size()))
        return -2;
#endif
      edgeId = tetraEdgeList_[cellId][localEdgeId];
      return 0;
    }
 
    inline SimplexId
      getCellEdgeNumberInternal(const SimplexId &cellId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((cellId < 0) || (cellId >= (SimplexId)tetraEdgeList_.size()))
        return -1;
#endif
      return tetraEdgeList_[cellId].size();
    }
 
    template <std::size_t N>
    inline void
      convertToVector(const std::vector<std::array<SimplexId, N>> &table,
                      std::vector<std::vector<SimplexId>> &vec) {
      for(size_t i = 0; i < table.size(); ++i) {
        vec[i] = {table[i].begin(), table[i].end()};
      }
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getCellEdgesInternal() override {
 
      convertToVector(tetraEdgeList_, cellEdgeVector_);
      return &cellEdgeVector_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getCellNeighbor)(
      const SimplexId &cellId,
      const int &localNeighborId,
      SimplexId &neighborId) const override {
 
      neighborId = cellNeighborData_[cellId][localNeighborId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getCellNeighborNumber)(
      const SimplexId &cellId) const override {
      return cellNeighborData_.size(cellId);
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getCellNeighbors)() override {
      cellNeighborData_.copyTo(cellNeighborList_);
      return &cellNeighborList_;
    }
 
    inline int getCellTriangleInternal(const SimplexId &cellId,
                                       const int &localTriangleId,
                                       SimplexId &triangleId) const override {
 
#ifndef TTK_ENABLE_KAMIKAZE
      if((cellId < 0) || (cellId >= (SimplexId)tetraTriangleList_.size()))
        return -1;
      if((localTriangleId < 0)
         || (localTriangleId >= (SimplexId)tetraTriangleList_[cellId].size()))
        return -2;
#endif
      triangleId = tetraTriangleList_[cellId][localTriangleId];
 
      return 0;
    }
 
    inline SimplexId
      getCellTriangleNumberInternal(const SimplexId &cellId) const override {
 
#ifndef TTK_ENABLE_KAMIKAZE
      if((cellId < 0) || (cellId >= (SimplexId)tetraTriangleList_.size()))
        return -1;
#endif
 
      return tetraTriangleList_[cellId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getCellTrianglesInternal() override {
 
      convertToVector(tetraTriangleList_, cellTriangleVector_);
      return &cellTriangleVector_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getCellVertex)(
      const SimplexId &cellId,
      const int &localVertexId,
      SimplexId &vertexId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((!cellArray_) || (!cellNumber_))
        return -1;
#endif
      vertexId = cellArray_->getCellVertex(cellId, localVertexId);
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getCellVertexNumber)(
      const SimplexId &cellId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((!cellArray_) || (!cellNumber_))
        return -1;
#endif
      return cellArray_->getCellVertexNumber(cellId);
    }
 
    int TTK_TRIANGULATION_INTERNAL(getDimensionality)() const override {
      return maxCellDim_;
    }
 
    inline const std::vector<std::array<SimplexId, 2>> *
      TTK_TRIANGULATION_INTERNAL(getEdges)() override {
      return &edgeList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getEdgeLink)(
      const SimplexId &edgeId,
      const int &localLinkId,
      SimplexId &linkId) const override {
 
      linkId = edgeLinkData_[edgeId][localLinkId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getEdgeLinkNumber)(
      const SimplexId &edgeId) const override {
      return edgeLinkData_.size(edgeId);
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getEdgeLinks)() override {
      edgeLinkData_.copyTo(edgeLinkList_);
      return &edgeLinkList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getEdgeStar)(
      const SimplexId &edgeId,
      const int &localStarId,
      SimplexId &starId) const override {
 
      starId = edgeStarData_[edgeId][localStarId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getEdgeStarNumber)(
      const SimplexId &edgeId) const override {
      return edgeStarData_.size(edgeId);
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getEdgeStars)() override {
      edgeStarData_.copyTo(edgeStarList_);
      return &edgeStarList_;
    }
 
    inline int getEdgeTriangleInternal(const SimplexId &edgeId,
                                       const int &localTriangleId,
                                       SimplexId &triangleId) const override {
      triangleId = edgeTriangleData_[edgeId][localTriangleId];
      return 0;
    }
 
    inline SimplexId
      getEdgeTriangleNumberInternal(const SimplexId &edgeId) const override {
      return edgeTriangleData_.size(edgeId);
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getEdgeTrianglesInternal() override {
      edgeTriangleData_.copyTo(edgeTriangleList_);
      return &edgeTriangleList_;
    }
 
    inline int getEdgeVertexInternal(const SimplexId &edgeId,
                                     const int &localVertexId,
                                     SimplexId &vertexId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((edgeId < 0) || (edgeId >= (SimplexId)edgeList_.size()))
        return -1;
      if((localVertexId != 0) && (localVertexId != 1))
        return -2;
#endif
      if(!localVertexId)
        vertexId = edgeList_[edgeId][0];
      else
        vertexId = edgeList_[edgeId][1];
      return 0;
    }
 
    inline SimplexId
      TTK_TRIANGULATION_INTERNAL(getNumberOfCells)() const override {
      return cellNumber_;
    }
 
    inline SimplexId getNumberOfEdgesInternal() const override {
      return edgeList_.size();
    }
 
    inline SimplexId getNumberOfTrianglesInternal() const override {
      return triangleList_.size();
    }
 
    inline SimplexId
      TTK_TRIANGULATION_INTERNAL(getNumberOfVertices)() const override {
      return vertexNumber_;
    }
 
    inline const std::vector<std::array<SimplexId, 3>> *
      TTK_TRIANGULATION_INTERNAL(getTriangles)() override {
      return &triangleList_;
    }
 
    inline int getTriangleEdgeInternal(const SimplexId &triangleId,
                                       const int &localEdgeId,
                                       SimplexId &edgeId) const override {
 
#ifndef TTK_ENABLE_KAMIKAZE
      if((triangleId < 0)
         || (triangleId >= (SimplexId)triangleEdgeList_.size()))
        return -1;
      if((localEdgeId < 0) || (localEdgeId > 2))
        return -2;
#endif
 
      edgeId = triangleEdgeList_[triangleId][localEdgeId];
 
      return 0;
    }
 
    inline SimplexId getTriangleEdgeNumberInternal(
      const SimplexId &triangleId) const override {
 
#ifndef TTK_ENABLE_KAMIKAZE
      if((triangleId < 0)
         || (triangleId >= (SimplexId)triangleEdgeList_.size()))
        return -1;
#endif
 
      return triangleEdgeList_[triangleId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getTriangleEdgesInternal() override {
 
      convertToVector(triangleEdgeList_, triangleEdgeVector_);
      return &triangleEdgeVector_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getTriangleLink)(
      const SimplexId &triangleId,
      const int &localLinkId,
      SimplexId &linkId) const override {
 
      linkId = triangleLinkData_[triangleId][localLinkId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getTriangleLinkNumber)(
      const SimplexId &triangleId) const override {
      return triangleLinkData_[triangleId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getTriangleLinks)() override {
      triangleLinkData_.copyTo(triangleLinkList_);
      return &triangleLinkList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getTriangleStar)(
      const SimplexId &triangleId,
      const int &localStarId,
      SimplexId &starId) const override {
      starId = triangleStarData_[triangleId][localStarId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getTriangleStarNumber)(
      const SimplexId &triangleId) const override {
      return triangleStarData_[triangleId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getTriangleStars)() override {
      triangleStarData_.copyTo(triangleStarList_);
      return &triangleStarList_;
    }
 
    inline int getTriangleVertexInternal(const SimplexId &triangleId,
                                         const int &localVertexId,
                                         SimplexId &vertexId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((triangleId < 0) || (triangleId >= (SimplexId)triangleList_.size()))
        return -1;
      if((localVertexId < 0)
         || (localVertexId >= (SimplexId)triangleList_[triangleId].size()))
        return -2;
#endif
      vertexId = triangleList_[triangleId][localVertexId];
      return 0;
    }
 
    inline int getVertexEdgeInternal(const SimplexId &vertexId,
                                     const int &localEdgeId,
                                     SimplexId &edgeId) const override {
      edgeId = vertexEdgeData_[vertexId][localEdgeId];
      return 0;
    }
 
    inline SimplexId
      getVertexEdgeNumberInternal(const SimplexId &vertexId) const override {
      return vertexEdgeData_[vertexId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getVertexEdgesInternal() override {
      vertexEdgeData_.copyTo(vertexEdgeList_);
      return &vertexEdgeList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getVertexLink)(
      const SimplexId &vertexId,
      const int &localLinkId,
      SimplexId &linkId) const override {
 
      linkId = vertexLinkData_[vertexId][localLinkId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getVertexLinkNumber)(
      const SimplexId &vertexId) const override {
      return vertexLinkData_[vertexId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getVertexLinks)() override {
      vertexLinkData_.copyTo(vertexLinkList_);
      return &vertexLinkList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getVertexNeighbor)(
      const SimplexId &vertexId,
      const int &localNeighborId,
      SimplexId &neighborId) const override {
 
      neighborId = vertexNeighborData_[vertexId][localNeighborId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getVertexNeighborNumber)(
      const SimplexId &vertexId) const override {
      return vertexNeighborData_[vertexId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getVertexNeighbors)() override {
      vertexNeighborData_.copyTo(vertexNeighborList_);
      return &vertexNeighborList_;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getVertexPoint)(
      const SimplexId &vertexId, float &x, float &y, float &z) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((vertexId < 0) || (vertexId >= vertexNumber_))
        return -1;
#endif
 
      if(doublePrecision_) {
        x = ((const double *)pointSet_)[3 * vertexId];
        y = ((const double *)pointSet_)[3 * vertexId + 1];
        z = ((const double *)pointSet_)[3 * vertexId + 2];
      } else {
        x = ((const float *)pointSet_)[3 * vertexId];
        y = ((const float *)pointSet_)[3 * vertexId + 1];
        z = ((const float *)pointSet_)[3 * vertexId + 2];
      }
 
      return 0;
    }
 
    inline int TTK_TRIANGULATION_INTERNAL(getVertexStar)(
      const SimplexId &vertexId,
      const int &localStarId,
      SimplexId &starId) const override {
      starId = vertexStarData_[vertexId][localStarId];
      return 0;
    }
 
    inline SimplexId TTK_TRIANGULATION_INTERNAL(getVertexStarNumber)(
      const SimplexId &vertexId) const override {
      return vertexStarData_[vertexId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      TTK_TRIANGULATION_INTERNAL(getVertexStars)() override {
      vertexStarData_.copyTo(vertexStarList_);
      return &vertexStarList_;
    }
 
    inline int getVertexTriangleInternal(const SimplexId &vertexId,
                                         const int &localTriangleId,
                                         SimplexId &triangleId) const override {
      triangleId = vertexTriangleData_[vertexId][localTriangleId];
      return 0;
    }
 
    inline SimplexId getVertexTriangleNumberInternal(
      const SimplexId &vertexId) const override {
      return vertexTriangleData_[vertexId].size();
    }
 
    inline const std::vector<std::vector<SimplexId>> *
      getVertexTrianglesInternal() override {
      vertexTriangleData_.copyTo(vertexTriangleList_);
      return &vertexTriangleList_;
    }
 
    inline bool TTK_TRIANGULATION_INTERNAL(isEdgeOnBoundary)(
      const SimplexId &edgeId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((edgeId < 0) || (edgeId >= (SimplexId)boundaryEdges_.size()))
        return false;
#endif
      return boundaryEdges_[edgeId];
    }
 
    inline bool isEmpty() const override {
      return !vertexNumber_;
    }
 
    inline bool TTK_TRIANGULATION_INTERNAL(isTriangleOnBoundary)(
      const SimplexId &triangleId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((triangleId < 0)
         || (triangleId >= (SimplexId)boundaryTriangles_.size()))
        return false;
#endif
      return boundaryTriangles_[triangleId];
    }
 
    inline bool TTK_TRIANGULATION_INTERNAL(isVertexOnBoundary)(
      const SimplexId &vertexId) const override {
#ifndef TTK_ENABLE_KAMIKAZE
      if((vertexId < 0) || (vertexId >= (SimplexId)boundaryVertices_.size()))
        return false;
#endif
      return boundaryVertices_[vertexId];
    }
 
    int preconditionBoundaryEdgesInternal() override;
    int preconditionBoundaryTrianglesInternal() override;
    int preconditionBoundaryVerticesInternal() override;
 
    int preconditionCellEdgesInternal() override;
    int preconditionCellNeighborsInternal() override;
    int preconditionCellTrianglesInternal() override;
 
    int preconditionEdgesInternal() override;
    int preconditionEdgeLinksInternal() override;
    int preconditionEdgeStarsInternal() override;
    int preconditionEdgeTrianglesInternal() override;
 
    int preconditionTrianglesInternal() override;
    int preconditionTriangleEdgesInternal() override;
    int preconditionTriangleLinksInternal() override;
    int preconditionTriangleStarsInternal() override;
 
    int preconditionVertexEdgesInternal() override;
    int preconditionVertexLinksInternal() override;
    int preconditionVertexNeighborsInternal() override;
    int preconditionVertexStarsInternal() override;
    int preconditionVertexTrianglesInternal() override;
 
    int preconditionManifoldInternal() override;
 
#ifdef TTK_CELL_ARRAY_NEW
    // Layout with connectivity + offset array (new)
    inline int setInputCells(const SimplexId &cellNumber,
                             const LongSimplexId *connectivity,
                             const LongSimplexId *offset) {
 
      // Cell Check
      {
        if(cellNumber > 0) {
          const auto &cellDimension = offset[1] - offset[0] - 1;
 
          if(cellDimension < 0 || cellDimension > 3) {
            this->printErr("Unable to create triangulation for cells of "
                           "dimension 4 or higher ("
                           + std::to_string(cellDimension) + ").");
            return -1;
          }
 
          bool error = false;
 
#ifdef TTK_ENABLE_OPENMP
#pragma omp parallel for num_threads(this->threadNumber_)
#endif
          for(SimplexId i = 0; i < cellNumber; i++) {
            if(offset[i + 1] - offset[i] - 1 != cellDimension) {
#ifdef TTK_ENABLE_OPENMP
#pragma omp atomic write
#endif // TTK_ENABLE_OPENMP
              error = true;
            }
          }
 
          if(error) {
            this->printErr("Unable to create triangulation for "
                           "inhomogeneous\ncell dimensions.");
            return -2;
          }
        }
      }
 
      if(cellNumber_)
        clear();
 
      cellNumber_ = cellNumber;
 
      cellArray_
        = std::make_shared<CellArray>(connectivity, offset, cellNumber);
 
      // TODO: ASSUME Regular Mesh Here to compute dimension!
      if(cellNumber) {
        maxCellDim_ = cellArray_->getCellVertexNumber(0) - 1;
      }
      return 0;
    }
#else
    // Flat layout with a single array (legacy & default one)
    inline int setInputCells(const SimplexId &cellNumber,
                             const LongSimplexId *cellArray) {
      if(cellNumber_)
        clear();
 
      cellNumber_ = cellNumber;
 
      if(cellNumber) {
        // assume regular mesh here to compute dimension
        cellArray_ = std::make_shared<CellArray>(
          cellArray, cellNumber, cellArray[0] - 1);
        maxCellDim_ = cellArray[0] - 1;
      }
      return 0;
    }
#endif
 
    inline int setInputPoints(const SimplexId &pointNumber,
                              const void *pointSet,
                              const bool &doublePrecision = false) {
 
      if(vertexNumber_)
        clear();
 
      vertexNumber_ = pointNumber;
      pointSet_ = pointSet;
      doublePrecision_ = doublePrecision;
      return 0;
    }

    int writeToFile(std::ofstream &stream) const;
    int writeToFileASCII(std::ofstream &stream) const;
    int readFromFile(std::ifstream &stream);
 
#ifdef TTK_ENABLE_MPI
 
    inline void setCellsGlobalIds(const LongSimplexId *const cellGid) {
      this->cellGid_ = cellGid;
    }
    inline void setVertsGlobalIds(const LongSimplexId *array) {
      this->vertGid_ = array;
    }
 
    inline SimplexId
      getVertexGlobalIdInternal(const SimplexId lvid) const override {
      return this->vertGid_[lvid];
    }
 
    inline SimplexId
      getVertexLocalIdInternal(const SimplexId gvid) const override {
      const auto it{this->vertexGidToLid_.find(gvid)};
      if(it == this->vertexGidToLid_.end()) {
        return -1;
      }
      return it->second;
    }
 
    inline SimplexId
      getCellGlobalIdInternal(const SimplexId lcid) const override {
      return this->cellGid_[lcid];
    }
 
    inline SimplexId
      getCellLocalIdInternal(const SimplexId gcid) const override {
      const auto it{this->cellGidToLid_.find(gcid)};
#ifndef TTK_ENABLE_KAMIKAZE
      if(it == this->cellGidToLid_.end()) {
        return -1;
      }
#endif // TTK_ENABLE_KAMIKAZE
      return it->second;
    }
 
    inline SimplexId
      getEdgeGlobalIdInternal(const SimplexId leid) const override {
      return this->edgeLidToGid_[leid];
    }
 
    inline SimplexId
      getEdgeLocalIdInternal(const SimplexId geid) const override {
      const auto it = this->edgeGidToLid_.find(geid);
#ifndef TTK_ENABLE_KAMIKAZE
      if(it == this->edgeGidToLid_.end()) {
        return -1;
      }
#endif // TTK_ENABLE_KAMIKAZE
      return it->second;
    }
 
    inline SimplexId
      getTriangleGlobalIdInternal(const SimplexId ltid) const override {
      return this->triangleLidToGid_[ltid];
    }
 
    inline SimplexId
      getTriangleLocalIdInternal(const SimplexId gtid) const override {
      const auto it = this->triangleGidToLid_.find(gtid);
#ifndef TTK_ENABLE_KAMIKAZE
      if(it == this->triangleGidToLid_.end()) {
        return -1;
      }
#endif // TTK_ENABLE_KAMIKAZE
      return it->second;
    }
 
    inline int setVertexRankArray(const int *rankArray) override {
      vertexRankArray_.resize(vertexNumber_);
      std::copy(rankArray, rankArray + vertexNumber_, vertexRankArray_.begin());
      return 0;
    }
 
    inline int setCellRankArray(const int *rankArray) override {
      cellRankArray_.resize(cellNumber_);
      std::copy(rankArray, rankArray + cellNumber_, cellRankArray_.begin());
      return 0;
    }
 
    inline int getVertexRankInternal(const SimplexId lvid) const override {
      return this->vertexRankArray_[lvid];
    }
 
    inline int getEdgeRankInternal(const SimplexId lvid) const override {
      return this->edgeRankArray_[lvid];
    }
 
    inline int getTriangleRankInternal(const SimplexId lvid) const override {
      return this->triangleRankArray_[lvid];
    }
 
    inline std::unordered_map<SimplexId, SimplexId> &getVertexGlobalIdMap() {
      return this->vertexGidToLid_;
    }
 
  protected:
    template <typename Func0, typename Func1, typename Func2>
    int exchangeDistributedInternal(const Func0 &getGlobalSimplexId,
                                    const Func1 &storeGlobalSimplexId,
                                    const Func2 &iterCond,
                                    const int nSimplicesPerCell);
 
    int preconditionDistributedCellRanges();
    size_t
      computeCellRangeOffsets(std::vector<size_t> &nSimplicesPerRange) const;
 
    int preconditionDistributedCells() override;
    int preconditionExchangeGhostCells() override;
    int preconditionDistributedEdges() override;
    int preconditionDistributedVertices() override;
    int preconditionExchangeGhostVertices() override;
    int preconditionDistributedTriangles() override;
    int preconditionVertexRankArray();
    int preconditionCellRankArray();
    int preconditionEdgeRankArray() override;
    int preconditionTriangleRankArray() override;
 
    // range of (local) cells owned by the current rank that have
    // contiguous global ids (to label edges & triangles)
    struct CellRange {
      // rank-local range id
      size_t id;
      // range beginning (global cell id)
      size_t begin;
      // range end (inclusive, global cell id)
      size_t end;
      // owner rank
      size_t rank;
 
      static inline MPI_Datatype getMPIType() {
        MPI_Datatype res{};
        const auto cellRangeSize = sizeof(CellRange) / sizeof(size_t);
        MPI_Type_contiguous(cellRangeSize, ttk::getMPIType(size_t{}), &res);
        return res;
      }
    };
    // cell ranges per rank
    std::vector<CellRange> localCellRanges_{};
    // cell ranges from all ranks (gathered on rank 0)
    std::vector<CellRange> gatheredCellRanges_{};
    // number of CellRanges per rank
    std::vector<int> nRangesPerRank_{};
 
    // "GlobalCellIds" from "Generate Global Ids"
    const LongSimplexId *cellGid_{};
    // "GlobalPointIds" from "Generate Global Ids"
    const LongSimplexId *vertGid_{};
 
    // inverse of vertGid_
    std::unordered_map<SimplexId, SimplexId> vertexGidToLid_{};
    // inverse of cellGid_
    std::unordered_map<SimplexId, SimplexId> cellGidToLid_{};
 
    std::vector<SimplexId> edgeLidToGid_{};
    std::unordered_map<SimplexId, SimplexId> edgeGidToLid_{};
    std::vector<SimplexId> triangleLidToGid_{};
    std::unordered_map<SimplexId, SimplexId> triangleGidToLid_{};
 
    std::vector<int> vertexRankArray_{};
    std::vector<int> cellRankArray_{};
    std::vector<int> edgeRankArray_{};
    std::vector<int> triangleRankArray_{};
 
#endif // TTK_ENABLE_MPI
 
  private:
    bool doublePrecision_;
    SimplexId cellNumber_, vertexNumber_;
    const void *pointSet_;
    int maxCellDim_;
    std::shared_ptr<CellArray> cellArray_;
 
    FlatJaggedArray vertexNeighborData_{};
    FlatJaggedArray cellNeighborData_{};
    FlatJaggedArray vertexEdgeData_{};
    FlatJaggedArray vertexTriangleData_{};
    FlatJaggedArray edgeTriangleData_{};
    FlatJaggedArray vertexStarData_{};
    FlatJaggedArray edgeStarData_{};
    FlatJaggedArray triangleStarData_{};
    FlatJaggedArray vertexLinkData_{};
    FlatJaggedArray edgeLinkData_{};
    FlatJaggedArray triangleLinkData_{};
 
    // Char array that identifies the file format.
    static const char *magicBytes_;
    // Current version of the file format. To be incremented at every
    // breaking change to keep backward compatibility.
    static const unsigned long formatVersion_;
  };
} // namespace ttk