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vtkVectorFieldTopology.cxx
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vtkVectorFieldTopology.cxx
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/*=========================================================================
Program: Visualization Toolkit
Module: vtkVectorFieldTopology.cxx
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 <vtkVectorFieldTopology.h>
// VTK includes
#include <vtkAppendPolyData.h>
#include <vtkCellArray.h>
#include <vtkCellData.h>
#include <vtkCellDataToPointData.h>
#include <vtkCellLocator.h>
#include <vtkCellTypes.h>
#include <vtkContourFilter.h>
#include <vtkDataSet.h>
#include <vtkDataSetSurfaceFilter.h>
#include <vtkDataSetTriangleFilter.h>
#include <vtkDoubleArray.h>
#include <vtkFeatureEdges.h>
#include <vtkGeometryFilter.h>
#include <vtkIdFilter.h>
#include <vtkImageData.h>
#include <vtkInformation.h>
#include <vtkInformationVector.h>
#include <vtkIntersectionPolyDataFilter.h>
#include <vtkLine.h>
#include <vtkMath.h>
#include <vtkMatrix3x3.h>
#include <vtkNew.h>
#include <vtkObjectFactory.h>
#include <vtkPointData.h>
#include <vtkPointLocator.h>
#include <vtkPoints.h>
#include <vtkPolyData.h>
#include <vtkPolyLine.h>
#include <vtkProbeFilter.h>
#include <vtkQuad.h>
#include <vtkRegularPolygonSource.h>
#include <vtkRuledSurfaceFilter.h>
#include <vtkSelectEnclosedPoints.h>
#include <vtkSmartPointer.h>
#include <vtkStreamSurface.h>
#include <vtkStreamTracer.h>
#include <vtkTetra.h>
#include <vtkTriangle.h>
#include <vtkUnstructuredGrid.h>
#include <vtkVector.h>
#include <vtkVectorFieldTopology.h>
#include <vtkVertex.h>
// Eigen3
#include <vtk_eigen.h>
#include VTK_EIGEN(Eigenvalues)
#include <cmath>
#include <map>
#define epsilon (1e-10)
//----------------------------------------------------------------------------
vtkStandardNewMacro(vtkVectorFieldTopology);
//----------------------------------------------------------------------------
vtkVectorFieldTopology::vtkVectorFieldTopology()
{
this->SetNumberOfInputPorts(1);
this->SetNumberOfOutputPorts(5);
// by default process active point vectors
this->SetInputArrayToProcess(
0, 0, 0, vtkDataObject::FIELD_ASSOCIATION_POINTS, vtkDataSetAttributes::VECTORS);
}
//----------------------------------------------------------------------------
vtkVectorFieldTopology::~vtkVectorFieldTopology() = default;
//----------------------------------------------------------------------------
void vtkVectorFieldTopology::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os, indent);
os << indent << "MaxNumSteps = " << this->MaxNumSteps << "\n";
os << indent << "IntegrationStepSize = " << this->IntegrationStepSize << "\n";
os << indent << "SeparatrixDistance = " << this->SeparatrixDistance << "\n";
os << indent << "UseIterativeSeeding = " << this->UseIterativeSeeding << "\n";
os << indent << "InterpolatorType = " << this->InterpolatorType << "\n";
os << indent << "ComputeSurfaces = " << this->ComputeSurfaces << "\n";
os << indent << "vtkStreamSurface: \n";
this->StreamSurface->PrintSelf(os, indent.GetNextIndent());
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::FillInputPortInformation(int port, vtkInformation* info)
{
if (port == 0)
{
info->Set(vtkAlgorithm::INPUT_REQUIRED_DATA_TYPE(), "vtkDataSet");
}
return 1;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::FillOutputPortInformation(int port, vtkInformation* info)
{
if (port < 5)
{
info->Set(vtkDataObject::DATA_TYPE_NAME(), "vtkPolyData");
}
return 1;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::Validate()
{
if (UseBoundarySwitchPoints && ExcludeBoundary)
{
vtkErrorMacro(
"vtkVectorFieldTopology: both UseBoundarySwitchPoints and ExcludeBoundary are true.");
return 0;
}
return 1;
}
//----------------------------------------------------------------------------
void vtkVectorFieldTopology::SetInterpolatorType(int interpType)
{
this->InterpolatorType = interpType;
if (interpType != vtkStreamTracer::INTERPOLATOR_WITH_DATASET_POINT_LOCATOR &&
interpType != vtkStreamTracer::INTERPOLATOR_WITH_CELL_LOCATOR)
vtkErrorMacro(
"The interpolator type is neither vtkStreamTracer::INTERPOLATOR_WITH_CELL_LOCATOR nor "
"vtkStreamTracer::INTERPOLATOR_WITH_DATASET_POINT_LOCATOR.");
}
//----------------------------------------------------------------------------
void vtkVectorFieldTopology::SetInterpolatorTypeToCellLocator()
{
SetInterpolatorType(static_cast<int>(vtkStreamTracer::INTERPOLATOR_WITH_CELL_LOCATOR));
}
//----------------------------------------------------------------------------
void vtkVectorFieldTopology::SetInterpolatorTypeToDataSetPointLocator()
{
SetInterpolatorType(static_cast<int>(vtkStreamTracer::INTERPOLATOR_WITH_DATASET_POINT_LOCATOR));
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::Classify2D(int countComplex, int countPos, int countNeg)
{
// make simple type that corresponds to the number of positive eigenvalues
// SOURCE_2D 2, SADDLE_2D 1, SINK_2D 0, (CENTER_2D 3)
// in analogy to ttk, where the type corresponds to the down directions
int critType = vtkVectorFieldTopology::DEGENERATE_2D;
if (countPos + countNeg == 2)
{
switch (countPos)
{
case 0:
critType = vtkVectorFieldTopology::SINK_2D;
break;
case 1:
critType = vtkVectorFieldTopology::SADDLE_2D;
break;
case 2:
critType = vtkVectorFieldTopology::SOURCE_2D;
break;
default:
break;
}
}
else if (countComplex == 2)
{
critType = vtkVectorFieldTopology::CENTER_2D;
}
return critType;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ClassifyDetailed2D(int countComplex, int countPos, int countNeg)
{
// determine which type of critical point we have including distinction between node and spiral
// ATTRACTING_NODE_2D 0, ATTRACTING_FOCUS_2D 1, NODE_SADDLE_2D 2, REPELLING_NODE_2D 3,
// REPELLING_FOCUS_2D 4, CENTER_DETAILED_2D 5
int critType = vtkVectorFieldTopology::DEGENERATE_2D;
if (countPos + countNeg == 2)
{
switch (countPos)
{
case 0:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::ATTRACTING_NODE_2D;
}
else
{
critType = vtkVectorFieldTopology::ATTRACTING_FOCUS_2D;
}
break;
case 1:
critType = vtkVectorFieldTopology::NODE_SADDLE_2D;
break;
case 2:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::REPELLING_NODE_2D;
}
else
{
critType = vtkVectorFieldTopology::REPELLING_FOCUS_2D;
}
break;
default:
break;
}
}
else if (countComplex == 2)
{
critType = vtkVectorFieldTopology::CENTER_DETAILED_2D;
}
return critType;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::Classify3D(int countComplex, int countPos, int countNeg)
{
// make simple type that corresponds to the number of positive eigenvalues
// SOURCE_3D 3, SADDLE_2_3D 2, SADDLE_1_3D 1, SINK_3D 0, (CENTER_3D 4)
// in analogy to ttk, where the type corresponds to the down directions
int critType = vtkVectorFieldTopology::DEGENERATE_3D;
if (countPos + countNeg == 3)
{
switch (countPos)
{
case 0:
critType = vtkVectorFieldTopology::SINK_3D;
break;
case 1:
critType = vtkVectorFieldTopology::SADDLE_1_3D;
break;
case 2:
critType = vtkVectorFieldTopology::SADDLE_2_3D;
break;
case 3:
critType = vtkVectorFieldTopology::SOURCE_3D;
break;
default:
break;
}
}
else if (countComplex > 0)
{
critType = vtkVectorFieldTopology::CENTER_3D;
}
return critType;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ClassifyDetailed3D(int countComplex, int countPos, int countNeg)
{
// determine which type of critical point we have including distinction between node and spiral
// ATTRACTING_NODE_3D 0, ATTRACTING_FOCUS_3D 1, NODE_SADDLE_1_3D 2, FOCUS_SADDLE_1_3D 3,
// NODE_SADDLE_2_3D 4, FOCUS_SADDLE_2_3D 5, REPELLING_NODE_3D 6, REPELLING_FOCUS_3D 7,
// CENTER_DETAILED_3D 8
int critType = vtkVectorFieldTopology::DEGENERATE_3D;
if (countPos + countNeg == 3)
{
switch (countPos)
{
case 0:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::ATTRACTING_NODE_3D;
}
else
{
critType = vtkVectorFieldTopology::ATTRACTING_FOCUS_3D;
}
break;
case 1:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::NODE_SADDLE_1_3D;
}
else
{
critType = vtkVectorFieldTopology::FOCUS_SADDLE_1_3D;
}
break;
case 2:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::NODE_SADDLE_2_3D;
}
else
{
critType = vtkVectorFieldTopology::FOCUS_SADDLE_2_3D;
}
break;
case 3:
if (countComplex == 0)
{
critType = vtkVectorFieldTopology::REPELLING_NODE_3D;
}
else
{
critType = vtkVectorFieldTopology::REPELLING_FOCUS_3D;
}
break;
default:
break;
}
}
else if (countComplex > 0)
{
critType = vtkVectorFieldTopology::CENTER_DETAILED_3D;
}
return critType;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ComputeCriticalPoints2D(
vtkSmartPointer<vtkPolyData> criticalPoints, vtkSmartPointer<vtkUnstructuredGrid> tridataset)
{
for (int cellId = 0; cellId < tridataset->GetNumberOfCells(); cellId++)
{
auto cell = tridataset->GetCell(cellId);
if (cell->GetCellType() != VTK_TRIANGLE)
{
continue;
}
vtkIdType indices[3] = { cell->GetPointId(0), cell->GetPointId(1), cell->GetPointId(2) };
// array with the coordinates of the three triagle points: coords[point][component]
vtkVector3d coords[3] = { vtkVector3d(tridataset->GetPoint(indices[0])),
vtkVector3d(tridataset->GetPoint(indices[1])),
vtkVector3d(tridataset->GetPoint(indices[2])) };
// array with the vector values at the three triagle points: values[point][component]
vtkVector3d values[3] = {
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[0])),
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[1])),
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[2]))
};
// matrix f(T) to convert to barycentric coordinates
vtkNew<vtkMatrix3x3> valueMatrix;
vtkNew<vtkMatrix3x3> coordsMatrix;
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
valueMatrix->SetElement(j, i, values[i + 1][j] - values[0][j]);
coordsMatrix->SetElement(j, i, coords[i + 1][j] - coords[0][j]);
}
}
if (valueMatrix->Determinant() != 0)
{
valueMatrix->Invert();
// barycentric corrdinates of the zero: lambda = f(T)^-1 (-values[0])
double lambda[3] = { -values[0][0], -values[0][1], -values[0][2] };
valueMatrix->MultiplyPoint(lambda, lambda);
// barycentric interpolation f(r) = f(T) * lambda + values[0] set to zero and solved for r
// with lambda = T^-1 (r-r_0) results in r = T * f(T)^-1 (-values[0]) + coords[0]
double zeroPos[3] = { coords[0][0] + lambda[0] * (coords[1][0] - coords[0][0]) +
lambda[1] * (coords[2][0] - coords[0][0]),
coords[0][1] + lambda[0] * (coords[1][1] - coords[0][1]) +
lambda[1] * (coords[2][1] - coords[0][1]),
coords[0][2] + lambda[0] * (coords[1][2] - coords[0][2]) +
lambda[1] * (coords[2][2] - coords[0][2]) };
// Check if zeroPos is inside the cell, i.e. if 0 <= lambda <= 1
if (valueMatrix->Determinant() != 0 && lambda[0] >= -epsilon && lambda[1] >= -epsilon &&
lambda[0] + lambda[1] <= 1.0 + epsilon)
{
bool isNewPoint = true;
for (int i = 0; i < criticalPoints->GetNumberOfPoints(); ++i)
{
if (vtkMath::Distance2BetweenPoints(zeroPos, criticalPoints->GetPoint(i)) < epsilon)
{
isNewPoint = false;
}
}
if (isNewPoint)
{
// gradient = f(T)T^-1
vtkNew<vtkMatrix3x3> gradientMatrix;
vtkMatrix3x3::Multiply3x3(coordsMatrix, valueMatrix, gradientMatrix);
gradientMatrix->Invert();
criticalPoints->GetPoints()->InsertNextPoint(zeroPos);
criticalPoints->GetPointData()
->GetArray("gradient")
->InsertNextTuple9(gradientMatrix->GetElement(0, 0), gradientMatrix->GetElement(0, 1),
gradientMatrix->GetElement(0, 2), gradientMatrix->GetElement(1, 0),
gradientMatrix->GetElement(1, 1), gradientMatrix->GetElement(1, 2),
gradientMatrix->GetElement(2, 0), gradientMatrix->GetElement(2, 1),
gradientMatrix->GetElement(2, 2));
vtkNew<vtkVertex> vertex;
vertex->GetPointIds()->SetId(0, criticalPoints->GetNumberOfPoints() - 1);
criticalPoints->GetVerts()->InsertNextCell(vertex);
}
}
}
}
return 1;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ComputeCriticalPoints3D(
vtkSmartPointer<vtkPolyData> criticalPoints, vtkSmartPointer<vtkUnstructuredGrid> tridataset)
{
for (int cellId = 0; cellId < tridataset->GetNumberOfCells(); cellId++)
{
auto cell = tridataset->GetCell(cellId);
if (cell->GetCellType() != VTK_TETRA)
{
continue;
}
vtkIdType indices[4] = { cell->GetPointId(0), cell->GetPointId(1), cell->GetPointId(2),
cell->GetPointId(3) };
vtkVector3d coords[4] = { vtkVector3d(tridataset->GetPoint(indices[0])),
vtkVector3d(tridataset->GetPoint(indices[1])), vtkVector3d(tridataset->GetPoint(indices[2])),
vtkVector3d(tridataset->GetPoint(indices[3])) };
vtkVector3d values[4] = {
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[0])),
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[1])),
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[2])),
vtkVector3d(
tridataset->GetPointData()->GetArray(this->NameOfVectorArray)->GetTuple(indices[3]))
};
vtkNew<vtkMatrix3x3> valueMatrix;
vtkNew<vtkMatrix3x3> coordsMatrix;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
valueMatrix->SetElement(j, i, values[3][j] - values[i][j]);
coordsMatrix->SetElement(j, i, coords[3][j] - coords[i][j]);
}
}
if (valueMatrix->Determinant() != 0)
{
valueMatrix->Invert();
double lambda[3] = { values[3][0], values[3][1], values[3][2] };
valueMatrix->MultiplyPoint(lambda, lambda);
double zeroPos[3] = { coords[0][0] * lambda[0] + coords[1][0] * lambda[1] +
coords[2][0] * lambda[2] + coords[3][0] * (1.0 - lambda[0] - lambda[1] - lambda[2]),
coords[0][1] * lambda[0] + coords[1][1] * lambda[1] + coords[2][1] * lambda[2] +
coords[3][1] * (1.0 - lambda[0] - lambda[1] - lambda[2]),
coords[0][2] * lambda[0] + coords[1][2] * lambda[1] + coords[2][2] * lambda[2] +
coords[3][2] * (1.0 - lambda[0] - lambda[1] - lambda[2]) };
// Check if zeroPos is inside the cell
if (valueMatrix->Determinant() != 0 && lambda[0] >= -epsilon && lambda[1] >= -epsilon &&
lambda[2] >= -epsilon && lambda[0] + lambda[1] + lambda[2] <= 1.0 + epsilon)
{
bool isNewPoint = true;
for (int i = 0; i < criticalPoints->GetNumberOfPoints(); ++i)
{
if (vtkMath::Distance2BetweenPoints(zeroPos, criticalPoints->GetPoint(i)) < epsilon)
{
isNewPoint = false;
}
}
if (isNewPoint)
{
// gradient = f(T)T^-1
vtkNew<vtkMatrix3x3> gradientMatrix;
vtkMatrix3x3::Multiply3x3(coordsMatrix, valueMatrix, gradientMatrix);
gradientMatrix->Invert();
criticalPoints->GetPoints()->InsertNextPoint(zeroPos);
criticalPoints->GetPointData()
->GetArray("gradient")
->InsertNextTuple9(gradientMatrix->GetElement(0, 0), gradientMatrix->GetElement(0, 1),
gradientMatrix->GetElement(0, 2), gradientMatrix->GetElement(1, 0),
gradientMatrix->GetElement(1, 1), gradientMatrix->GetElement(1, 2),
gradientMatrix->GetElement(2, 0), gradientMatrix->GetElement(2, 1),
gradientMatrix->GetElement(2, 2));
vtkNew<vtkVertex> vertex;
vertex->GetPointIds()->SetId(0, criticalPoints->GetNumberOfPoints() - 1);
criticalPoints->GetVerts()->InsertNextCell(vertex);
}
}
}
}
return 1;
}
//----------------------------------------------------------------------------
void vtkVectorFieldTopology::InterpolateVector(
double x0, double x1, double x, const double v0[3], const double v1[3], double v[3])
{
double y0[3], y1[3];
vtkMath::Assign(v0, y0);
vtkMath::MultiplyScalar(y0, x1 - x);
vtkMath::Assign(v1, y1);
vtkMath::MultiplyScalar(y1, x - x0);
vtkMath::Add(y0, y1, v);
vtkMath::MultiplyScalar(v, 1 / (x1 - x0));
// vtkMath::Assign(v0, v);
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ComputeBoundarySwitchPoints(
vtkPolyData* boundarySwitchPoints, vtkUnstructuredGrid* tridataset)
{
vtkDataArray* vectors = tridataset->GetPointData()->GetArray(this->NameOfVectorArray);
vtkNew<vtkDoubleArray> BoundarySwitchTypeArray;
BoundarySwitchTypeArray->SetNumberOfComponents(1);
BoundarySwitchTypeArray->SetName("BoundarySwitchType");
BoundarySwitchTypeArray->SetNumberOfTuples(tridataset->GetNumberOfPoints());
boundarySwitchPoints->GetPointData()->AddArray(BoundarySwitchTypeArray);
vtkNew<vtkDoubleArray> BoundarySwitchPointVector;
BoundarySwitchPointVector->SetNumberOfComponents(3);
BoundarySwitchPointVector->SetName("Vector");
BoundarySwitchPointVector->SetNumberOfTuples(tridataset->GetNumberOfPoints());
boundarySwitchPoints->GetPointData()->AddArray(BoundarySwitchPointVector);
vtkNew<vtkDoubleArray> BoundarySwitchPointNormal;
BoundarySwitchPointNormal->SetNumberOfComponents(3);
BoundarySwitchPointNormal->SetName("Normal");
BoundarySwitchPointNormal->SetNumberOfTuples(tridataset->GetNumberOfPoints());
boundarySwitchPoints->GetPointData()->AddArray(BoundarySwitchPointNormal);
vtkNew<vtkGeometryFilter> geometry;
geometry->SetInputData(tridataset);
geometry->Update();
vtkNew<vtkFeatureEdges> surface;
surface->SetInputData(geometry->GetOutput());
surface->Update();
vtkNew<vtkCellLocator> cellLocator;
cellLocator->SetDataSet(tridataset);
cellLocator->BuildLocator();
cellLocator->Update();
int numPoint = 0;
// main loop
for (int i = 0; i < surface->GetOutput()->GetNumberOfCells(); i++)
{
// compute tangent and line normal of the line in the ith cell
vtkCell* cell = surface->GetOutput()->GetCell(i);
double p0[3], p1[3];
surface->GetOutput()->GetPoint(cell->GetPointId(0), p0);
surface->GetOutput()->GetPoint(cell->GetPointId(1), p1);
double normal[3], tangent[3];
normal[0] = p1[1] - p0[1];
normal[1] = -(p1[0] - p0[0]);
normal[2] = 0;
double norm = vtkMath::Norm(normal);
if (norm == 0)
continue;
tangent[0] = p1[0] - p0[0];
tangent[1] = p1[1] - p0[1];
tangent[2] = 0;
// makse sure that the line normal points inward
double offset[3], shiftedPoint[3];
vtkMath::Assign(normal, offset);
vtkMath::MultiplyScalar(offset, 0.1);
vtkMath::Subtract(p0, offset, shiftedPoint);
if (cellLocator->FindCell(shiftedPoint) == -1)
{
vtkMath::Subtract(p1, offset, shiftedPoint);
if (cellLocator->FindCell(shiftedPoint) == -1)
{
normal[0] = -normal[0];
normal[1] = -normal[1];
}
}
// get vectors at the two end points of the line
double vector0[3], vector0Normalized[3];
surface->GetOutput()
->GetPointData()
->GetArray(vectors->GetName())
->GetTuple(cell->GetPointId(0), vector0);
double vector0Norm = vtkMath::Norm(vector0);
vtkMath::Assign(vector0, vector0Normalized);
vtkMath::MultiplyScalar(vector0Normalized, 1 / vector0Norm);
double vector1[3], vector1Normalized[3];
surface->GetOutput()
->GetPointData()
->GetArray(vectors->GetName())
->GetTuple(cell->GetPointId(1), vector1);
double vector1Norm = vtkMath::Norm(vector1);
vtkMath::Assign(vector1, vector1Normalized);
vtkMath::MultiplyScalar(vector1Normalized, 1 / vector1Norm);
// find the location of boundary switch point using the inverse of linear interpolate function.
double x, y, vn0, vn1, point[3], vector[3];
vn0 = vtkMath::Dot(vector0, normal);
vn1 = vtkMath::Dot(vector1, normal);
y = vn0 - vn1;
// when vn0 == 0 or vn1 == 0, the vectors are parallel to the boundary
// when vn0 * vn1 > 0, both of the vectors are neither inflow nor outflow.
if (vn0 * vn1 >= 0)
continue;
x = vn0 / y;
// if the location is inbwteen the two end points of the line
if (x > 0 && x < 1)
{
InterpolateVector(0, 1, x, vector0, vector1, vector);
double vectorNorm = vtkMath::Norm(vector);
// if the verctor at the boundary switch point is not a zero vector
if (vectorNorm > 1e-16)
{
vtkMath::MultiplyScalar(vector, 1 / vectorNorm);
double cosTheta = vtkMath::Dot(vector0Normalized, vector1Normalized);
if (fabs(cosTheta) <= this->VectorAngleThreshold)
{
// inflow boundary switch point
if ((vtkMath::Dot(vector, tangent) > 0 && vn1 < 0) ||
(vtkMath::Dot(vector, tangent) < 0 && vn0 < 0))
{
InterpolateVector(0, 1, x, p0, p1, point);
boundarySwitchPoints->GetPoints()->InsertNextPoint(point);
BoundarySwitchTypeArray->SetTuple1(numPoint, 0);
vtkNew<vtkVertex> vertex;
vertex->GetPointIds()->SetId(0, boundarySwitchPoints->GetNumberOfPoints() - 1);
boundarySwitchPoints->GetVerts()->InsertNextCell(vertex);
}
// outflow boundary switch point
else if ((vtkMath::Dot(vector, tangent) > 0 && vn1 > 0) ||
(vtkMath::Dot(vector, tangent) < 0 && vn0 > 0))
{
InterpolateVector(0, 1, x, p0, p1, point);
boundarySwitchPoints->GetPoints()->InsertNextPoint(point);
BoundarySwitchTypeArray->SetTuple1(numPoint, 1);
vtkNew<vtkVertex> vertex;
vertex->GetPointIds()->SetId(0, boundarySwitchPoints->GetNumberOfPoints() - 1);
boundarySwitchPoints->GetVerts()->InsertNextCell(vertex);
}
else
continue;
BoundarySwitchPointVector->SetTuple3(numPoint, vector[0], vector[1], vector[2]);
BoundarySwitchPointNormal->SetTuple3(numPoint, normal[0], normal[1], normal[2]);
numPoint++;
}
}
}
}
BoundarySwitchTypeArray->SetNumberOfTuples(numPoint);
BoundarySwitchPointVector->SetNumberOfTuples(numPoint);
BoundarySwitchPointNormal->SetNumberOfTuples(numPoint);
return 1;
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ComputeSurface(int numberOfSeparatingSurfaces, bool isBackward,
double normal[3], double zeroPos[3], vtkPolyData* streamSurfaces, vtkDataSet* dataset,
int vtkNotUsed(integrationStepUnit), double dist, double vtkNotUsed(stepSize), int maxNumSteps,
bool useIterativeSeeding)
{
// generate circle and add first point again in the back to avoid gap
vtkNew<vtkRegularPolygonSource> circle;
circle->GeneratePolygonOff();
circle->SetNumberOfSides(8);
circle->SetRadius(dist);
circle->SetCenter(zeroPos);
circle->SetNormal(normal);
circle->Update();
// close circle exactly with a point instead of an edge to correctly treat points exiting the
// boundary
circle->GetOutput()->GetPoints()->InsertNextPoint(circle->GetOutput()->GetPoint(0));
vtkNew<vtkPolyData> currentCircle;
currentCircle->SetPoints(circle->GetOutput()->GetPoints());
// vtkNew<vtkDoubleArray> integrationTimeArray;
// integrationTimeArray->SetName("IntegrationTime");
// currentCircle->GetPointData()->AddArray(integrationTimeArray);
// for (int i = 0; i < currentCircle->GetNumberOfPoints(); ++i)
// {
// integrationTimeArray->InsertNextTuple1(0);
// }
this->StreamSurface->SetInputData(0, dataset);
this->StreamSurface->SetInputData(1, currentCircle);
this->StreamSurface->SetUseIterativeSeeding(useIterativeSeeding);
this->StreamSurface->SetIntegratorTypeToRungeKutta4();
this->StreamSurface->SetIntegrationStepUnit(this->IntegrationStepUnit);
this->StreamSurface->SetInitialIntegrationStep(this->IntegrationStepSize);
this->StreamSurface->SetIntegrationDirection(isBackward);
this->StreamSurface->SetComputeVorticity(false);
this->StreamSurface->SetMaximumNumberOfSteps(maxNumSteps);
this->StreamSurface->SetSourceData(currentCircle);
this->StreamSurface->SetMaximumPropagation(dist * maxNumSteps);
this->StreamSurface->SetInputArrayToProcess(
0, 0, 0, vtkDataObject::FIELD_ASSOCIATION_POINTS, this->NameOfVectorArray);
this->StreamSurface->Update();
vtkNew<vtkDoubleArray> indexArray;
indexArray->SetName("index");
indexArray->SetNumberOfTuples(StreamSurface->GetOutput()->GetNumberOfPoints());
indexArray->Fill(numberOfSeparatingSurfaces);
StreamSurface->GetOutput()->GetPointData()->AddArray(indexArray);
// add current surface to existing surfaces
vtkNew<vtkAppendPolyData> appendSurfaces;
appendSurfaces->AddInputData(this->StreamSurface->GetOutput());
appendSurfaces->AddInputData(streamSurfaces);
appendSurfaces->Update();
streamSurfaces->DeepCopy(appendSurfaces->GetOutput());
this->StreamSurface->SetInputData(0, nullptr);
this->StreamSurface->SetInputData(1, nullptr);
return (streamSurfaces != nullptr);
}
//----------------------------------------------------------------------------
int vtkVectorFieldTopology::ComputeSeparatricesBoundarySwitchPoints(
vtkPolyData* boundarySwitchPoints, vtkPolyData* separatrices, vtkDataSet* dataset,
vtkPoints* interestPoints, int integrationStepUnit, double dist, int maxNumSteps)
{
double offsetAwayFromBoundary = this->OffsetAwayFromBoundary;
if (integrationStepUnit == vtkStreamTracer::CELL_LENGTH_UNIT)
{
dist *= sqrt(static_cast<double>(dataset->GetCell(0)->GetLength2()));
offsetAwayFromBoundary *= sqrt(static_cast<double>(dataset->GetCell(0)->GetLength2()));
}
vtkNew<vtkStreamTracer> streamTracer;
streamTracer->SetInputData(dataset);
streamTracer->SetIntegratorTypeToRungeKutta4();
streamTracer->SetIntegrationStepUnit(this->IntegrationStepUnit);
streamTracer->SetInitialIntegrationStep(this->IntegrationStepSize);
streamTracer->SetComputeVorticity(false);
streamTracer->SetMaximumNumberOfSteps(maxNumSteps);
streamTracer->SetMaximumPropagation(dist * maxNumSteps);
streamTracer->SetTerminalSpeed(epsilon);
streamTracer->SetInputArrayToProcess(
0, 0, 0, vtkDataObject::FIELD_ASSOCIATION_POINTS, this->NameOfVectorArray);
streamTracer->SetInterpolatorType(this->InterpolatorType);
int numberOfSeparatingLines = 0;
for (int i = 0; i < boundarySwitchPoints->GetNumberOfPoints(); i++)
{
if (boundarySwitchPoints->GetPointData()->GetArray("BoundarySwitchType")->GetTuple1(i) == 1)
continue;
double point[3], vector[3], normal[3];
boundarySwitchPoints->GetPoint(i, point);
boundarySwitchPoints->GetPointData()->GetArray("Vector")->GetTuple(i, vector);
boundarySwitchPoints->GetPointData()->GetArray("Normal")->GetTuple(i, normal);
double normalNorm = vtkMath::Norm(normal);
vtkMath::MultiplyScalar(normal, offsetAwayFromBoundary / normalNorm);
double vectorNorm = vtkMath::Norm(vector);
vtkMath::MultiplyScalar(vector, 1 / vectorNorm);
for (int k = 0; k < 2; k++)
{
// insert seed with small offset
vtkNew<vtkPolyData> seeds;
vtkNew<vtkPoints> seedPoints;
vtkNew<vtkCellArray> seedCells;
seeds->SetPoints(seedPoints);
seeds->SetVerts(seedCells);
int sign = pow(-1, k);
double offset[3], shiftedPoint[3], shiftedPoint1[3];
vtkMath::Assign(vector, offset);
vtkMath::MultiplyScalar(offset, sign * dist);
vtkMath::Add(point, offset, shiftedPoint);
vtkMath::Subtract(shiftedPoint, normal, shiftedPoint1);
seedPoints->InsertNextPoint(shiftedPoint1);
vtkNew<vtkVertex> vertex;
vertex->GetPointIds()->SetId(0, seedPoints->GetNumberOfPoints() - 1);
seedCells->InsertNextCell(vertex);
// integrate
if (k == 0)
streamTracer->SetIntegrationDirection(false);
else
streamTracer->SetIntegrationDirection(true);
streamTracer->SetSourceData(seeds);
streamTracer->Update();
if (streamTracer->GetOutput()->GetNumberOfPoints() > 0)
{
// close gap to the boundary switch point at the beginning
streamTracer->GetOutput()->GetPoints()->InsertNextPoint(boundarySwitchPoints->GetPoint(i));
for (int j = 0; j < streamTracer->GetOutput()->GetPointData()->GetNumberOfArrays(); j++)
{
streamTracer->GetOutput()->GetPointData()->GetArray(j)->InsertNextTuple(
streamTracer->GetOutput()->GetPointData()->GetArray(j)->GetTuple(0));
}
// this polyline with the 2 new points will replace the old polyline
vtkSmartPointer<vtkPolyLine> polyLine = vtkSmartPointer<vtkPolyLine>::New();
polyLine->GetPointIds()->SetNumberOfIds(streamTracer->GetOutput()->GetNumberOfPoints());
polyLine->GetPointIds()->SetId(0, streamTracer->GetOutput()->GetNumberOfPoints() - 1);
for (int l = 1; l < streamTracer->GetOutput()->GetNumberOfPoints(); l++)
{
polyLine->GetPointIds()->SetId(l, l - 1);
}
// close gap to the boundary switch point at the end
int closestBoundarySwitchPointToEnd = 0;
double closestDistance[3];
vtkMath::Subtract(
streamTracer->GetOutput()->GetPoint(streamTracer->GetOutput()->GetNumberOfPoints() - 2),
interestPoints->GetPoint(closestBoundarySwitchPointToEnd), closestDistance);
double currentDistance[3];
// find closest BoundarySwitch point to endpoint
for (int j = 0; j < interestPoints->GetNumberOfPoints(); j++)
{
vtkMath::Subtract(
streamTracer->GetOutput()->GetPoint(streamTracer->GetOutput()->GetNumberOfPoints() - 2),
interestPoints->GetPoint(j), currentDistance);
if (vtkMath::Norm(currentDistance) < vtkMath::Norm(closestDistance))
{
closestBoundarySwitchPointToEnd = j;
for (int d = 0; d < 3; d++)
{
closestDistance[d] = currentDistance[d];
}
}
}
if (vtkMath::Norm(closestDistance) < dist)
{
// find closest point on streamline to that Boundary Switch point to avoid self
// intersection
int firstClosePointToBoundarySwitchPoint = 0;
for (int j = 0; j < streamTracer->GetOutput()->GetNumberOfPoints(); j++)
{
vtkMath::Subtract(streamTracer->GetOutput()->GetPoint(j),
interestPoints->GetPoint(closestBoundarySwitchPointToEnd), currentDistance);
if (vtkMath::Norm(currentDistance) < dist)
{
firstClosePointToBoundarySwitchPoint = j;
for (int d = 0; d < 3; d++)
{
closestDistance[d] = currentDistance[d];
}
break;
}
}
// insert new point
streamTracer->GetOutput()->GetPoints()->InsertNextPoint(
interestPoints->GetPoint(closestBoundarySwitchPointToEnd));
for (int j = 0; j < streamTracer->GetOutput()->GetPointData()->GetNumberOfArrays(); j++)
{
streamTracer->GetOutput()->GetPointData()->GetArray(j)->InsertNextTuple(
streamTracer->GetOutput()->GetPointData()->GetArray(j)->GetTuple(0));
}
// remove superfluous lines in the tail and connect to Boundary Switch point instead
polyLine->GetPointIds()->SetNumberOfIds(firstClosePointToBoundarySwitchPoint + 2);
polyLine->GetPointIds()->SetId(firstClosePointToBoundarySwitchPoint + 1,
streamTracer->GetOutput()->GetNumberOfPoints() - 1);
}
vtkSmartPointer<vtkCellArray> cells = vtkSmartPointer<vtkCellArray>::New();
cells->InsertNextCell(polyLine);
streamTracer->GetOutput()->SetLines(cells);
// fill arrays
vtkNew<vtkDoubleArray> iterationArray;
iterationArray->SetName("iteration");
iterationArray->SetNumberOfTuples(streamTracer->GetOutput()->GetNumberOfPoints());
streamTracer->GetOutput()->GetPointData()->AddArray(iterationArray);
vtkNew<vtkDoubleArray> indexArray;
indexArray->SetName("index");
indexArray->SetNumberOfTuples(streamTracer->GetOutput()->GetNumberOfPoints());
streamTracer->GetOutput()->GetPointData()->AddArray(indexArray);
for (int j = 0; j < streamTracer->GetOutput()->GetNumberOfPoints(); j++)
{
iterationArray->SetTuple1(j, j + 1);
indexArray->SetTuple1(j, numberOfSeparatingLines);
}
// iterationArray->SetTuple1(streamTracer->GetOutput()->GetNumberOfPoints() - 1, 0);
// the inserted points will get iteration 0
iterationArray->SetTuple1(streamTracer->GetOutput()->GetNumberOfPoints() - 1, 0);
if (vtkMath::Norm(closestDistance) < dist)
{
iterationArray->SetTuple1(streamTracer->GetOutput()->GetNumberOfPoints() - 2, 0);
}
// combine lines of this separatrix with existing ones
vtkNew<vtkAppendPolyData> appendFilter;
appendFilter->AddInputData(separatrices);
appendFilter->AddInputData(streamTracer->GetOutput());
appendFilter->Update();
separatrices->DeepCopy(appendFilter->GetOutput());
numberOfSeparatingLines++;
}
}
}
return 1;
}
int vtkVectorFieldTopology::ComputeSeparatricesBoundarySwitchLines(vtkPolyData* boundarySwitchLines,
vtkPolyData* separatrices, vtkDataSet* dataset, int integrationStepUnit, double dist,
int maxNumSteps, bool computeSurfaces, bool useIterativeSeeding)
{
double offsetAwayFromBoundary = this->OffsetAwayFromBoundary;
if (integrationStepUnit == vtkStreamTracer::CELL_LENGTH_UNIT)
{
dist *= sqrt(static_cast<double>(dataset->GetCell(0)->GetLength2()));
offsetAwayFromBoundary *= sqrt(static_cast<double>(dataset->GetCell(0)->GetLength2()));
}
vtkDataArray* vectors = dataset->GetPointData()->GetArray(this->NameOfVectorArray);
vtkNew<vtkGeometryFilter> geometry;
geometry->SetInputData(dataset);
geometry->Update();
vtkNew<vtkDataSetSurfaceFilter> surface;
surface->SetInputData(geometry->GetOutput());
surface->Update();
vtkNew<vtkDoubleArray> normals;
normals->SetNumberOfComponents(3);
normals->SetName("Normals");
normals->SetNumberOfTuples(dataset->GetNumberOfCells());
surface->GetOutput()->GetCellData()->AddArray(normals);
vtkNew<vtkDoubleArray> scalarProduct;
scalarProduct->SetNumberOfComponents(1);
scalarProduct->SetName("ScalarProduct");
scalarProduct->SetNumberOfTuples(dataset->GetNumberOfPoints());
surface->GetOutput()->GetPointData()->AddArray(scalarProduct);
// compute surface normals and store them as cell data
for (int i = 0; i < surface->GetOutput()->GetNumberOfCells(); i++)
{
vtkCell* cell = surface->GetOutput()->GetCell(i);
if (cell->GetNumberOfPoints() < 3)
vtkErrorMacro(
"vtkVectorFieldTopology::ComputeBoundarySwitchLines: the number of points in a cell is "
"less then 3. This cell should represent a 2D surface and should have at least 3 points");
double p0[3], p1[3], p2[3];
surface->GetOutput()->GetPoint(cell->GetPointId(0), p0);
surface->GetOutput()->GetPoint(cell->GetPointId(1), p1);
surface->GetOutput()->GetPoint(cell->GetPointId(2), p2);
double t0[3], t1[3];
vtkMath::Subtract(p1, p0, t0);
vtkMath::Subtract(p2, p0, t1);
double n[3];