text: //============================================================================
  //  Copyright (c) Kitware, Inc.
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  //  This software is distributed WITHOUT ANY WARRANTY; without even
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  //
  //  Copyright 2014 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
  //  Copyright 2014 UT-Battelle, LLC.
  //  Copyright 2014 Los Alamos National Security.
  //
  //  Under the terms of Contract DE-NA0003525 with NTESS,
  //  the U.S. Government retains certain rights in this software.
  //
  //  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
  //  Laboratory (LANL), the U.S. Government retains certain rights in
  //  this software.
  //============================================================================
  //  Copyright (c) 2016, Los Alamos National Security, LLC
  //  All rights reserved.
  //
  //  Copyright 2016. Los Alamos National Security, LLC.
  //  This software was produced under U.S. Government contract DE-AC52-06NA25396
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  //  Los Alamos National Security, LLC for the U.S. Department of Energy.
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  //============================================================================
  
  //  This code is based on the algorithm presented in the paper:
  //  “Parallel Peak Pruning for Scalable SMP Contour Tree Computation.”
  //  Hamish Carr, Gunther Weber, Christopher Sewell, and James Ahrens.
  //  Proceedings of the IEEE Symposium on Large Data Analysis and Visualization
  //  (LDAV), October 2016, Baltimore, Maryland.
  
  //=======================================================================================
  //
  // COMMENTS:
  //
  // This functor replaces a parallel loop examining neighbours - again, for arbitrary
  // meshes, it needs to be a reduction, but for regular meshes, it's faster this way.
  //
  // Any vector needed by the functor for lookup purposes will be passed as a parameter to
  // the constructor and saved, with the actual function call being the operator ()
  //
  // Vectors marked I/O are intrinsically risky unless there is an algorithmic guarantee
  // that the read/writes are completely independent - which for our case actually occurs
  // The I/O vectors should therefore be justified in comments both here & in caller
  //
  //=======================================================================================
  
  #ifndef vtkm_worklet_contourtree_mesh2d_dem_saddle_starter_h
  #define vtkm_worklet_contourtree_mesh2d_dem_saddle_starter_h
  
  #include <vtkm/exec/ExecutionWholeArray.h>
  #include <vtkm/worklet/WorkletMapField.h>
  #include <vtkm/worklet/contourtree/Mesh2D_DEM_Triangulation_Macros.h>
  
  namespace vtkm
  {
  namespace worklet
  {
  namespace contourtree
  {
  
  // Worklet for setting initial chain maximum value
  class Mesh2D_DEM_SaddleStarter : public vtkm::worklet::WorkletMapField
  {
  public:
    struct PairType : vtkm::ListTagBase<vtkm::Pair<vtkm::Id, vtkm::Id>>
    {
    };
  
    typedef void ControlSignature(
      FieldIn<IdType> vertex,             // (input) index into active vertices
      FieldIn<PairType> outDegFirstEdge,  // (input) out degree/first edge of vertex
      FieldIn<IdType> valueIndex,         // (input) index into regular graph
      WholeArrayIn<IdType> linkMask,      // (input) neighbors of vertex
      WholeArrayIn<IdType> arcArray,      // (input) chain extrema per vertex
      WholeArrayIn<IdType> inverseIndex,  // (input) permutation of index
      WholeArrayOut<IdType> edgeNear,     // (output) low end of edges
      WholeArrayOut<IdType> edgeFar,      // (output) high end of edges
      WholeArrayOut<IdType> activeEdges); // (output) active edge list
    typedef void ExecutionSignature(_1, _2, _3, _4, _5, _6, _7, _8, _9);
    typedef _1 InputDomain;
  
    vtkm::Id nRows; // (input) number of rows in 2D
    vtkm::Id nCols; // (input) number of cols in 2D
    bool ascending; // (input) ascending or descending (join or split)
  
    // Constructor
    VTKM_EXEC_CONT
    Mesh2D_DEM_SaddleStarter(vtkm::Id NRows, vtkm::Id NCols, bool Ascending)
      : nRows(NRows)
      , nCols(NCols)
      , ascending(Ascending)
    {
    }
  
    // operator() routine that executes the loop
    template <typename InFieldPortalType, typename OutFieldPortalType>
    VTKM_EXEC void operator()(const vtkm::Id& vertex,
                              const vtkm::Pair<vtkm::Id, vtkm::Id>& outDegFirstEdge,
                              const vtkm::Id& valueIndex,
                              const InFieldPortalType& linkMask,
                              const InFieldPortalType& arcArray,
                              const InFieldPortalType& inverseIndex,
                              const OutFieldPortalType& edgeNear,
                              const OutFieldPortalType& edgeFar,
                              const OutFieldPortalType& activeEdges) const
    {
      vtkm::Id outdegree = outDegFirstEdge.first;
      vtkm::Id firstEdge = outDegFirstEdge.second;
      // skip local extrema
      if (outdegree == 0)
        return;
  
      // get the saddle mask for the vertex
      vtkm::Id nbrMask = linkMask.Get(valueIndex);
  
      // get the row and column
      vtkm::Id row = VERTEX_ROW(valueIndex, nCols);
      vtkm::Id col = VERTEX_COL(valueIndex, nCols);
  
      // we now know which edges are starts, so we count to get the outdegree
      vtkm::Id outDegree = 0;
      vtkm::Id farEnds[MAX_OUTDEGREE];
  
      // copy into the temporary array
      if ((nbrMask & 0x30) == 0x20)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row - 1, col, nCols)));
      if ((nbrMask & 0x18) == 0x10)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row - 1, col - 1, nCols)));
      if ((nbrMask & 0x0C) == 0x08)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row, col - 1, nCols)));
      if ((nbrMask & 0x06) == 0x04)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row + 1, col, nCols)));
      if ((nbrMask & 0x03) == 0x02)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row + 1, col + 1, nCols)));
      if ((nbrMask & 0x21) == 0x01)
        farEnds[outDegree++] = inverseIndex.Get(arcArray.Get(VERTEX_ID(row, col + 1, nCols)));
  
      // now we check them against each other
      if ((outDegree == 2) && (farEnds[0] == farEnds[1]))
      { // outDegree 2 & both match
        // treat as a regular point
        outDegree = 1;
      } // outDegree 2 & both match
      else if (outDegree == 3)
      { // outDegree 3
        if (farEnds[0] == farEnds[1])
        { // first two match
          if (farEnds[0] == farEnds[2])
          { // triple match
            // all match - treat as regular point
            outDegree = 1;
          } // triple match
          else
          { // first two match, but not third
            // copy third down one place
            farEnds[1] = farEnds[2];
            // and reset the count
            outDegree = 2;
          } //
        }   // first two match
        else if ((farEnds[0] == farEnds[2]) || (farEnds[1] == farEnds[2]))
        { // second one matches either of the first two
          // decrease the count, keeping 0 & 1
          outDegree = 2;
        } // second one matches either of the first two
      }   // outDegree 3
  
      // now the farEnds array holds the far ends we can reach
      for (vtkm::Id edge = 0; edge < outDegree; edge++)
      {
        // compute the edge index in the edge arrays
        vtkm::Id edgeID = firstEdge + edge;
  
        // now set the near and far ends and save the edge itself
        edgeNear.Set(edgeID, vertex);
        edgeFar.Set(edgeID, farEnds[edge]);
        activeEdges.Set(edgeID, edgeID);
      } // per start
    }   // operator()
  
  }; // Mesh2D_DEM_SaddleStarter
  }
  }
  }
  
  #endif
  