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

Program:   Visualization Toolkit
Module:    $RCSfile: vtkStreamTracer.cxx,v $

Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE.  See the above copyright notice for more information.

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

#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkDataSetAttributes.h"
#include "vtkDoubleArray.h"
#include "vtkExecutive.h"
#include "vtkGenericCell.h"
#include "vtkIdList.h"
#include "vtkInformation.h"
#include "vtkInformationVector.h"
#include "vtkIntArray.h"
#include "vtkInterpolatedVelocityField.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPointSet.h"
#include "vtkPolyData.h"
#include "vtkPolyLine.h"
#include "vtkRungeKutta2.h"
#include "vtkRungeKutta4.h"
#include "vtkRungeKutta45.h"

vtkCxxRevisionMacro(vtkStreamTracer, "$Revision: 1.35.6.1 $");
vtkStandardNewMacro(vtkStreamTracer);
vtkCxxSetObjectMacro(vtkStreamTracer,Integrator,vtkInitialValueProblemSolver);
vtkCxxSetObjectMacro(vtkStreamTracer,InterpolatorPrototype,vtkInterpolatedVelocityField);

const double vtkStreamTracer::EPSILON = 1.0E-12;

vtkStreamTracer::vtkStreamTracer()
{
  this->Integrator = vtkRungeKutta2::New();
  this->IntegrationDirection = FORWARD;
  for(int i=0; i<3; i++)
    {
    this->StartPosition[i] = 0.0;
    }
  this->MaximumPropagation.Unit = LENGTH_UNIT;
  this->MaximumPropagation.Interval = 1.0;

  this->MinimumIntegrationStep.Unit = CELL_LENGTH_UNIT;
  this->MinimumIntegrationStep.Interval = 1.0E-2;

  this->MaximumIntegrationStep.Unit = CELL_LENGTH_UNIT;
  this->MaximumIntegrationStep.Interval = 1.0;

  this->InitialIntegrationStep.Unit = CELL_LENGTH_UNIT;
  this->InitialIntegrationStep.Interval = 0.5;

  this->MaximumError = 1.0e-6;

  this->MaximumNumberOfSteps = 2000;

  this->TerminalSpeed = EPSILON;

  this->ComputeVorticity = 1;
  this->RotationScale = 1.0;

  this->LastUsedTimeStep = 0.0;

  this->GenerateNormalsInIntegrate = 1;

  this->InterpolatorPrototype = 0;

  this->SetNumberOfInputPorts(2);

  // by default process active point vectors
  this->SetInputArrayToProcess(0,0,0,vtkDataObject::FIELD_ASSOCIATION_POINTS,
                               vtkDataSetAttributes::VECTORS);
}

vtkStreamTracer::~vtkStreamTracer()
{
  this->SetIntegrator(0);
  this->SetInterpolatorPrototype(0);
}

void vtkStreamTracer::SetSourceConnection(vtkAlgorithmOutput* algOutput)
{
  this->SetInputConnection(1, algOutput);
}

void vtkStreamTracer::SetSource(vtkDataSet *source)
{
  this->SetInput(1, source);
}

vtkDataSet *vtkStreamTracer::GetSource()
{
  if (this->GetNumberOfInputConnections(1) < 1)
    {
    return 0;
    }
  return vtkDataSet::SafeDownCast(
    this->GetExecutive()->GetInputData(1, 0));
}

void vtkStreamTracer::AddInput(vtkDataSet* input)
{
  this->Superclass::AddInput(input);
}

int vtkStreamTracer::GetIntegratorType()
{
  if (!this->Integrator)
    {
    return NONE;
    }
  if (!strcmp(this->Integrator->GetClassName(), "vtkRungeKutta2"))
    {
    return RUNGE_KUTTA2;
    }
  if (!strcmp(this->Integrator->GetClassName(), "vtkRungeKutta4"))
    {
    return RUNGE_KUTTA4;
    }
  if (!strcmp(this->Integrator->GetClassName(), "vtkRungeKutta45"))
    {
    return RUNGE_KUTTA45;
    }
  return UNKNOWN;
}

void vtkStreamTracer::SetIntegratorType(int type)
{
  vtkInitialValueProblemSolver* ivp=0;
  switch (type)
    {
    case RUNGE_KUTTA2:
      ivp = vtkRungeKutta2::New();
      break;
    case RUNGE_KUTTA4:
      ivp = vtkRungeKutta4::New();
      break;
    case RUNGE_KUTTA45:
      ivp = vtkRungeKutta45::New();
      break;
    default:
      vtkWarningMacro("Unrecognized integrator type. Keeping old one.");
      break;
    }
  if (ivp)
    {
    this->SetIntegrator(ivp);
    ivp->Delete();
    }
}

void vtkStreamTracer::SetIntervalInformation(
  int unit, vtkStreamTracer::IntervalInformation& currentValues)
{
  if ( unit == currentValues.Unit )
    {
    return;
    }

  if ( (unit < TIME_UNIT) || (unit > CELL_LENGTH_UNIT) )
    {
    vtkWarningMacro("Unrecognized unit. Using TIME_UNIT instead.");
    currentValues.Unit = TIME_UNIT;
    }
  else
    {
    currentValues.Unit = unit;
    }

  this->Modified();
}

void vtkStreamTracer::SetIntervalInformation(
  int unit, double interval, vtkStreamTracer::IntervalInformation& currentValues)
{
  if ( (unit == currentValues.Unit) && (interval == currentValues.Interval) )
    {
    return;
    }

  this->SetIntervalInformation(unit, currentValues);

  currentValues.Interval = interval;
  this->Modified();
}

void vtkStreamTracer::SetMaximumPropagation(int unit, double max)
{
  this->SetIntervalInformation(unit, max, this->MaximumPropagation);
}
void vtkStreamTracer::SetMaximumPropagation( double max)
{
  if ( max == this->MaximumPropagation.Interval )
    {
    return;
    }
  this->MaximumPropagation.Interval = max;
  this->Modified();
}
void vtkStreamTracer::SetMaximumPropagationUnit(int unit)
{
  this->SetIntervalInformation(unit, this->MaximumPropagation);
}
int vtkStreamTracer::GetMaximumPropagationUnit()
{
  return this->MaximumPropagation.Unit;
}
double vtkStreamTracer::GetMaximumPropagation()
{
  return this->MaximumPropagation.Interval;
}

void vtkStreamTracer::SetMinimumIntegrationStep(int unit, double step)
{
  this->SetIntervalInformation(unit, step, this->MinimumIntegrationStep);
}
void vtkStreamTracer::SetMinimumIntegrationStepUnit(int unit)
{
  this->SetIntervalInformation(unit, this->MinimumIntegrationStep);
}
void vtkStreamTracer::SetMinimumIntegrationStep(double step)
{
  if ( step == this->MinimumIntegrationStep.Interval )
    {
    return;
    }
  this->MinimumIntegrationStep.Interval = step;
  this->Modified();
}
int vtkStreamTracer::GetMinimumIntegrationStepUnit()
{
  return this->MinimumIntegrationStep.Unit;
}
double vtkStreamTracer::GetMinimumIntegrationStep()
{
  return this->MinimumIntegrationStep.Interval;
}

void vtkStreamTracer::SetMaximumIntegrationStep(int unit, double step)
{
  this->SetIntervalInformation(unit, step, this->MaximumIntegrationStep);
}
void vtkStreamTracer::SetMaximumIntegrationStepUnit(int unit)
{
  this->SetIntervalInformation(unit, this->MaximumIntegrationStep);
}
void vtkStreamTracer::SetMaximumIntegrationStep(double step)
{
  if ( step == this->MaximumIntegrationStep.Interval )
    {
    return;
    }
  this->MaximumIntegrationStep.Interval = step;
  this->Modified();
}
int vtkStreamTracer::GetMaximumIntegrationStepUnit()
{
  return this->MaximumIntegrationStep.Unit;
}
double vtkStreamTracer::GetMaximumIntegrationStep()
{
  return this->MaximumIntegrationStep.Interval;
}

void vtkStreamTracer::SetInitialIntegrationStep(int unit, double step)
{
  this->SetIntervalInformation(unit, step, this->InitialIntegrationStep);
}
void vtkStreamTracer::SetInitialIntegrationStepUnit(int unit)
{
  this->SetIntervalInformation(unit, this->InitialIntegrationStep);
}
void vtkStreamTracer::SetInitialIntegrationStep(double step)
{
  if ( step == this->InitialIntegrationStep.Interval )
    {
    return;
    }
  this->InitialIntegrationStep.Interval = step;
  this->Modified();
}
int vtkStreamTracer::GetInitialIntegrationStepUnit()
{
  return this->InitialIntegrationStep.Unit;
}
double vtkStreamTracer::GetInitialIntegrationStep()
{
  return this->InitialIntegrationStep.Interval;
}

double vtkStreamTracer::ConvertToTime(
  vtkStreamTracer::IntervalInformation& interval, double cellLength, double speed)
{
  double retVal = 0.0;
  switch (interval.Unit)
    {
    case TIME_UNIT:
      retVal = interval.Interval;
      break;
    case LENGTH_UNIT:
      retVal = interval.Interval/speed; 
      break;
    case CELL_LENGTH_UNIT:
      retVal = interval.Interval*cellLength/speed; 
      break;
    }
  return retVal;
}

double vtkStreamTracer::ConvertToLength(
  vtkStreamTracer::IntervalInformation& interval, double cellLength, double speed)
{
  double retVal = 0.0;
  switch (interval.Unit)
    {
    case TIME_UNIT:
      retVal = interval.Interval * speed;
      break;
    case LENGTH_UNIT:
      retVal = interval.Interval; 
      break;
    case CELL_LENGTH_UNIT:
      retVal = interval.Interval*cellLength; 
      break;
    }
  return retVal;
}

double vtkStreamTracer::ConvertToCellLength(
  vtkStreamTracer::IntervalInformation& interval, double cellLength, double speed)
{
  double retVal = 0.0;
  switch (interval.Unit)
    {
    case TIME_UNIT:
      retVal = (interval.Interval * speed)/cellLength;
      break;
    case LENGTH_UNIT:
      retVal = interval.Interval/cellLength; 
      break;
    case CELL_LENGTH_UNIT:
      retVal = interval.Interval; 
      break;
    }
  return retVal;
}

double vtkStreamTracer::ConvertToUnit(
  vtkStreamTracer::IntervalInformation& interval, 
  int unit, 
  double cellLength, 
  double speed)
{
  double retVal = 0.0;
  switch (unit)
    {
    case TIME_UNIT:
      retVal = ConvertToTime(interval, cellLength, speed);
      break;
    case LENGTH_UNIT:
      retVal = ConvertToLength(interval, cellLength, speed);
      break;
    case CELL_LENGTH_UNIT:
      retVal = ConvertToCellLength(interval, cellLength, speed);
      break;
    }
  return retVal;
}

void vtkStreamTracer::ConvertIntervals(double& step, double& minStep,
                                       double& maxStep, int direction,
                                       double cellLength, double speed)
{
  step = direction * this->ConvertToTime(
    this->InitialIntegrationStep, cellLength, speed);
  if ( this->MinimumIntegrationStep.Interval <= 0.0 )
    {
    minStep = step;
    }
  else
    {
    minStep = this->ConvertToTime(this->MinimumIntegrationStep, cellLength,  
                                  speed);
    }
  if ( this->MaximumIntegrationStep.Interval <= 0.0 )
    {
    maxStep = step;
    }
  else
    {
    maxStep = this->ConvertToTime(this->MaximumIntegrationStep,cellLength, 
                                  speed);
    }
}

void vtkStreamTracer::CalculateVorticity(vtkGenericCell* cell, 
                                         double pcoords[3],
                                         vtkDoubleArray* cellVectors, 
                                         double vorticity[3])
{
  double* cellVel;
  double derivs[9];

  cellVel = cellVectors->GetPointer(0);
  cell->Derivatives(0, pcoords, cellVel, 3, derivs);
  vorticity[0] = derivs[7] - derivs[5];
  vorticity[1] = derivs[2] - derivs[6];
  vorticity[2] = derivs[3] - derivs[1];
  
}

void vtkStreamTracer::InitializeSeeds(vtkDataArray*& seeds,
                                      vtkIdList*& seedIds,
                                      vtkIntArray*& integrationDirections,
                                      vtkDataSet *source)
{
  seedIds = vtkIdList::New();
  integrationDirections = vtkIntArray::New();
  seeds=0;

  if (source)
    {
    int i;
    vtkIdType numSeeds = source->GetNumberOfPoints();
    if (numSeeds > 0)
      {
      // For now, one thread will do all

      if (this->IntegrationDirection == BOTH)
        {
        seedIds->SetNumberOfIds(2*numSeeds);
        for (i=0; i<numSeeds; i++)
          {
          seedIds->SetId(i, i);
          seedIds->SetId(numSeeds + i, i);
          }
        }
      else
        {
        seedIds->SetNumberOfIds(numSeeds);
        for (i=0; i<numSeeds; i++)
          {
          seedIds->SetId(i, i);
          }
        }
      // Check if the source is a PointSet
      vtkPointSet* seedPts = vtkPointSet::SafeDownCast(source);
      if (seedPts)
        {
        // If it is, use it's points as source
        vtkDataArray* orgSeeds = seedPts->GetPoints()->GetData();
        seeds = orgSeeds->NewInstance();
        seeds->DeepCopy(orgSeeds);
        }
      else
        {
        // Else, create a seed source
        seeds = vtkDoubleArray::New();
        seeds->SetNumberOfComponents(3);
        seeds->SetNumberOfTuples(numSeeds);
        for (i=0; i<numSeeds; i++)
          {
          seeds->SetTuple(i, source->GetPoint(i));
          }
        }
      }
    }
  else
    {
    seeds = vtkDoubleArray::New();
    seeds->SetNumberOfComponents(3);
    seeds->InsertNextTuple(this->StartPosition);
    seedIds->InsertNextId(0);
    if (this->IntegrationDirection == BOTH)
      {
      seedIds->InsertNextId(0);
      }
    }

  if (seeds)
    {
    vtkIdType i;
    vtkIdType numSeeds = seeds->GetNumberOfTuples();
    if (this->IntegrationDirection == BOTH)
      {
      for(i=0; i<numSeeds; i++)
        {
        integrationDirections->InsertNextValue(FORWARD);
        }
      for(i=0; i<numSeeds; i++)
        {
        integrationDirections->InsertNextValue(BACKWARD);
        }
      }
    else
      {
      for(i=0; i<numSeeds; i++)
        {
        integrationDirections->InsertNextValue(this->IntegrationDirection);
        }
      }
    }
}

int vtkStreamTracer::RequestData(
  vtkInformation *vtkNotUsed(request),
  vtkInformationVector **inputVector,
  vtkInformationVector *outputVector)
{
  vtkInformation *sourceInfo = inputVector[1]->GetInformationObject(0);
  vtkDataSet *source = 0;
  if (sourceInfo)
    {
    source = vtkDataSet::SafeDownCast(
      sourceInfo->Get(vtkDataObject::DATA_OBJECT()));
    }

  vtkInformation *inInfo = inputVector[0]->GetInformationObject(0);
  vtkDataSet *input = vtkDataSet::SafeDownCast(
    inInfo->Get(vtkDataObject::DATA_OBJECT()));
  vtkInformation *outInfo = outputVector->GetInformationObject(0);
  vtkPolyData *output = vtkPolyData::SafeDownCast(
    outInfo->Get(vtkDataObject::DATA_OBJECT()));

  vtkDataArray* seeds = 0;
  vtkIdList* seedIds = 0;
  vtkIntArray* integrationDirections = 0;
  this->InitializeSeeds(seeds, seedIds, integrationDirections, source);
  
  if (seeds)
    {
    double lastPoint[3];
    vtkInterpolatedVelocityField* func;
    int maxCellSize = 0;
    if (this->CheckInputs(func, &maxCellSize, inputVector) != VTK_OK)
      {
      vtkDebugMacro("No appropriate inputs have been found. Can not execute.");
      func->Delete();
      seeds->Delete();
      integrationDirections->Delete();
      seedIds->Delete();
      return 1;
      }
    vtkDataArray *vectors = this->GetInputArrayToProcess(0,inputVector);
    if (vectors)
      {
      const char *vecName = vectors->GetName();
      this->Integrate(input, output,
                    seeds, seedIds, 
                    integrationDirections, 
                    lastPoint, func,
                    maxCellSize, vecName);
      }
    func->Delete();
    seeds->Delete();
    }

  integrationDirections->Delete();
  seedIds->Delete();

  return 1;
}

int vtkStreamTracer::CheckInputs(vtkInterpolatedVelocityField*& func,
                                 int* maxCellSize,
                                 vtkInformationVector **inputVector)
{
  // Set the function set to be integrated
  if (!this->InterpolatorPrototype)
    {
    func = vtkInterpolatedVelocityField::New();
    }
  else
    {
    func = this->InterpolatorPrototype->NewInstance();
    func->CopyParameters(this->InterpolatorPrototype);
    }
  vtkDataArray *vectors = this->GetInputArrayToProcess(0,inputVector);
  if (!vectors)
    {
    return 1;
    }
  const char *vecName = vectors->GetName();
  func->SelectVectors(vecName);
 
  // Add all the inputs ( except source, of course ) which
  // have the appropriate vectors and compute the maximum
  // cell size.
  int numInputs = 0;
  int numInputConnections = this->GetNumberOfInputConnections(0);
  for (int i = 0; i < numInputConnections; i++)
    {
    vtkInformation *info = inputVector[0]->GetInformationObject(i);
    vtkDataSet* inp = 0;
    if (info)
      {
      inp = vtkDataSet::SafeDownCast(
        info->Get(vtkDataObject::DATA_OBJECT()));
      }
    if (inp)
      {
      if (!inp->GetPointData()->GetVectors(vecName))
        {
        vtkDebugMacro("Input " << i << "does not contain a velocity vector.");
        continue;
        }
      int cellSize = inp->GetMaxCellSize();
      if ( cellSize > *maxCellSize )
        {
        *maxCellSize = cellSize;
        }
      func->AddDataSet(inp);
      numInputs++;
      }
    }
  if ( numInputs == 0 )
    {
    vtkDebugMacro("No appropriate inputs have been found. Can not execute.");
    return VTK_ERROR;
    }
  return VTK_OK;
}

void vtkStreamTracer::Integrate(vtkDataSet *input0,
                                vtkPolyData* output,
                                vtkDataArray* seedSource, 
                                vtkIdList* seedIds,
                                vtkIntArray* integrationDirections,
                                double lastPoint[3],
                                vtkInterpolatedVelocityField* func,
                                int maxCellSize,
                                const char *vecName)
{
  int i;
  vtkIdType numLines = seedIds->GetNumberOfIds();

  // Useful pointers
  vtkDataSetAttributes* outputPD = output->GetPointData();
  vtkDataSetAttributes* outputCD = output->GetCellData();
  vtkPointData* inputPD;
  vtkDataSet* input;
  vtkDataArray* inVectors;

  int direction=1;

  double* weights = 0;
  if ( maxCellSize > 0 )
    {
    weights = new double[maxCellSize];
    }

  if (this->GetIntegrator() == 0)
    {
    vtkErrorMacro("No integrator is specified.");
    return;
    }

  // Used in GetCell() 
  vtkGenericCell* cell = vtkGenericCell::New();

  // Create a new integrator, the type is the same as Integrator
  vtkInitialValueProblemSolver* integrator = 
    this->GetIntegrator()->NewInstance();
  integrator->SetFunctionSet(func);

  // Since we do not know what the total number of points
  // will be, we do not allocate any. This is important for
  // cases where a lot of streamers are used at once. If we
  // were to allocate any points here, potentially, we can
  // waste a lot of memory if a lot of streamers are used.
  // Always insert the first point
  vtkPoints* outputPoints = vtkPoints::New();
  vtkCellArray* outputLines = vtkCellArray::New();

  // We will keep track of time in this array
  vtkDoubleArray* time = vtkDoubleArray::New();
  time->SetName("IntegrationTime");

  // This array explains why the integration stopped
  vtkIntArray* retVals = vtkIntArray::New();
  retVals->SetName("ReasonForTermination");

  vtkDoubleArray* cellVectors = 0;
  vtkDoubleArray* vorticity = 0;
  vtkDoubleArray* rotation = 0;
  vtkDoubleArray* angularVel = 0;
  if (this->ComputeVorticity)
    {
    cellVectors = vtkDoubleArray::New();
    cellVectors->SetNumberOfComponents(3);
    cellVectors->Allocate(3*VTK_CELL_SIZE);
    
    vorticity = vtkDoubleArray::New();
    vorticity->SetName("Vorticity");
    vorticity->SetNumberOfComponents(3);

    rotation = vtkDoubleArray::New();
    rotation->SetName("Rotation");

    angularVel = vtkDoubleArray::New();
    angularVel->SetName("AngularVelocity");
    }
  
  // We will interpolate all point attributes of the input on
  // each point of the output (unless they are turned off)
  // Note that we are using only the first input, if there are more
  // than one, the attributes have to match.
  outputPD->InterpolateAllocate(input0->GetPointData());
  // Note:  It is an overestimation to have the estimate the same number of
  // output points and input points.  We sill have to squeeze at end.

  vtkIdType numPtsTotal=0;
  double velocity[3];

  int shouldAbort = 0;

  for(int currentLine = 0; currentLine < numLines; currentLine++)
    {

    double progress = static_cast<double>(currentLine)/numLines;
    this->UpdateProgress(progress);

    switch (integrationDirections->GetValue(currentLine))
      {
      case FORWARD:
        direction = 1;
        break;
      case BACKWARD:
        direction = -1;
        break;
      }

    // temporary variables used in the integration
    double point1[3], point2[3], pcoords[3], vort[3], omega;
    vtkIdType index, numPts=0;
    
    // Clear the last cell to avoid starting a search from
    // the last point in the streamline
    func->ClearLastCellId();

    // Initial point
    seedSource->GetTuple(seedIds->GetId(currentLine), point1);
    memcpy(point2, point1, 3*sizeof(double));
    if (!func->FunctionValues(point1, velocity))
      {
      continue;
      }

    numPts++;
    numPtsTotal++;
    vtkIdType nextPoint = outputPoints->InsertNextPoint(point1);
    time->InsertNextValue(0.0);

    // We will always pass a time step to the integrator.
    // If the user specifies a step size with another unit, we will 
    // have to convert it to time.
    IntervalInformation delT;
    delT.Unit = TIME_UNIT;
    delT.Interval = 0;
    IntervalInformation aStep;
    aStep.Unit = this->MaximumPropagation.Unit;
    double propagation = 0.0, step, minStep=0, maxStep=0;
    double stepTaken, accumTime=0;
    double speed;
    double cellLength;
    int retVal=OUT_OF_TIME, tmp;

    // Make sure we use the dataset found by the vtkInterpolatedVelocityField
    input = func->GetLastDataSet();
    inputPD = input->GetPointData();
    inVectors = inputPD->GetVectors(vecName);

    // Convert intervals to time unit
    input->GetCell(func->GetLastCellId(), cell);
    cellLength = sqrt(static_cast<double>(cell->GetLength2()));
    speed = vtkMath::Norm(velocity);

    // Never call conversion methods if speed == 0
    if (speed != 0.0)
      {
      this->ConvertIntervals(delT.Interval, minStep, maxStep, direction, 
                             cellLength, speed);
      }

    // Interpolate all point attributes on first point
    func->GetLastWeights(weights);
    outputPD->InterpolatePoint(inputPD, nextPoint, cell->PointIds, weights);
    
    // Compute vorticity if required
    // This can be used later for streamribbon generation.
    if (this->ComputeVorticity)
      {
      inVectors->GetTuples(cell->PointIds, cellVectors);
      func->GetLastLocalCoordinates(pcoords);
      vtkStreamTracer::CalculateVorticity(cell, pcoords, cellVectors, vort);
      vorticity->InsertNextTuple(vort);
      // rotation
      // local rotation = vorticity . unit tangent ( i.e. velocity/speed )
      if (speed != 0.0)
        {
        omega = vtkMath::Dot(vort, velocity);
        omega /= speed;
        omega *= this->RotationScale;
        }
      else
        {
        omega = 0.0;
        }
      angularVel->InsertNextValue(omega);
      rotation->InsertNextValue(0.0);
      }

    vtkIdType numSteps = 0;
    double error = 0;
    // Integrate until the maximum propagation length is reached, 
    // maximum number of steps is reached or until a boundary is encountered.
    // Begin Integration
    while ( propagation < this->MaximumPropagation.Interval )
      {

      if (numSteps > this->MaximumNumberOfSteps)
        {
        retVal = OUT_OF_STEPS;
        break;
        }

      if ( numSteps++ % 1000 == 1 )
        {
        progress = 
          (currentLine + propagation / this->MaximumPropagation.Interval) /
          numLines ;
        this->UpdateProgress(progress);

        if (this->GetAbortExecute())
          {
          shouldAbort = 1;
          break;
          }
        }

      // Never call conversion methods if speed == 0
      if ( (speed == 0) || (speed <= this->TerminalSpeed) )
        {
        retVal = STAGNATION;
        break;
        }

      // If, with the next step, propagation will be larger than
      // max, reduce it so that it is (approximately) equal to max.
      aStep.Interval = fabs(this->ConvertToUnit(delT, 
                                                this->MaximumPropagation.Unit,
                                                cellLength, speed));
      if ( (propagation + aStep.Interval) >  
           this->MaximumPropagation.Interval )
        {
        aStep.Interval = this->MaximumPropagation.Interval - propagation;
        if (delT.Interval >= 0)
          {
          delT.Interval = this->ConvertToTime(aStep, cellLength, speed);
          }
        else
          {
          delT.Interval = -1.0 * this->ConvertToTime(aStep, cellLength, speed);
          }
        maxStep = delT.Interval;
        }
      this->LastUsedTimeStep = delT.Interval;
          
      // Calculate the next step using the integrator provided
      // Break if the next point is out of bounds.
      if ((tmp=
           integrator->ComputeNextStep(point1, point2, 0, delT.Interval, 
                                       stepTaken, minStep, maxStep, 
                                       this->MaximumError, error)) != 0)
        {
        retVal = tmp;
        memcpy(lastPoint, point2, 3*sizeof(double));
        break;
        }

      // It is not enough to use the starting point for stagnation calculation
      // Use delX/delT to calculate speed and check if it is below
      // stagnation threshold
      double disp[3];
      for (i=0; i<3; i++)
        {
        disp[i] = point2[i] - point1[i];
        }
      if ( (delT.Interval == 0) ||  
           (vtkMath::Norm(disp) / fabs(delT.Interval) <= this->TerminalSpeed) )
        {
        retVal = STAGNATION;
        break;
        }

      accumTime += stepTaken;
      // Calculate propagation (using the same units as MaximumPropagation
      propagation += fabs(this->ConvertToUnit(delT, 
                                              this->MaximumPropagation.Unit,
                                              cellLength, speed));



      // This is the next starting point
      for(i=0; i<3; i++)
        {
        point1[i] = point2[i];
        }

      // Interpolate the velocity at the next point
      if ( !func->FunctionValues(point2, velocity) )
        {
        retVal = OUT_OF_DOMAIN;
        memcpy(lastPoint, point2, 3*sizeof(double));
        break;
        }
      // Make sure we use the dataset found by the vtkInterpolatedVelocityField
      input = func->GetLastDataSet();
      inputPD = input->GetPointData();
      inVectors = inputPD->GetVectors(vecName);

      // Point is valid. Insert it.
      numPts++;
      numPtsTotal++;
      nextPoint = outputPoints->InsertNextPoint(point1);
      time->InsertNextValue(accumTime);

      // Calculate cell length and speed to be used in unit conversions
      input->GetCell(func->GetLastCellId(), cell);
      cellLength = sqrt(static_cast<double>(cell->GetLength2()));
      speed = vtkMath::Norm(velocity);

      // Interpolate all point attributes on current point
      func->GetLastWeights(weights);
      outputPD->InterpolatePoint(inputPD, nextPoint, cell->PointIds, weights);

      // Compute vorticity if required
      // This can be used later for streamribbon generation.
      if (this->ComputeVorticity)
        {
        inVectors->GetTuples(cell->PointIds, cellVectors);
        func->GetLastLocalCoordinates(pcoords);
        vtkStreamTracer::CalculateVorticity(cell, pcoords, cellVectors, vort);
        vorticity->InsertNextTuple(vort);
        // rotation
        // angular velocity = vorticity . unit tangent ( i.e. velocity/speed )
        // rotation = sum ( angular velocity * delT )
        omega = vtkMath::Dot(vort, velocity);
        omega /= speed;
        omega *= this->RotationScale;
        index = angularVel->InsertNextValue(omega);
        rotation->InsertNextValue(rotation->GetValue(index-1) +
                                  (angularVel->GetValue(index-1) + omega)/2 * 
                                  (accumTime - time->GetValue(index-1)));
        }

      // Never call conversion methods if speed == 0
      if ( (speed == 0) || (speed <= this->TerminalSpeed) )
        {
        retVal = STAGNATION;
        break;
        }

      // Convert all intervals to time
      this->ConvertIntervals(step, minStep, maxStep, direction, 
                             cellLength, speed);


      // If the solver is adaptive and the next time step (delT.Interval)
      // that the solver wants to use is smaller than minStep or larger 
      // than maxStep, re-adjust it. This has to be done every step
      // because minStep and maxStep can change depending on the cell
      // size (unless it is specified in time units)
      if (integrator->IsAdaptive())
        {
        if (fabs(delT.Interval) < fabs(minStep))
          {
          delT.Interval = fabs(minStep) * delT.Interval/fabs(delT.Interval);
          }
        else if (fabs(delT.Interval) > fabs(maxStep))
          {
          delT.Interval = fabs(maxStep) * delT.Interval/fabs(delT.Interval);
          }
        }
      else
        {
        delT.Interval = step;
        }

      // End Integration
      }

    if (shouldAbort)
      {
      break;
      }

    if (numPts > 1)
      {
      outputLines->InsertNextCell(numPts);
      for (i=numPtsTotal-numPts; i<numPtsTotal; i++)
        {
        outputLines->InsertCellPoint(i);
        }
      retVals->InsertNextValue(retVal);
      }
    }

  if (!shouldAbort)
    {
    // Create the output polyline
    output->SetPoints(outputPoints);
    outputPD->AddArray(time);
    if (vorticity)
      {
      outputPD->AddArray(vorticity);
      outputPD->AddArray(rotation);
      outputPD->AddArray(angularVel);
      }
    
    vtkIdType numPts = outputPoints->GetNumberOfPoints();
    if ( numPts > 1 )
      {
      // Assign geometry and attributes
      output->SetLines(outputLines);
      if (this->GenerateNormalsInIntegrate)
        {
        this->GenerateNormals(output, 0, vecName);
        }

      outputCD->AddArray(retVals);
      }
    }

  if (vorticity)
    {
    vorticity->Delete();
    rotation->Delete();
    angularVel->Delete();
    }

  if (cellVectors)
    {
    cellVectors->Delete();
    }
  retVals->Delete();

  outputPoints->Delete();
  outputLines->Delete();

  time->Delete();


  integrator->Delete();
  cell->Delete();

  delete[] weights;
  
  output->Squeeze();
  return;
}

void vtkStreamTracer::GenerateNormals(vtkPolyData* output, double* firstNormal, 
                                      const char *vecName)
{
  // Useful pointers
  vtkDataSetAttributes* outputPD = output->GetPointData();

  vtkPoints* outputPoints = output->GetPoints();
  vtkCellArray* outputLines = output->GetLines();

  vtkDataArray* rotation = outputPD->GetArray("Rotation");

  vtkIdType numPts = outputPoints->GetNumberOfPoints();
  if ( numPts > 1 )
    {
    if (this->ComputeVorticity)
      {
      vtkPolyLine* lineNormalGenerator = vtkPolyLine::New();
      vtkDoubleArray* normals = vtkDoubleArray::New();
      normals->SetNumberOfComponents(3);
      normals->SetNumberOfTuples(numPts);
      // Make sure the normals are initialized in case 
      // GenerateSlidingNormals() fails and returns before
      // creating all normals
      for(vtkIdType idx=0; idx<numPts; idx++)
        {
        normals->SetTuple3(idx, 1, 0, 0);
        }

      lineNormalGenerator->GenerateSlidingNormals(outputPoints,
                                                  outputLines,
                                                  normals,
                                                  firstNormal);
      lineNormalGenerator->Delete();

      vtkIdType i;
      int j;
      double normal[3], local1[3], local2[3], theta, costheta, sintheta, length;
      double velocity[3];
      normals->SetName("Normals");
      vtkDataArray* newVectors = 
        outputPD->GetVectors(vecName);
      for(i=0; i<numPts; i++)
        {
        normals->GetTuple(i, normal);
        if (newVectors == NULL)
          { // This should never happen.
          vtkErrorMacro("Could not find output array.");
          return;
          }
        newVectors->GetTuple(i, velocity);
        // obtain two unit orthogonal vectors on the plane perpendicular to
        // the streamline
        for(j=0; j<3; j++) { local1[j] = normal[j]; }
        length = vtkMath::Normalize(local1);
        vtkMath::Cross(local1, velocity, local2);
        vtkMath::Normalize(local2);
        // Rotate the normal with theta
        rotation->GetTuple(i, &theta);
        costheta = cos(theta);
        sintheta = sin(theta);
        for(j=0; j<3; j++)
          {
          normal[j] = length* (costheta*local1[j] + sintheta*local2[j]);
          }
        normals->SetTuple(i, normal);
        }
      outputPD->AddArray(normals);
      outputPD->SetActiveAttribute("Normals", vtkDataSetAttributes::VECTORS);
      normals->Delete();
      }
    }
}


// This is used by sub-classes in certain situations. It
// does a lot less (for example, does not compute attributes)
// than Integrate.
void vtkStreamTracer::SimpleIntegrate(double seed[3], 
                                      double lastPoint[3], 
                                      double delt,
                                      vtkInterpolatedVelocityField* func)
{
  vtkIdType numSteps = 0;
  vtkIdType maxSteps = 20;
  double error = 0;
  double stepTaken;
  double point1[3], point2[3];
  double velocity[3];
  double speed;

  (void)seed; // Seed is not used

  memcpy(point1, lastPoint, 3*sizeof(double));

  // Create a new integrator, the type is the same as Integrator
  vtkInitialValueProblemSolver* integrator = 
    this->GetIntegrator()->NewInstance();
  integrator->SetFunctionSet(func);

  while ( 1 )
    {

    if (numSteps++ > maxSteps)
      {
      break;
      }

    // Calculate the next step using the integrator provided
    // Break if the next point is out of bounds.
    if (integrator->ComputeNextStep(point1, point2, 0, delt, 
                                    stepTaken, 0, 0, 0, error) != 0)
      {
      memcpy(lastPoint, point2, 3*sizeof(double));
      break;
      }


    // This is the next starting point
    for(int i=0; i<3; i++)
      {
      point1[i] = point2[i];
      }

    // Interpolate the velocity at the next point
    if ( !func->FunctionValues(point2, velocity) )
      {
      memcpy(lastPoint, point2, 3*sizeof(double));
      break;
      }

    speed = vtkMath::Norm(velocity);

    // Never call conversion methods if speed == 0
    if ( (speed == 0) || (speed <= this->TerminalSpeed) )
      {
      break;
      }

    memcpy(point1, point2, 3*sizeof(double));
    // End Integration
    }

  integrator->Delete();
}

int vtkStreamTracer::FillInputPortInformation(int port, vtkInformation *info)
{
  if (port == 0)
    {
    info->Set(vtkAlgorithm::INPUT_IS_REPEATABLE(), 1);
    }
  else if (port == 1)
    {
    info->Set(vtkAlgorithm::INPUT_IS_OPTIONAL(), 1);
    }
  info->Set(vtkAlgorithm::INPUT_REQUIRED_DATA_TYPE(), "vtkDataSet");
  return 1;
}

void vtkStreamTracer::PrintSelf(ostream& os, vtkIndent indent)
{
  this->Superclass::PrintSelf(os,indent);
  os << indent << "Start position: " 
     << this->StartPosition[0] << " "
     << this->StartPosition[1] << " "
     << this->StartPosition[2] << endl;
  os << indent << "Terminal speed: " << this->TerminalSpeed << endl;
  os << indent << "Maximum propagation: " << this->MaximumPropagation.Interval
     << " unit: ";
  switch (this->MaximumPropagation.Unit)
    {
    case TIME_UNIT:
      os << "time.";
      break;
    case LENGTH_UNIT:
      os << "length.";
      break;
    case CELL_LENGTH_UNIT:
      os << "cell length.";
      break;
    }
  os << endl;
  
  os << indent << "Min. integration step: " 
     << this->MinimumIntegrationStep.Interval
     << " unit: ";
  switch (this->MinimumIntegrationStep.Unit)
    {
    case TIME_UNIT:
      os << "time.";
      break;
    case LENGTH_UNIT:
      os << "length.";
      break;
    case CELL_LENGTH_UNIT:
      os << "cell length.";
      break;
    }
  os << endl;

  os << indent << "Max. integration step: " 
     << this->MaximumIntegrationStep.Interval
     << " unit: ";
  switch (this->MaximumIntegrationStep.Unit)
    {
    case TIME_UNIT:
      os << "time.";
      break;
    case LENGTH_UNIT:
      os << "length.";
      break;
    case CELL_LENGTH_UNIT:
      os << "cell length.";
      break;
    }
  os << endl;

  os << indent << "Initial integration step: " 
     << this->InitialIntegrationStep.Interval
     << " unit: ";
  switch (this->InitialIntegrationStep.Unit)
    {
    case TIME_UNIT:
      os << "time.";
      break;
    case LENGTH_UNIT:
      os << "length.";
      break;
    case CELL_LENGTH_UNIT:
      os << "cell length.";
      break;
    }
  os << endl;

  os << indent << "Integration direction: ";
  switch (this->IntegrationDirection)
    {
    case FORWARD:
      os << "forward.";
      break;
    case BACKWARD:
      os << "backward.";
      break;
    }
  os << endl;

  os << indent << "Integrator: " << this->Integrator << endl;
  os << indent << "Maximum error: " << this->MaximumError << endl;
  os << indent << "Max. number of steps: " << this->MaximumNumberOfSteps 
     << endl;
  os << indent << "Vorticity computation: " 
     << (this->ComputeVorticity ? " On" : " Off") << endl;
  os << indent << "Rotation scale: " << this->RotationScale << endl;
}