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// ************************************************************************* //
//                          avtGradientExpression.C                          //
// ************************************************************************* //

#include <avtGradientExpression.h>

#include <math.h>

#include <vtkCell.h>
#include <vtkCellData.h>
#include <vtkCellDataToPointData.h>
#include <vtkCellDerivatives.h>
#include <vtkDataSet.h>
#include <vtkDoubleArray.h>
#include <vtkIdList.h>
#include <vtkPointData.h>
#include <vtkPointDataToCellData.h>
#include <vtkRectilinearGrid.h>
#include <vtkStructuredGrid.h>

#include <avtExprNode.h>
#include <avtCallback.h>

#include <DebugStream.h>
#include <ExpressionException.h>
#include <StackTimer.h>

#ifdef _OPENMP
# include <omp.h>
#endif

#include <string>
#include <vector>

// ****************************************************************************
//  Method: avtGradientExpression constructor
//
//  Programmer: Akira Haddox <Transferred by Hank Childs>
//  Creation:   August 18, 2002
//
//  Modifications:
//
//    Hank Childs, Sat Dec 13 10:57:57 PST 2003
//    Added pd2cd.
//
//    Hank Childs, Fri Mar  4 08:21:04 PST 2005
//    Removed centering conversion modules.
//
//    Hank Childs, Mon Feb 13 15:08:41 PST 2006
//    Add support for logical gradients.
//
//    Cyrus Harrison, Wed Aug  8 11:19:10 PDT 2007
//    Add support for multiple gradient algorithms.
//
// ****************************************************************************

avtGradientExpression::avtGradientExpression()
{
     gradientAlgo = SAMPLE;
}


// ****************************************************************************
//  Method: avtGradientExpression destructor
//
//  Programmer: Akira Haddox <Transferred by Hank Childs>
//  Creation:   August 18, 2002
//
//  Modifications:
//
//    Hank Childs, Sat Dec 13 10:57:57 PST 2003
//    Added pd2cd.
//
//    Hank Childs, Fri Mar  4 08:21:04 PST 2005
//    Removed centering conversion modules.
//
// ****************************************************************************

avtGradientExpression::~avtGradientExpression()
{
    ;
}


// ****************************************************************************
//  Method: avtGradientExpression::ProcessArguments
//
//  Purpose:
//      Parses optional algorithm argument.
//
//  Arguments:
//      args      Expression arguments
//      state     Expression pipeline state
//
//  Programmer:   Cyrus Harrison
//  Creation:     August 8, 2007
//
//  Modifications:
//
//    Hank Childs, Fri Jan  9 15:59:41 PST 2009
//    Added support for the fast gradient.
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Use the enumerated type gradientAlgo, instead of using an int.
//
// ****************************************************************************

void
avtGradientExpression::ProcessArguments(ArgsExpr *args,
                                        ExprPipelineState *state)
{
    // get the argument list and # of arguments
    std::vector<ArgExpr*> *arguments = args->GetArgs();
    size_t nargs = arguments->size();

    // check for call with no args
    if (nargs == 0)
    {
        EXCEPTION2(ExpressionException, outputVariableName,
                   "gradient() Incorrect syntax.\n"
                   " usage: gradient(varname,algo)\n"
                   " The algo parameter is optional "
                   "and specifies which gradient algorithm is used.\n"
                   "Valid Options:\n"
                   " type: 0,1,2,3 or \"sample\",\"logical\","
                   "\"nzqh\",\"fast\"\n"
                   "(Default: algo = sample)");
    }

    // first argument is the var name, let it do its own magic
    ArgExpr *first_arg = (*arguments)[0];
    avtExprNode *first_tree = dynamic_cast<avtExprNode*>(first_arg->GetExpr());
    first_tree->CreateFilters(state);

    // Check to see if the user passed in the 2nd argument (optional)
    // that specifies the gradient algo

    // Options:
    //  sample  (0) - calc by sampling in x,y(,z) dir
    //  logical (1) - calc on logical mesh
    //  nzqh    (2) - nodal to zonal logical gradient for strucuted grids made
    //                of quadrilaterals or hexahedrons
    //  fast    (3) - fast calculation used for ray casting
    // Default: sample

    if (nargs > 1 )
    {
        ArgExpr *second_arg= (*arguments)[1];
        ExprParseTreeNode *second_tree= second_arg->GetExpr();
        std::string second_type = second_tree->GetTypeName();

        // check for arg passed as integer
        if((second_type == "IntegerConst"))
        {
            int gt = dynamic_cast<IntegerConstExpr*>(second_tree)->GetValue();
            if(gt < 0 || gt > 3)
            {
                EXCEPTION2(ExpressionException, outputVariableName,
                "avtGradientExpression: Invalid second argument.\n"
                " Valid options are: 0,1,2,3 or \"sample\",\"logical\",\"nzqh\",\"fast\"");
            }
            gradientAlgo = (GradientAlgorithmType) gt;
        }
        // check for arg passed as string
        else if((second_type == "StringConst"))
        {
            std::string sval =
                        dynamic_cast<StringConstExpr*>(second_tree)->GetValue();

            if(sval == "sample")
                gradientAlgo= SAMPLE;
            else if(sval == "logical")
                gradientAlgo= LOGICAL;
            else if(sval == "nzqh")
                gradientAlgo= NODAL_TO_ZONAL_QUAD_HEX;
            else if(sval == "fast")
                gradientAlgo= FAST;
            else
            {
                EXCEPTION2(ExpressionException, outputVariableName,
                "avtGradientExpression: Invalid second argument.\n"
                " Valid options are: 0,1,2,3 or \"sample\",\"logical\",\"nzqh\",\"fast\"");
            }
        }
        else // invalid arg type
        {

            EXCEPTION2(ExpressionException, outputVariableName,
            "avtGradientExpression: Expects an integer or string second "
            "argument.\n"
            " Valid options are: 0,1,2,3 or \"sample\",\"logical\",\"nzqh\",\"fast\"");
        }
    }

    debug5 << "avtGradientExpression: Gradient Algo = " << gradientAlgo << endl;
}



// ****************************************************************************
//  Method: avtGradientExpression::PreExecute
//
//  Purpose:
//      Initializes a flag saying whether or not we've issued a warning.
//
//  Programmer: Hank Childs
//  Creation:   February 13, 2006
//
//  Modifications:
//
//   Hank Childs, Sun Jan 24 19:43:21 PST 2010
//   Issue a warning when operating on point meshes.
//
// ****************************************************************************

void
avtGradientExpression::PreExecute(void)
{
    avtSingleInputExpressionFilter::PreExecute();

    static bool issuedWarningAboutPointMeshes = false;
    if (GetInput()->GetInfo().GetAttributes().GetTopologicalDimension() == 0)
    {
        if (! issuedWarningAboutPointMeshes)
        {
            avtCallback::IssueWarning("VisIt is unable to evaluate a "
                           "gradient over a point mesh.  You have asked VisIt "
                           "to do this explicitly (through expressions) or "
                           "indirectly (for example by making a lit volume "
                           "plot of a point mesh).  All 0's will be used for "
                           "the gradient field.  In the case of volume "
                           "rendering, no lighting will appear.  This message "
                           "will only be issued once per VisIt session.");
            issuedWarningAboutPointMeshes = true;
        }
    }
}


// ****************************************************************************
//  Method: avtGradientExpression::DeriveVariable
//
//  Purpose:
//      Derives a variable based on the input dataset.
//
//  Arguments:
//      inDS      The input dataset.
//
//  Returns:      The derived variable.  The calling class must free this
//                memory.
//
//  Programmer:   Akira Haddox 
//  Creation:     July 30, 2002
//
//  Modifications:
//
//    Hank Childs, Wed Nov 13 13:55:52 PST 2002
//    Fixed memory mismanagement issue that caused a crash on successive calls
//    and fixed memory leak.
//
//    Kathleen Bonnell, Fri Dec 13 14:07:15 PST 2002  
//    Use NewInstance instead of MakeObject, new vtkapi.
// 
//    Akira Haddox, Wed Jun 18 13:03:23 PDT 2003
//    Added proper error check for scalar data, and check for 2D data.
// 
//    Hank Childs, Tue Nov 25 17:12:17 PST 2003
//    Do a better job of updating progress.
//
//    Hank Childs, Sat Dec 13 10:46:55 PST 2003
//    Optimize for rectilinear data.  Also allow the cell data to stay as
//    cell data in the output.
//
//    Hank Childs, Fri Mar  4 08:21:04 PST 2005
//    Create centering conversion modules if needed.
//
//    Hank Childs, Fri Mar 11 16:01:21 PST 2005
//    Fix memory leak.
//
//    Hank Childs, Mon Feb 13 15:08:41 PST 2006
//    Add support for logical gradients ['4385].
//
//    Cyrus Harrison, Wed Aug  8 11:20:14 PDT 2007
//    Add support for nzqh gradient
//
//    Hank Childs, Fri Jan  9 15:59:41 PST 2009
//    Add support for fast gradients.
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Split most of this routine off into a static function that can be called 
//    from other modules.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::DeriveVariable(vtkDataSet *in_ds, int currentDomainsIndex)
{
    if (GetInput()->GetInfo().GetAttributes().GetTopologicalDimension() == 0)
    {
        vtkIdType nPoints = in_ds->GetNumberOfPoints();
        vtkDataArray *results = CreateArrayFromMesh(in_ds);
        results->SetNumberOfComponents(3);
        results->SetNumberOfTuples(nPoints);        
        for (vtkIdType i = 0 ; i < nPoints ; i++)
            results->SetTuple3(i, 0., 0., 0);
        return results;
    }

    return CalculateGradient(in_ds, outputVariableName, gradientAlgo);
}


// ****************************************************************************
//  Method: avtGradientExpression::CalculateGradient
//
//  Purpose:
//      Calculates a gradient for a single VTK data set.  This is a static 
//      function, meaning it can be called from other modules.
//
//  Arguments:
//      in_ds                The dataset to calculate a gradient for.  The field
//                           to calculate the gradient of should be the active 
//                           variable.
//      outputVariableName   The name to assign to the output variable.
//      gradientAlgo         The flavor of gradient algorithm to use.
//
//  Programmer: Hank Childs
//  Creation:   December 4, 2010
//
//  Modifications:
//    Eric Brugger, Tue May 17 16:15:27 PDT 2011
//    I modified the general gradient calculating code so that it ignored
//    neighboring cells that had an extent of zero in either of the x, y
//    or z directions, since this caused a divide by zero.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::CalculateGradient(vtkDataSet *in_ds,
                                         const char *outputVariableName, 
                                         GradientAlgorithmType gradientAlgo)
{
    if (in_ds->GetDataObjectType() == VTK_RECTILINEAR_GRID)
    {
        return RectilinearGradient((vtkRectilinearGrid *) in_ds,
                                   outputVariableName);
    }

    if (gradientAlgo == LOGICAL)
    {
#ifdef _OPENMP
        StackTimer t0("CalculateGradients OpenMP");
#else
        StackTimer t0("CalculateGradients");
#endif
        if (in_ds->GetDataObjectType() != VTK_STRUCTURED_GRID)
        {
            static bool haveIssuedWarning = false;
            if (!haveIssuedWarning)
                avtCallback::IssueWarning("You can only do logical gradients "
                                          "on structured grids.");
            haveIssuedWarning = true;
            vtkIdType nvals = 0;
            if (in_ds->GetPointData()->GetScalars() != NULL)
                nvals = in_ds->GetNumberOfPoints();
            else
                nvals = in_ds->GetNumberOfCells();
            vtkDataArray *rv = CreateArrayFromMesh(in_ds);
            rv->SetNumberOfComponents(3);
            rv->SetNumberOfTuples(nvals);
            for (int i = 0 ; i < nvals ; i++)
                rv->SetTuple3(i, 0., 0., 0);
            return rv;
        }

        return LogicalGradient((vtkStructuredGrid *) in_ds, outputVariableName);
    }
    else if (gradientAlgo == NODAL_TO_ZONAL_QUAD_HEX)
    {
        if (in_ds->GetDataObjectType() != VTK_STRUCTURED_GRID)
        {
            static bool haveIssuedWarning = false;
            if (!haveIssuedWarning)
                avtCallback::IssueWarning("You can only do nzqh gradients "
                                          "on structured grids.");
            haveIssuedWarning = true;
            vtkIdType nvals = 0;
            if (in_ds->GetPointData()->GetScalars() != NULL)
                nvals = in_ds->GetNumberOfPoints();
            else
                nvals = in_ds->GetNumberOfCells();
            vtkDataArray *rv = CreateArrayFromMesh(in_ds);
            rv->SetNumberOfComponents(3);
            rv->SetNumberOfTuples(nvals);
            for (vtkIdType i = 0 ; i < nvals ; i++)
                rv->SetTuple3(i, 0., 0., 0);
            return rv;
        }

        return NodalToZonalQuadHexGrad((vtkStructuredGrid *) in_ds,
                                        outputVariableName);
    }
    else if (gradientAlgo == FAST)
    {
        vtkDataArray *rv = FastGradient(in_ds, outputVariableName);
        if (rv != NULL)
            return rv;
        // else fall thru to normal gradient processing.
    }

    vtkDataArray *scalarValues = in_ds->GetPointData()->GetScalars();
    bool recentered = false;
    
    if (!scalarValues)
    {
        if (!(in_ds->GetCellData()->GetScalars()))
        {
            EXCEPTION2(ExpressionException, outputVariableName, 
                       "the scalar variable could not be found.");
        }

        vtkCellDataToPointData *cd2pd = vtkCellDataToPointData::New();
        cd2pd->SetInputData(in_ds);
        cd2pd->Update();

        scalarValues = cd2pd->GetOutput()->GetPointData()->GetScalars();
        scalarValues->Register(NULL); // so we don't lose it
        recentered = true;
        cd2pd->Delete();
    }
    vtkIdType nPoints = in_ds->GetNumberOfPoints();

    vtkDataArray *results = CreateArrayFromMesh(in_ds);
    results->SetNumberOfComponents(3);
    results->SetNumberOfTuples(nPoints);

    for (vtkIdType nodeId = 0 ; nodeId < nPoints; nodeId++)
    {
        double xDELTA=1e6, yDELTA=1e6, zDELTA=1e6;
       
        double nodeCoords[3]; 
        in_ds->GetPoint(nodeId, nodeCoords);
        double  nodeValue  = scalarValues->GetComponent(nodeId, 0);
        
        vtkIdList *neighborCellIds = vtkIdList::New();
        vtkIdList *myNodeId = vtkIdList::New();

        myNodeId->SetNumberOfIds(1);
        myNodeId->SetId(0, nodeId);
        
        in_ds->GetCellNeighbors(-1, myNodeId, neighborCellIds);

        myNodeId->Delete();

        vtkIdType nCells=neighborCellIds->GetNumberOfIds();

        // Find appropriate deltas
        for (vtkIdType ci = 0 ; ci < nCells ; ci++)
        {
            double *bounds = in_ds->GetCell(neighborCellIds->GetId(ci))
                                                                 ->GetBounds();
            if ((bounds[1]-bounds[0] < xDELTA*5) && (bounds[1]-bounds[0] != 0))
            {
                xDELTA = (bounds[1]-bounds[0]) / 5.0;
            }
            if ((bounds[3]-bounds[2] < yDELTA*5) && (bounds[3]-bounds[2] != 0))
            {
                yDELTA = (bounds[3]-bounds[2]) / 5.0;
            }
            if ((bounds[5]-bounds[4] < zDELTA*5) && (bounds[3]-bounds[2] != 0))
            {
                zDELTA = (bounds[5]-bounds[4]) / 5.0;
            }
        }
        
        double xComponent, yComponent, zComponent;
        
        xComponent=EvaluateComponent(nodeCoords[0],nodeCoords[1],nodeCoords[2],
                xDELTA, 0, 0, nodeValue, in_ds, scalarValues, neighborCellIds);
        yComponent=EvaluateComponent(nodeCoords[0],nodeCoords[1],nodeCoords[2],
                0, yDELTA, 0, nodeValue, in_ds, scalarValues, neighborCellIds);
        if (zDELTA == 0)
            zComponent = 0;
        else
            zComponent=EvaluateComponent(nodeCoords[0],nodeCoords[1],
                                         nodeCoords[2], 0, 0, zDELTA, 
                                         nodeValue, in_ds, scalarValues,
                                         neighborCellIds);

        neighborCellIds->Delete();
        results->SetTuple3(nodeId, xComponent, yComponent, zComponent);
    }
    
    if (recentered)
    {
        vtkDataSet *new_ds = (vtkDataSet*)in_ds->NewInstance();
        new_ds->CopyStructure(in_ds);
        new_ds->GetPointData()->SetVectors(results);

        vtkPointDataToCellData *pd2cd = vtkPointDataToCellData::New();
        pd2cd->SetInputData(new_ds);
        pd2cd->Update();
        
        vtkDataArray *new_results = pd2cd->GetOutput()->GetCellData()
                                                                ->GetVectors();
        new_results->Register(NULL); // so we don't lose it

        results->Delete();
        results = new_results;

        new_ds->Delete();
        pd2cd->Delete();
        scalarValues->Delete();
    }

    return results;
}

// ****************************************************************************
//  Method: avtGradientExpression::IsPointVariable
//
//  Purpose:
//      Report proper centering. 
//
//  Programmer: Cyrus Harrison
//  Creation:   April 1, 2008
//
//  Modifications:
//
// ****************************************************************************

bool
avtGradientExpression::IsPointVariable(void)
{
    bool is_point  = true;
    bool found_one = false;
    // NZQH always returns a cell centered result
    if (gradientAlgo == NODAL_TO_ZONAL_QUAD_HEX)
    {
        is_point = false;    
    }
    else
    {
        avtDataAttributes &atts = GetInput()->GetInfo().GetAttributes();

        if (activeVariable != NULL)
        {
            if (atts.ValidVariable(activeVariable))
            {
                is_point  = (atts.GetCentering(activeVariable) != AVT_ZONECENT);
                found_one = true;
            }
        }

        if (!found_one)
            if (atts.ValidActiveVariable())
                is_point = (atts.GetCentering() != AVT_ZONECENT);
    }
    
    return is_point;
}


// ****************************************************************************
//  Method: avtGradientExpression::EvaluateComponent
//
//  Purpose:
//      Calculate the directional derivative from the given point in the given
//      deltas.
//
//  Arguments:
//    x,y,z           The point.
//    dx, dy, dz      The direction, in delta scale: It is indended for (2/3)
//                    of them to be 0.
//    value           The value at the point.
//    in_ds           The dataset.
//    scalarValues    The values for the dataset.
//    neighborCells   The cells to look in.
//
//  Returns:      The value at that point.
//
//  Programmer:   Akira Haddox 
//  Creation:     July 30, 2002
//
// ****************************************************************************


double avtGradientExpression::EvaluateComponent(double x, double y, double z,
            double dx, double dy, double dz, double value, vtkDataSet *in_ds,
            vtkDataArray *scalarValues, vtkIdList *neighborCells)
{
    int deltaMultiplier = 2;
    double upper;
    bool  success = true;

    upper = EvaluateValue(x+dx, y+dy, z+dz, in_ds, scalarValues, neighborCells,
                        success);
    if (!success)
    {
        upper=value;
        --deltaMultiplier;
    }

    double lower;
    success = true;
    lower = EvaluateValue(x-dx, y-dy, z-dz, in_ds, scalarValues, neighborCells,
                          success);

    if (!success)
    {
        lower=value;
        --deltaMultiplier;
    }

    if (!deltaMultiplier)
        return 0;

    return (upper-lower)/ (double(deltaMultiplier)*(dx+dy+dz));
}


// ****************************************************************************
//  Method: avtGradientExpression::EvaluateValue
//
//  Purpose:
//      Calculate the value at a point.
//
//  Arguments:
//    x,y,z           The point.
//    in_ds           The dataset.
//    scalarValues    The values for the dataset.
//    neighborCells   The cells to look in.
//    success         Set to false if there is a problem.
//
//  Returns:      The value at that point.
//
//  Programmer:   Akira Haddox 
//  Creation:     July 30, 2002
//
//  Modifications:
//      Akira Haddox, Mon Jun 23 10:43:12 PDT 2003
//      Changed an accumulator from float to double for precision.
//
// ****************************************************************************


double avtGradientExpression::EvaluateValue(double x, double y, double z, 
                               vtkDataSet *in_ds, vtkDataArray *scalarValues,
                               vtkIdList *neighborCells, bool &success)
{
    // Find which cell contains this point
    double coords[3] = {x,y,z};
    int   junk2;
    double junk3[3];
    double junk4;
    double weights[8];  // This needs to be the max number of points a cell has

    double *abnormalWeights = NULL; // In case of more than 8 points
    
    vtkIdType cellId;
    vtkCell *c = NULL;
    for (cellId = 0 ; cellId < neighborCells->GetNumberOfIds() ; cellId++)
    {
        c = in_ds->GetCell(neighborCells->GetId(cellId));
    
        if (c->GetNumberOfPoints() > 8)
        {
            abnormalWeights = new double[c->GetNumberOfPoints()];
            if (c->EvaluatePosition(coords, NULL, junk2, junk3, junk4, 
                                    abnormalWeights) == 1)
            {
                break;
            }
            
            delete[] abnormalWeights;
            abnormalWeights=NULL;
        }
        
        else if (c->EvaluatePosition(coords, NULL, junk2, junk3, junk4, 
                                     weights) == 1)
        {
            break;
        }
    }

    if (cellId == neighborCells->GetNumberOfIds())
    {
        success = false;
        return 0.;
    }
    
    double value = 0.;
    if (abnormalWeights)
    {
        for (vtkIdType k=0 ; k < c->GetNumberOfPoints() ; k++)
        {
            vtkIdType pt = c->GetPointId(k);
            value += abnormalWeights[k] * scalarValues->GetComponent(pt,0);
        }
        delete [] abnormalWeights;
    }
    else
    {
        for (vtkIdType k = 0 ; k < c->GetNumberOfPoints() ; k++)
        {
            vtkIdType pt = c->GetPointId(k);
            value += weights[k] * scalarValues->GetComponent(pt, 0);
        }
    }
    return value;    
} 


// ****************************************************************************
//  Method: avtGradientExpression::RectilinearGradient
//
//  Purpose:
//      Determines the gradient of a rectilinear dataset.
//
//  Programmer: Hank Childs
//  Creation:   December 13, 2003
//
//  Modifications:
//    Jeremy Meredith, Fri Jul  2 15:58:01 PDT 2004
//    Added a check to make sure the scalars existed before proceeding.
//
//    Hank Childs, Mon Feb 13 16:12:23 PST 2006
//    Removed misleading comment.
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Add an argument for the output variable name, since this is now a static
//    function.
//
// ****************************************************************************


template <typename XT, typename YT, typename ZT, typename OT>
void
avtGradientExpression_CalcRectGrad(bool isNodal, int dims[3], XT *x,
    YT *y, ZT *z, OT *in, OT *out)
{
    bool deleteX = false;
    bool deleteY = false;
    bool deleteZ = false;
    if (!isNodal)
    {
         dims[0] -= 1;
         dims[1] -= 1;
         dims[2] -= 1;

         XT *x_new = new XT[dims[0]];
         for (int i = 0 ; i < dims[0] ; i++)
             x_new[i] = (x[i] + x[i+1]) / 2.;
         x = x_new;

         deleteX = true;
         YT *y_new = new YT[dims[1]];
         for (int i = 0 ; i < dims[1] ; i++)
             y_new[i] = (y[i] + y[i+1]) / 2.;
         y = y_new;
         deleteY = true;

         if (dims[2] > 1)
         {
             ZT *z_new = new ZT[dims[2]];
             for (int i = 0 ; i < dims[2] ; i++)
                 z_new[i] = (z[i] + z[i+1]) / 2.;
             z = z_new;
             deleteZ = true;
         }
    }

    //
    // Now come up with the divisors.  A gradient is the change in variable
    // value divided by the span (in space).  Division is a killer when it
    // comes to performance.  Since we will be dividing by the same things 
    // repeatedly, calculate them once and then re-use them.
    //
    XT *x_div = new XT[dims[0]];
    x_div[0] = 1. / (x[1] - x[0]);
    x_div[dims[0]-1] = 1. / (x[dims[0]-1] - x[dims[0]-2]);
    for (int i = 1 ; i < dims[0]-1 ; i++)
        x_div[i] = 1. / (x[i+1] - x[i-1]);

    YT *y_div = new YT[dims[1]];
    y_div[0] = 1. / (y[1] - y[0]);
    y_div[dims[1]-1] = 1. / (y[dims[1]-1] - y[dims[1]-2]);
    for (int i = 1 ; i < dims[1]-1 ; i++)
        y_div[i] = 1. / (y[i+1] - y[i-1]);

    ZT *z_div = NULL;
    if (dims[2] > 1)
    {
        z_div = new ZT[dims[2]];
        z_div[0] = 1. / (z[1] - z[0]);
        z_div[dims[2]-1] = 1. / (z[dims[2]-1] - z[dims[2]-2]);
        for (int i = 1 ; i < dims[2]-1 ; i++)
            z_div[i] = 1. / (z[i+1] - z[i-1]);
    }

    const int dims0 = dims[0];
    const int dims1 = dims[1];
    const int dims2 = dims[2];
    const int iskip = 1;
    const int jskip = dims0;
    const int kskip = dims0*dims1;
    if (dims2 <= 1)
    {
        for (int j = 0 ; j < dims1 ; j++)
        {
            for (int i = 0 ; i < dims0 ; i++)
            {
                int index     = j*jskip + i*iskip;
                int vec_index = 3*index;

                if ((i > 0) && (i < (dims0-1)))
                    out[vec_index] = in[index+iskip] - in[index-iskip];
                else if (i == 0)
                    out[vec_index] = in[index+iskip] - in[index];
                else // i == dims0-1
                    out[vec_index] = in[index] - in[index-iskip];
                out[vec_index++] *= x_div[i];

                if ((j > 0) && (j < (dims1-1)))
                    out[vec_index] = in[index+jskip] - in[index-jskip];
                else if (j == 0)
                    out[vec_index] = in[index+jskip] - in[index];
                else // j == dims1-1
                    out[vec_index] = in[index] - in[index-jskip];
                out[vec_index++] *= y_div[j];
                out[vec_index++] = 0.;
            }
        }
    }
    else
    {
        for (int k = 0 ; k < dims2 ; k++)
        {
            for (int j = 0 ; j < dims1 ; j++)
            {
                for (int i = 0 ; i < dims0 ; i++)
                {
                    int index     = k*kskip + j*jskip + i*iskip;
                    int vec_index = 3*index;

                    if ((i > 0) && (i < (dims0-1)))
                        out[vec_index] = in[index+iskip]-in[index-iskip];
                    else if (i == 0)
                        out[vec_index] = in[index+iskip] - in[index];
                    else // i == dims0-1
                        out[vec_index] = in[index] - in[index-iskip];
                    out[vec_index++] *= x_div[i];

                    if ((j > 0) && (j < (dims1-1)))
                        out[vec_index] = in[index+jskip] - in[index-jskip];
                    else if (j == 0)
                        out[vec_index] = in[index+jskip] - in[index];
                    else // j == dims1-1
                        out[vec_index] = in[index] - in[index-jskip];
                    out[vec_index++] *= y_div[j];

                    if ((k > 0) && (k < (dims2-1)))
                        out[vec_index] = in[index+kskip] - in[index-kskip];
                    else if (k == 0)
                        out[vec_index] = in[index+kskip] - in[index];
                    else // k == dims2-1
                        out[vec_index] = in[index] - in[index-kskip];
                    out[vec_index++] *= z_div[k];
                }
            }
        }
    }

    if (deleteX)
        delete [] x;
    if (deleteY)
        delete [] y;
    if (deleteZ)
        delete [] z;
    delete [] x_div;
    delete [] y_div;
    if (z_div != NULL)
        delete [] z_div;
}

// ****************************************************************************
//
//  Modifications:
//    Kathleen Biagas, Thu Jun 13 09:58:06 PDT 2013
//    Handle non-float/double scalars.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::RectilinearGradient(vtkRectilinearGrid *rg, 
                                           const char *outputVariableName)
{
    bool isNodal = true;
    vtkDataArray *s = rg->GetPointData()->GetScalars();
    if (s == NULL)
    {
         s = rg->GetCellData()->GetScalars();
         if (s == NULL)
         {
             EXCEPTION2(ExpressionException, outputVariableName, 
                        "the scalar variable could not be found.");
         }

         isNodal = false;
    }
    bool sNeedsDeleting = false;
    vtkDataArray *xc = rg->GetXCoordinates();
    vtkDataArray *yc = rg->GetYCoordinates();
    vtkDataArray *zc = rg->GetZCoordinates();

    int xt = xc->GetDataType();
    int yt = yc->GetDataType();
    int zt = zc->GetDataType();
    int ot = s->GetDataType();

    if (ot != VTK_DOUBLE && ot != VTK_FLOAT)
    {
       vtkDataArray *tmp = vtkDataArray::CreateDataArray(xt);
       tmp->DeepCopy(s);
       s = tmp;
       sNeedsDeleting = true;
       ot = xt;
    }
    vtkDataArray *out_array = s->NewInstance();
    out_array->SetNumberOfComponents(3);
    out_array->SetNumberOfTuples(s->GetNumberOfTuples());

    int dims[3];
    rg->GetDimensions(dims);

#define typeOUT(xtype, ytype, ztype) \
{ \
    if (ot == VTK_DOUBLE) \
    { \
        avtGradientExpression_CalcRectGrad(isNodal, dims,  \
            (xtype*) xc->GetVoidPointer(0), \
            (ytype*) yc->GetVoidPointer(0), \
            (ztype*) zc->GetVoidPointer(0), \
            (double*) s->GetVoidPointer(0), \
            (double*) out_array->GetVoidPointer(0)); \
    } \
    else \
    { \
        avtGradientExpression_CalcRectGrad(isNodal, dims,  \
            (xtype*) xc->GetVoidPointer(0), \
            (ytype*) yc->GetVoidPointer(0), \
            (ztype*) zc->GetVoidPointer(0), \
            (float*) s->GetVoidPointer(0), \
            (float*) out_array->GetVoidPointer(0)); \
    } \
}

#define typeZ(xtype, ytype) \
{ \
    if (zt == VTK_DOUBLE) \
    { \
        typeOUT(xtype, ytype, double); \
    } \
    else \
    { \
        typeOUT(xtype, ytype, float); \
    } \
}

#define typeY(xtype) \
{ \
    if (yt == VTK_DOUBLE) \
    { \
        typeZ(xtype, double); \
    } \
    else \
    { \
        typeZ(xtype, float); \
    } \
}

    if (xt == VTK_DOUBLE)
    {
        typeY(double);
    }
    else
    {
        typeY(float);
    }

    if (sNeedsDeleting)
       s->Delete();

    return out_array;
}


// ****************************************************************************
//  Method: avtGradientExpression::LogicalGradient
//
//  Purpose:
//      Determines the logical gradient of a curvilinear dataset.
//
//  Programmer: Hank Childs
//  Creation:   February 13, 2006
//
//  Modifications:
//
//    Hank Childs / Cyrus Harrison, Wed May 16 11:37:53 PDT 2007
//    Fix memory leak.
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Added a static method for calculating expressions.  This allows for other
//    places in VisIt to access a gradient without instantiating the filter.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::LogicalGradient(vtkStructuredGrid *sg,
                                       const char *outputVariableName)
{
    int i, j, k;

    vtkPoints *vtkpts = sg->GetPoints();
    float *pts = (float *) vtkpts->GetVoidPointer(0);
    bool deletePoints = false;

    int dims[3];
    sg->GetDimensions(dims);
    vtkDataArray *s = sg->GetPointData()->GetScalars();
    if (s == NULL)
    {
         s = sg->GetCellData()->GetScalars();
         if (s == NULL)
         {
             EXCEPTION2(ExpressionException, outputVariableName, "the scalar variable could not"
                                             " be found.");
         }

         dims[0] -= 1;
         dims[1] -= 1;
         dims[2] -= 1;

         float *pts2 = NULL;
         if (dims[2] > 1)
         {
             pts2 = new float[3*dims[0]*dims[1]*dims[2]];
             for (k = 0 ; k < dims[2] ; k++)
             {
                 for (j = 0 ; j < dims[1] ; j++)
                 {
                     for (i = 0 ; i < dims[0] ; i++)
                     {
                         int c_idx = k*(dims[0])*(dims[1]) + j*dims[0] + i;
                         float *p = pts2 + 3*c_idx;
                         p[0] = 0.;
                         p[1] = 0.;
                         p[2] = 0.;
                         for (int l = 0 ; l < 8 ; l++)
                         {
                             int p_idx = (l&1 ? i+1 : i);
                             p_idx += (l&2 ? j+1 : j)*(dims[0]+1);
                             p_idx += (l&4 ? k+1 : k)*(dims[0]+1)*(dims[1]+1);
                             p[0] += pts[3*p_idx] / 8.;
                             p[1] += pts[3*p_idx+1] / 8.;
                             p[2] += pts[3*p_idx+2] / 8.;
                         }
                     }
                 }
             }
         }
         else
         {
             pts2 = new float[3*dims[0]*dims[1]];
             for (j = 0 ; j < dims[1] ; j++)
             {
                 for (i = 0 ; i < dims[0] ; i++)
                 {
                     int c_idx = j*dims[0] + i;
                     float *p = pts2 + 3*c_idx;
                     p[0] = 0.;
                     p[1] = 0.;
                     p[2] = 0.;
                     for (int l = 0 ; l < 4 ; l++)
                     {
                         int p_idx = (l&1 ? i+1 : i);
                         p_idx += (l&2 ? j+1 : j)*(dims[0]+1);
                         p[0] += pts[3*p_idx] / 4.;
                         p[1] += pts[3*p_idx+1] / 4.;
                     }
                 }
             }
         }

         pts = pts2;
         deletePoints = true;
    }

    vtkDataArray *out_array = s->NewInstance();
    out_array->SetNumberOfComponents(3);
    out_array->SetNumberOfTuples(s->GetNumberOfTuples());

    float *in  = (float *) s->GetVoidPointer(0);
    float *out = (float *) out_array->GetVoidPointer(0);

    const int dims0 = dims[0];
    const int dims1 = dims[1];
    const int dims2 = dims[2];
    const int iskip = 1;
    const int jskip = dims0;
    const int kskip = dims0*dims1;
    if (dims2 <= 1)
    {
        for (j = 0 ; j < dims1 ; j++)
        {
            for (i = 0 ; i < dims0 ; i++)
            {
                int index     = j*jskip + i*iskip;
                int vec_index = 3*index;

                float *pt1 = pts + 3*(index+iskip);
                float *pt2 = pts + 3*(index-iskip);
                if ((i > 0) && (i < (dims0-1)))
                    out[vec_index] = in[index+iskip] - in[index-iskip];
                else if (i == 0)
                {
                    pt2 = pts + 3*index;
                    out[vec_index] = in[index+iskip] - in[index];
                }
                else // i == dims0-1
                {
                    pt1 = pts + 3*index;
                    out[vec_index] = in[index] - in[index-iskip];
                }
                float diff[3];
                diff[0] = pt1[0] - pt2[0];
                diff[1] = pt1[1] - pt2[1];
                diff[2] = pt1[2] - pt2[2];
                float dist = sqrt(diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]);
                if (dist == 0.)
                    out[vec_index++] = 0.;
                else
                    out[vec_index++] /= dist;

                pt1 = pts + 3*(index+jskip);
                pt2 = pts + 3*(index-jskip);
                if ((j > 0) && (j < (dims1-1)))
                    out[vec_index] = in[index+jskip] - in[index-jskip];
                else if (j == 0)
                {
                    pt2 = pts + 3*index;
                    out[vec_index] = in[index+jskip] - in[index];
                }
                else // j == dims1-1
                {
                    pt1 = pts + 3*index;
                    out[vec_index] = in[index] - in[index-jskip];
                }
                diff[0] = pt1[0] - pt2[0];
                diff[1] = pt1[1] - pt2[1];
                diff[2] = pt1[2] - pt2[2];
                dist = sqrt(diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]);
                if (dist == 0.)
                    out[vec_index++] = 0.;
                else
                    out[vec_index++] /= dist;
                out[vec_index++] = 0.;
            }
        }
    }
    else
    {
#ifdef _OPENMP
#pragma message("Compiling for OpenMP.")
#endif
        #pragma omp parallel for private(i,j,k) shared(in,out)
        for (k = 0 ; k < dims2 ; k++)
        {
            for (j = 0 ; j < dims1 ; j++)
            {
                for (i = 0 ; i < dims0 ; i++)
                {
                    int index     = k*kskip + j*jskip + i*iskip;
                    int vec_index = 3*index;

                    float *pt1 = pts + 3*(index+iskip);
                    float *pt2 = pts + 3*(index-iskip);
                    if ((i > 0) && (i < (dims0-1)))
                        out[vec_index] = in[index+iskip]-in[index-iskip];
                    else if (i == 0)
                    {
                        pt2 = pts + 3*index;
                        out[vec_index] = in[index+iskip] - in[index];
                    }
                    else // i == dims0-1
                    {
                        pt1 = pts + 3*index;
                        out[vec_index] = in[index] - in[index-iskip];
                    }
                    float diff[3];
                    diff[0] = pt1[0] - pt2[0];
                    diff[1] = pt1[1] - pt2[1];
                    diff[2] = pt1[2] - pt2[2];
                    float dist = sqrt(diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]);
                    if (dist == 0.)
                        out[vec_index++] = 0.;
                    else
                        out[vec_index++] /= dist;

                    pt1 = pts + 3*(index+jskip);
                    pt2 = pts + 3*(index-jskip);
                    if ((j > 0) && (j < (dims1-1)))
                        out[vec_index] = in[index+jskip] - in[index-jskip];
                    else if (j == 0)
                    {
                        pt2 = pts + 3*index;
                        out[vec_index] = in[index+jskip] - in[index];
                    }
                    else // j == dims1-1
                    {
                        pt1 = pts + 3*index;
                        out[vec_index] = in[index] - in[index-jskip];
                    }
                    diff[0] = pt1[0] - pt2[0];
                    diff[1] = pt1[1] - pt2[1];
                    diff[2] = pt1[2] - pt2[2];
                    dist = sqrt(diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]);
                    if (dist == 0.)
                        out[vec_index++] = 0.;
                    else
                        out[vec_index++] /= dist;

                    pt1 = pts + 3*(index+kskip);
                    pt2 = pts + 3*(index-kskip);
                    if ((k > 0) && (k < (dims2-1)))
                        out[vec_index] = in[index+kskip] - in[index-kskip];
                    else if (k == 0)
                    {
                        pt2 = pts + 3*index;
                        out[vec_index] = in[index+kskip] - in[index];
                    }
                    else // k == dims2-1
                    {
                        pt1 = pts + 3*index;
                        out[vec_index] = in[index] - in[index-kskip];
                    }
                    diff[0] = pt1[0] - pt2[0];
                    diff[1] = pt1[1] - pt2[1];
                    diff[2] = pt1[2] - pt2[2];
                    dist = sqrt(diff[0]*diff[0] + diff[1]*diff[1] + diff[2]*diff[2]);
                    if (dist == 0.)
                        out[vec_index++] = 0.;
                    else
                        out[vec_index++] /= dist;
                }
            }
        }
    }

    if (deletePoints)
        delete [] pts;
    return out_array;
}


// ****************************************************************************
//  Method: avtGradientExpression::NodalToZonalQuadHexGrad
//
//  Purpose:
//      Calculates a structured nodal to zonal gradient of a structured grid
//      made of quadrilaterals or hexahedrons
//
//  Programmer: Cyrus Harrison
//  Creation:   August 8, 2007
//
//  Modifications:
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Add an argument for the output variable name, since this is now a static
//    function.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::NodalToZonalQuadHexGrad(vtkStructuredGrid *in_ds,
                                               const char *outputVariableName)
{
    int topo_dim = 3;
    int dims[3];
    in_ds->GetDimensions(dims);
    if (dims[0] == 1)
        topo_dim--;
    if (dims[1] == 1)
        topo_dim--;
    if (dims[2] == 1)
        topo_dim--;

    bool own_values_array = false;
    // get input value
    vtkDataArray *val = in_ds->GetPointData()->GetScalars();

    if( val == NULL || val->GetNumberOfComponents() != 1 )
    {
        // nzqh only supports nodal data
        // we may have zonal data, if so recenter
        val = in_ds->GetCellData()->GetScalars();
        if( val != NULL)
        {
            vtkDataSet *new_ds = (vtkDataSet*) in_ds->NewInstance();
            vtkCellDataToPointData *cd2pd = vtkCellDataToPointData::New();
            if (new_ds != NULL && cd2pd != NULL)
            {
                new_ds->CopyStructure(in_ds);
                char *name = val->GetName();
                new_ds->GetCellData()->AddArray(val);
                cd2pd->SetInputData(new_ds);
                cd2pd->Update();
                val = cd2pd->GetOutput()->GetPointData()->GetArray(name);
                val->Register(NULL);
                own_values_array = true;
            }
            if (new_ds != NULL)
                new_ds->Delete();
            if (cd2pd != NULL)  
                cd2pd->Delete();
        }

        if( val == NULL || val->GetNumberOfComponents() != 1 )
            EXCEPTION2(ExpressionException, outputVariableName,
                       "avtGradientExpression: Unable to find var.");
    }

    // get number of cells
    int ncells = in_ds->GetNumberOfCells();

    // create the result dataset
    vtkDoubleArray *res_vec= vtkDoubleArray::New();
    res_vec->SetNumberOfComponents(3);
    res_vec->SetNumberOfTuples(ncells);

    // loop index and grad values
    int i=0;
    double res_vals[3];

    if(topo_dim == 2)
    {
        debug5 << "avtGradientExpression: NZQH 2D Case" << endl;

        if(ncells>0)
        {
            // make sure we have VTK_PIXEL or VTK_QUAD cells
            // for the 2d case
            int ctype = in_ds->GetCell(0)->GetCellType();
            if( !(ctype == VTK_PIXEL || ctype == VTK_QUAD) )
                EXCEPTION2(ExpressionException, outputVariableName,
                           "avtGradientExpression: 2D NZQH Graident "
                           " only supports quadrilateral cells.");

            for( i = 0; i < ncells; i++)
            {
                CalculateNodalToZonalQuadGrad(in_ds,val,i,res_vals);
                res_vec->SetTuple(i, res_vals);
            }
        }
    }
    else if(topo_dim == 3)
    {
        debug5 << "avtGradientExpression: NZQH 3D Case" << endl;

        if(ncells>0)
        {
            // make sure we have VTK_VOXEL or VTK_HEXAHEDRON cells
            // for the 2d case
            int ctype = in_ds->GetCell(0)->GetCellType();
            if( !(ctype == VTK_VOXEL || ctype == VTK_HEXAHEDRON) )
                EXCEPTION2(ExpressionException, outputVariableName,
                           "avtGradientExpression: 3D NZQH Graident "
                           " only supports hexahedral cells.");

            for (i = 0; i < ncells; i++)
            {
                CalculateNodalToZonalHexGrad(in_ds,val,i,res_vals);
                res_vec->SetTuple(i, res_vals);
            }
        }
    }

    if(own_values_array)
        val->Delete();

    return res_vec;
}

// ****************************************************************************
//  Method: avtGradientExpression::CalculateNodalToZonalQuadGrad
//
//  Purpose:
//      Calculate 2D Gradient.
//
//  Programmer: Cyrus Harrison
//  Creation:   July 19, 2007
//
//  Modifications:
//
//    Cyrus Harrison, Tue Sep  4 09:10:28 PDT 2007
//    Changed tiny to much smaller value.
//
//    Cyrus Harrison, Mon Nov 12 13:17:46 PST 2007
//    Tuned tiny again due to floating point issues on AIX.
//
// ****************************************************************************

void
avtGradientExpression::CalculateNodalToZonalQuadGrad(vtkDataSet *ds,
                                                 vtkDataArray *val,
                                                 int idx,
                                                 double *grad)
{
    // loop index
    int i;

    double tiny = 1.e-37;
    double xi,xj;
    double yi,yj;
    double vi,vj;

    double x[4];
    double y[4];
    double v[4];

    // get the cell points
    vtkCell   *cell = ds->GetCell(idx);
    vtkIdList *cids = cell->GetPointIds();

    // get ids that match the gradient template
    /*
        Gradient Template Order:

        c (1,0)      b (1,1)
           |----------|
           |          |
           |          |
           |          |
           |----------|
        d (0,0)       a(1,0)

        VisIt Order   |    Mapping:
         0,0                0 = 1
         1,0                1 = 2
         1,1                2 = 3
         0,1                3 = 0
    */

    int ids[4];
    ids[3] = cids->GetId(0);
    ids[0] = cids->GetId(1);
    ids[1] = cids->GetId(2);
    ids[2] = cids->GetId(3);

    for( i = 0; i< 4; i++)
    {
        int     id = ids[i];
        double *pt_val = ds->GetPoint(id);

        v[i]  = val->GetTuple1(id);
        x[i]  = pt_val[0];
        y[i]  = pt_val[1];
    }


    xi = .5 * ( x[0] + x[1] - x[2] - x[3]);
    xj = .5 * ( x[1] + x[2] - x[3] - x[0]);

    yi = .5 * ( y[0] + y[1] - y[2] - y[3]);
    yj = .5 * ( y[1] + y[2] - y[3] - y[0]);

    vi = .5 * ( v[0] + v[1] - v[2] - v[3]);
    vj = .5 * ( v[1] + v[2] - v[3] - v[0]);

    // calc det

    double area = xi * yj - xj * yi;
    area = 1.0 / ( area + tiny);

    grad[0] = area * (vi * yj - vj * yi);
    grad[1] = area * (vj * xi - vi * xj);
    grad[2] = 0;
}


// ****************************************************************************
//  Method: avtGradientExpression::CalculateNodalToZonalHexGrad
//
//  Purpose:
//      Calculate 3D Gradient.
//
//  Modifications:
//
//    Cyrus Harrison, Tue Sep  4 09:10:28 PDT 2007
//    Changed tiny to much smaller value.
//
//    Cyrus Harrison, Mon Nov 12 13:17:46 PST 2007
//    Tuned tiny again due to floating point issues on AIX.
//
// ****************************************************************************

void
avtGradientExpression::CalculateNodalToZonalHexGrad(vtkDataSet *ds,
                                                vtkDataArray *val,
                                                int idx,
                                                double *grad)
{
    int i;

    double tiny = 1.e-37;
    double xi,xj,xk;
    double yi,yj,yk;
    double zi,zj,zk;
    double vi,vj,vk;

    double x[8];
    double y[8];
    double z[8];
    double v[8];

    // get the cell points
    vtkCell   *cell = ds->GetCell(idx);
    vtkIdList *cids = cell->GetPointIds();

    // get ids that match the gradient template
    /*
        Gradient Template Order:

            Front Plane:                Back Plane:
      c (1,0,0)      b (1,1,0)     g (1,0,1)      f (1,1,1)
           |----------|                |----------|
           |          |                |          |
           |          |                |          |
           |          |                |          |
           |----------|                |----------|
      d (0,0,0)      a (1,0,0)     h (0,0,1)      e (1,0,1)

        VisIt Order   |    Mapping:
         0,0,0               0 = 1
         1,0,0               1 = 2
         1,1,0               2 = 3
         0,1,0               3 = 0
         0,0,1               4 = 5
         1,0,1               5 = 6
         1,1,1               6 = 7
         0,1,1               7 = 4
    */
    int ids[8];

    ids[0] = cids->GetId(1);
    ids[1] = cids->GetId(2);
    ids[2] = cids->GetId(3);
    ids[3] = cids->GetId(0);

    ids[4] = cids->GetId(5);
    ids[5] = cids->GetId(6);
    ids[6] = cids->GetId(7);
    ids[7] = cids->GetId(4);


    for (i = 0; i< 8; i++)
    {
        int     id = ids[i];
        double *pt_val = ds->GetPoint(id);

        v[i]  = val->GetTuple1(id);
        x[i]  = pt_val[0];
        y[i]  = pt_val[1];
        z[i]  = pt_val[2];
    }

    xi = .25 * ( (x[0] + x[1] + x[4] + x[5]) - (x[3] + x[2] + x[6] + x[7]) );
    xj = .25 * ( (x[1] + x[2] + x[6] + x[5]) - (x[0] + x[3] + x[7] + x[4]) );
    xk = .25 * ( (x[4] + x[5] + x[6] + x[7]) - (x[0] + x[1] + x[2] + x[3]) );

    yi = .25 * ( (y[0] + y[1] + y[4] + y[5]) - (y[3] + y[2] + y[6] + y[7]) );
    yj = .25 * ( (y[1] + y[2] + y[6] + y[5]) - (y[0] + y[3] + y[7] + y[4]) );
    yk = .25 * ( (y[4] + y[5] + y[6] + y[7]) - (y[0] + y[1] + y[2] + y[3]) );

    zi = .25 * ( (z[0] + z[1] + z[4] + z[5]) - (z[3] + z[2] + z[6] + z[7]) );
    zj = .25 * ( (z[1] + z[2] + z[6] + z[5]) - (z[0] + z[3] + z[7] + z[4]) );
    zk = .25 * ( (z[4] + z[5] + z[6] + z[7]) - (z[0] + z[1] + z[2] + z[3]) );

    vi = .25 * ( (v[0] + v[1] + v[4] + v[5]) - (v[3] + v[2] + v[6] + v[7]) );
    vj = .25 * ( (v[1] + v[2] + v[6] + v[5]) - (v[0] + v[3] + v[7] + v[4]) );
    vk = .25 * ( (v[4] + v[5] + v[6] + v[7]) - (v[0] + v[1] + v[2] + v[3]) );

    // calc det
    double vol =   xi * ( yj * zk - yk * zj)
                 - xj * ( yi * zk - yk * zi)
                 + xk * ( yi * zj - yj * zi);

    vol = 1.0 / ( vol + tiny);

    grad[0] = vol * (  vi * (yj*zk - yk*zj)
                     + vj * (yk*zi - yi*zk)
                     + vk * (yi*zj - yj*zi));

    grad[1] = vol * (  vi * (xk*zj - xj*zk)
                     + vj * (xi*zk - xk*zi)
                     + vk * (xj*zi - xi*zj));

    grad[2] = vol * (  vi * (xj*yk - xk*yj)
                     + vj * (xk*yi - xi*yk)
                     + vk * (xi*yj - xj*yi));

}


// ****************************************************************************
//  Method: avtGradientExpression::FastGradient
//
//  Purpose:
//      This gradient is basically for ray casted volume rendering.  The idea
//      is to do anything possible to speed it up.
//
//  Programmer: Hank Childs
//  Creation:   January 9, 2009
//
//  Modifications:
//
//    Hank Childs, Sat Dec  4 11:30:22 PST 2010
//    Add an argument for the output variable name, since this is now a static
//    function.
//
// ****************************************************************************

vtkDataArray *
avtGradientExpression::FastGradient(vtkDataSet *in_ds,
                                    const char *outputVariableName)
{
    vtkDataArray *arr = in_ds->GetPointData()->GetScalars();
    if (arr == NULL)
        // Only point-centered supported in this method (at this time)
        return NULL;

    bool allHexes = true;
    vtkIdType ncells = in_ds->GetNumberOfCells();
    for (vtkIdType i = 0 ; i < ncells ; i++)
        if (in_ds->GetCellType(i) != VTK_HEXAHEDRON)
            allHexes = false;
    if (!allHexes)
        return NULL;

    vtkDoubleArray *cellGrad = vtkDoubleArray::New();
    cellGrad->SetNumberOfComponents(3);
    cellGrad->SetNumberOfTuples(ncells);
    cellGrad->SetName("tmpGrad");
    for (vtkIdType i = 0; i < ncells; i++)
    {
        double grad[3];
        CalculateNodalToZonalHexGrad(in_ds,arr,i,grad);
        cellGrad->SetTuple(i, grad);
    }

    vtkDataSet *new_ds = (vtkDataSet*) in_ds->NewInstance();
    new_ds->CopyStructure(in_ds);
    new_ds->GetCellData()->AddArray(cellGrad);
    vtkCellDataToPointData *cd2pd = vtkCellDataToPointData::New();
    cd2pd->SetInputData(new_ds);
    cd2pd->Update();
    vtkDataArray *rv = cd2pd->GetOutput()->GetPointData()->GetArray("tmpGrad");
    rv->Register(NULL);
    new_ds->Delete();
    cd2pd->Delete();
    cellGrad->Delete();

    return rv;
}


// ****************************************************************************
//  Method: avtGradientExpression::ModifyContract
//
//  Purpose:
//      Request ghost zones.
//
//  Programmer: Hank Childs
//  Creation:   February 13, 2006
//
// ****************************************************************************

avtContract_p
avtGradientExpression::ModifyContract(avtContract_p in_spec)
{
    avtContract_p spec2 =
                   avtSingleInputExpressionFilter::ModifyContract(in_spec);
    spec2->GetDataRequest()->SetDesiredGhostDataType(GHOST_ZONE_DATA);
    return spec2;
}


