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CurvatureBandsWithGlyphs

Repository source: CurvatureBandsWithGlyphs

Description

In this example we are coloring the surface by partitioning the gaussian curvature into bands and using arrows to display the normals on the surface.

Rather beautiful surfaces are generated.

The banded contour filter and an indexed lookup table are used to generate the curvature bands on the surface. To further enhance the surface, the surface normals are glyphed and colored by elevation using a diverging lookup table.

Note that:

  • If the regions on a surface have zero Gaussian curvature, then they can be flattened into a plane with no distortion, and the geometry of the region is Euclidean geometry.

  • If the regions on a surface have positive Gaussian curvature, then the geometry of the surface is spherical geometry.

  • If the regions on the surface have a negative Gaussian curvature, then the geometry of the surface is hyperbolic geometry.

In the above image you can see that the random hills incorporate all of these geometries.

The surface selected is the parametric random hills surface. The problem with the random hills surface is:

  • Most of the gaussian curvatures will lie in the range -1 to 0.2 (say) with a few large values say 20 to 40 at the peaks of the hills.
  • The edges of the random hills surface also have large irregular values so we need to handle these also. In order to fix this, a function is provided to adjust the edges.

So we need to manually generate custom bands to group the curvatures. The bands selected in the examples show that the surface is mostly planar with some hyperbolic regions (saddle points) and some spherical regions.

Feel free to experiment with different color schemes and/or the other sources from the parametric function group or the torus etc.

You will usually need to adjust the parameters for maskPts, arrow and glyph for a nice appearance.

A histogram of the frequencies is also output to the console. This is useful if you want to get an idea of the distribution of the scalars in each band.

Other languages

See (Python)

Question

If you have a question about this example, please use the VTK Discourse Forum

Code

CurvatureBandsWithGlyphs.cxx

#include <vtkActor.h>
#include <vtkArrowSource.h>
#include <vtkBandedPolyDataContourFilter.h>
#include <vtkCamera.h>
#include <vtkCleanPolyData.h>
#include <vtkColorSeries.h>
#include <vtkColorTransferFunction.h>
#include <vtkCurvatures.h>
#include <vtkDelaunay2D.h>
#include <vtkDoubleArray.h>
#include <vtkElevationFilter.h>
#include <vtkFeatureEdges.h>
#include <vtkFloatArray.h>
#include <vtkGlyph3D.h>
#include <vtkIdList.h>
#include <vtkInteractorStyleTrackballCamera.h>
#include <vtkLookupTable.h>
#include <vtkMaskPoints.h>
#include <vtkNamedColors.h>
#include <vtkNew.h>
#include <vtkParametricFunctionSource.h>
#include <vtkParametricRandomHills.h>
#include <vtkParametricTorus.h>
#include <vtkPlaneSource.h>
#include <vtkPointData.h>
#include <vtkPolyData.h>
#include <vtkPolyDataMapper.h>
#include <vtkPolyDataNormals.h>
#include <vtkProperty.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkRenderer.h>
#include <vtkReverseSense.h>
#include <vtkScalarBarActor.h>
#include <vtkSmartPointer.h>
#include <vtkSphereSource.h>
#include <vtkSuperquadricSource.h>
#include <vtkTextProperty.h>
#include <vtkTransform.h>
#include <vtkTransformPolyDataFilter.h>
#include <vtkTriangleFilter.h>
#include <vtkVariant.h>
#include <vtkVariantArray.h>
#include <vtkVersion.h>

#if VTK_VERSION_NUMBER >= 90020210809ULL
#define HAS_COW
#include <vtkCameraOrientationWidget.h>
#endif

// vtkGenerateIds was introduced in VTK build version 20240504
#if VTK_BUILD_VERSION >= 20240504
#define USE_USE_GENERATE_IDS
#include <vtkGenerateIds.h>
#else
#include <vtkIdFilter.h>
#endif

#include <algorithm>
#include <array>
#include <cctype>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <numeric>
#include <set>
#include <sstream>
#include <string>
#include <vector>

namespace {

//! Adjust curvatures along the edges of the surface.
/*!
 * This function adjusts curvatures along the edges of the surface by replacing
 *  the value with the average value of the curvatures of points in the
 *  neighborhood.
 *
 * Remember to update the vtkCurvatures object before calling this.
 *
 * @param source - A vtkPolyData object corresponding to the vtkCurvatures
 * object.
 * @param curvatureName: The name of the curvature, "Gauss_Curvature" or
 * "Mean_Curvature".
 * @param epsilon: Curvature values less than this will be set to zero.
 * @return
 */
void AdjustEdgeCurvatures(vtkPolyData* source, std::string const& curvatureName,
                          double const& epsilon = 1.0e-08);

//! Constrain curvatures to the range [lower_bound ... upper_bound].
/*!
 * Remember to update the vtkCurvatures object before calling this.
 *
 * @param source - A vtkPolyData object corresponding to the vtkCurvatures
 * object.
 * @param curvatureName: The name of the curvature, "Gauss_Curvature" or
 * "Mean_Curvature".
 * @param lowerBound: The lower bound.
 * @param upperBound: The upper bound.
 * @return
 */
void ConstrainCurvatures(vtkPolyData* source, std::string const& curvatureName,
                         double const& lowerBound = 0.0,
                         double const& upperBound = 0.0);

//! Generate elevations over the surface.
/*!
@param src - the vtkPolyData source.
@return elev - the elevations.
*/
vtkSmartPointer<vtkPolyData> GetElevations(vtkPolyData* src);

vtkSmartPointer<vtkPolyData> GetHills();
vtkSmartPointer<vtkPolyData> GetParametricHills();
vtkSmartPointer<vtkPolyData> GetParametricTorus();
vtkSmartPointer<vtkPolyData> GetPlane();
vtkSmartPointer<vtkPolyData> GetSphere();
vtkSmartPointer<vtkPolyData> GetTorus();
vtkSmartPointer<vtkPolyData> GetSource(std::string const& source);

vtkSmartPointer<vtkColorSeries> GetColorSeries();

vtkSmartPointer<vtkLookupTable> GetCategoricalLUT();

vtkSmartPointer<vtkLookupTable> GetOrdinaLUT();

vtkSmartPointer<vtkLookupTable> GetDivergingLUT();

vtkSmartPointer<vtkLookupTable> ReverseLUT(vtkLookupTable* lut);

//!  Glyph the normals on the surface.
/*!
@param src - the vtkPolyData source.
#param scaleFactor - the scale factor for the glyphs.
@param reverseNormals - if True the normals on the surface are reversed.
@return The glyphs.
*/
vtkNew<vtkGlyph3D> GetGlyphs(vtkPolyData* src, double const& scaleFactor = 1.0,
                             bool const& reverseNormals = false);

std::map<int, std::vector<double>> GetBands(double const dR[2],
                                            int const& numberOfBands,
                                            int const& precision = 2,
                                            bool const& nearestInteger = false);

//! Divide a range into custom bands
/*!
You need to specify each band as an array [r1, r2] where r1 < r2 and
append these to a vector.
The vector should ultimately look
like this: [[r1, r2], [r2, r3], [r3, r4]...]

@param dR - [min, max] the range that is to be covered by the bands.
@param numberOfBands - the number of bands, a positive integer.
@param myBands - the bands.
@return  A map consisting of the band inxex and [min, midpoint, max] for each
band.
*/
std::map<int, std::vector<double>>
GetCustomBands(double const dR[2], int const& numberOfBands,
               std::vector<std::array<double, 2>> const& myBands);

//! Divide a range into integral bands
/*!
Divide a range into bands
@param dR - [min, max] the range that is to be covered by the bands.
@returnA map consisting of the band inxex and [min, midpoint, max] for each
band.
*/
std::map<int, std::vector<double>> GetIntegralBands(double const dR[2]);

//! Count the number of scalars in each band.
/*
 * The scalars used are the active scalars in the polydata.
 *
 * @param bands - the bands.
 * @param src - the vtkPolyData source.
 * @return The frequencies of the scalars in each band.
 */
std::map<int, int> GetFrequencies(std::map<int, std::vector<double>>& bands,
                                  vtkPolyData* src);
//!
/*
 * The bands and frequencies are adjusted so that the first and last
 *  frequencies in the range are non-zero.
 * @param bands: The bands.
 * @param freq: The frequencies.
 */
void AdjustFrequencyRanges(std::map<int, std::vector<double>>& bands,
                           std::map<int, int>& freq);

void PrintBandsFrequencies(std::map<int, std::vector<double>> const& bands,
                           std::map<int, int>& freq, int const& precision = 2);

} // namespace

int main(int, char*[])
{
  // Get the surface
  std::string desiredSurface{"RandomHills"};
  // desiredSurface = "Hills";
  // desiredSurface = "ParametricTorus";
  // desiredSurface = "Plane";
  // desiredSurface = "RandomHills";
  // desiredSurface = "Sphere";
  // desiredSurface = "Torus";
  auto source = GetSource(desiredSurface);

  // The length of the normal arrow glyphs.
  auto scaleFactor = 1.0;
  if (desiredSurface == "Hills")
  {
    scaleFactor = 0.5;
  }
  if (desiredSurface == "Sphere")
  {
    scaleFactor = 2.0;
  }
  std::cout << desiredSurface << std::endl;

  // Set this to false if you want mean curvatures.
  auto gaussianCurvature = true;
  std::string curvature =
      (gaussianCurvature) ? "Gauss_Curvature" : "Mean_Curvature";

  vtkNew<vtkCurvatures> cc;
  cc->SetInputData(source);
  std::vector<std::string> needsAdjusting{"Hills", "ParametricTorus", "Plane",
                                          "RandomHills", "Torus"};
  if (gaussianCurvature)
  {
    cc->SetCurvatureTypeToGaussian();
    cc->Update();
    if (std::find(needsAdjusting.begin(), needsAdjusting.end(),
                  desiredSurface) != needsAdjusting.end())
    {
      AdjustEdgeCurvatures(cc->GetOutput(), curvature);
    }
    if (desiredSurface == "Plane")
    {
      ConstrainCurvatures(cc->GetOutput(), curvature, 0.0, 0.0);
    }
    if (desiredSurface == "Sphere")
    {

      // Gaussian curvature is 1/r^2
      ConstrainCurvatures(cc->GetOutput(), curvature, 4.0, 4.0);
    }
  }
  else
  {

    cc->SetCurvatureTypeToMean();
    cc->Update();
    if (std::find(needsAdjusting.begin(), needsAdjusting.end(),
                  desiredSurface) != needsAdjusting.end())
    {
      AdjustEdgeCurvatures(cc->GetOutput(), curvature);
    }
    if (desiredSurface == "Plane")
    {
      ConstrainCurvatures(cc->GetOutput(), curvature, 0.0, 0.0);
    }
    if (desiredSurface == "Sphere")
    {

      // Mean curvature is 1/r
      ConstrainCurvatures(cc->GetOutput(), curvature, 2.0, 2.0);
    }
  }

  cc->GetOutput()->GetPointData()->SetActiveScalars(curvature.c_str());
  auto scalarRangeCurvatures = cc->GetOutput()
                                   ->GetPointData()
                                   ->GetScalars(curvature.c_str())
                                   ->GetRange();
  auto scalarRangeElevation =
      cc->GetOutput()->GetPointData()->GetScalars("Elevation")->GetRange();

  auto lut = GetCategoricalLUT();
  auto lut1 = GetDivergingLUT();
  lut->SetTableRange(scalarRangeCurvatures);
  lut1->SetTableRange(scalarRangeElevation);
  auto numberOfBands = lut->GetNumberOfTableValues();
  auto precision = 10;
  auto bands = GetBands(scalarRangeCurvatures, numberOfBands, precision, false);

  if (desiredSurface == "RandomHills")
  {
    // These are my custom bands.
    // Generated by first running:
    // bands = GetBands(scalarRangeCurvatures, numberOfBands, precision, false);
    // then:
    //  std::vector<int> freq = Frequencies(bands, src);
    //  PrintBandsFrequencies(bands, freq);
    // Finally using the output to create this table:
    // std::vector<std::array<double, 2>> myBands = {
    //    {-0.630, -0.190},  {-0.190, -0.043}, {-0.043, -0.0136},
    //    {-0.0136, 0.0158}, {0.0158, 0.0452}, {0.0452, 0.0746},12
    //    {0.0746, 0.104},   {0.104, 0.251},   {0.251, 1.131}};
    //  This demonstrates that the gaussian curvature of the surface
    //   is mostly planar with some hyperbolic regions (saddle points)
    //   and some spherical regions.
    std::vector<std::array<double, 2>> myBands = {
        {-0.630, -0.190}, {-0.190, -0.043}, {-0.043, 0.0452}, {0.0452, 0.0746},
        {0.0746, 0.104},  {0.104, 0.251},   {0.251, 1.131}};

    // Comment this out if you want to see how allocating
    // equally spaced bands works.
    bands = GetCustomBands(scalarRangeCurvatures, numberOfBands, myBands);
    // Adjust the number of table values
    lut->SetNumberOfTableValues(static_cast<vtkIdType>(bands.size()));
  }
  else if (desiredSurface == "Hills")
  {
    std::vector<std::array<double, 2>> myBands = {
        {-2.104, -0.15},   {-0.15, -0.1},   {-0.1, -0.05},
        {-0.05, -0.02},    {-0.02, -0.005}, {-0.005, -0.0005},
        {-0.0005, 0.0005}, {0.0005, 0.09},  {0.09, 4.972},
    };

    // Comment this out if you want to see how allocating
    // equally spaced bands works.
    bands = GetCustomBands(scalarRangeCurvatures, numberOfBands, myBands);
    // Adjust the number of table values
    lut->SetNumberOfTableValues(static_cast<vtkIdType>(bands.size()));
  }

  // Let's do a frequency table.
  auto freq = GetFrequencies(bands, cc->GetOutput());
  AdjustFrequencyRanges(bands, freq);
  PrintBandsFrequencies(bands, freq);

  scalarRangeCurvatures[0] = bands.begin()->second[0];
  scalarRangeCurvatures[1] = std::prev(bands.end())->second[2];
  lut->SetTableRange(scalarRangeCurvatures);
  lut->SetNumberOfTableValues(bands.size());

  // We will use the midpoint of the band as the label.
  std::vector<std::string> labels;
  for (std::map<int, std::vector<double>>::const_iterator p = bands.begin();
       p != bands.end(); ++p)
  {
    std::ostringstream os;
    os << std::fixed << std::setw(6) << std::setprecision(2) << p->second[1];
    labels.push_back(os.str());
  }

  // Annotate
  vtkNew<vtkVariantArray> values;
  for (size_t i = 0; i < labels.size(); ++i)
  {
    values->InsertNextValue(vtkVariant(labels[i]));
  }
  for (vtkIdType i = 0; i < values->GetNumberOfTuples(); ++i)
  {
    lut->SetAnnotation(i, values->GetValue(i).ToString());
  }

  // Create a lookup table with the colors reversed.
  auto lutr = ReverseLUT(lut);

  // Create the contour bands.
  vtkNew<vtkBandedPolyDataContourFilter> bcf;
  bcf->SetInputData(cc->GetOutput());
  // Use either the minimum or maximum value for each band.
  int i = 0;
  for (std::map<int, std::vector<double>>::const_iterator p = bands.begin();
       p != bands.end(); ++p)
  {
    bcf->SetValue(i, p->second[2]);
    ++i;
  }
  // We will use an indexed lookup table.
  bcf->SetScalarModeToIndex();
  bcf->GenerateContourEdgesOn();

  // Generate the glyphs on the original surface.

  auto glyph = GetGlyphs(cc->GetOutput(), scaleFactor, false);

  // ------------------------------------------------------------
  // Create the mappers and actors
  // ------------------------------------------------------------
  vtkNew<vtkNamedColors> colors;

  // Set the background color.
  colors->SetColor("BkgColor",
                   std::array<unsigned char, 4>{179, 204, 255, 255}.data());
  colors->SetColor("ParaViewBkg",
                   std::array<unsigned char, 4>{82, 87, 110, 255}.data());

  vtkNew<vtkPolyDataMapper> srcMapper;
  srcMapper->SetInputConnection(bcf->GetOutputPort());
  srcMapper->SetScalarRange(scalarRangeCurvatures);
  srcMapper->SetLookupTable(lut);
  srcMapper->SetScalarModeToUseCellData();

  vtkNew<vtkActor> srcActor;
  srcActor->SetMapper(srcMapper);

  // Create contour edges
  vtkNew<vtkPolyDataMapper> edgeMapper;
  edgeMapper->SetInputData(bcf->GetContourEdgesOutput());
  edgeMapper->SetResolveCoincidentTopologyToPolygonOffset();

  vtkNew<vtkActor> edgeActor;
  edgeActor->SetMapper(edgeMapper);
  edgeActor->GetProperty()->SetColor(colors->GetColor3d("Black").GetData());

  vtkNew<vtkPolyDataMapper> glyphMapper;
  glyphMapper->SetInputConnection(glyph->GetOutputPort());
  glyphMapper->SetScalarModeToUsePointFieldData();
  glyphMapper->SetColorModeToMapScalars();
  glyphMapper->ScalarVisibilityOn();
  glyphMapper->SelectColorArray("Elevation");
  // Colour by scalars.
  glyphMapper->SetLookupTable(lut1);
  glyphMapper->SetScalarRange(scalarRangeElevation);

  vtkNew<vtkActor> glyphActor;
  glyphActor->SetMapper(glyphMapper);

  auto windowWidth = 800;
  auto windowHeight = 800;

  // Add scalar bars.
  auto curvatureType = curvature;
  std::replace(curvatureType.begin(), curvatureType.end(), '_', '\n');

  vtkNew<vtkScalarBarActor> scalarBar;
  // This LUT puts the lowest value at the top of the scalar bar.
  // scalarBar->SetLookupTable(lut);
  // Use this LUT if you want the highest value at the top.
  scalarBar->SetLookupTable(lutr);
  scalarBar->SetTitle(curvatureType.c_str());
  scalarBar->GetTitleTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBar->GetLabelTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBar->GetAnnotationTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBar->UnconstrainedFontSizeOn();
  scalarBar->SetMaximumWidthInPixels(windowWidth / 8);
  scalarBar->SetMaximumHeightInPixels(windowHeight / 3);
  scalarBar->SetPosition(0.85, 0.05);

  vtkNew<vtkScalarBarActor> scalarBarElev;
  scalarBarElev->SetLookupTable(lut1);
  scalarBarElev->SetTitle("Elevation");
  scalarBarElev->GetTitleTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBarElev->GetLabelTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBarElev->GetAnnotationTextProperty()->SetColor(
      colors->GetColor3d("AliceBlue").GetData());
  scalarBarElev->UnconstrainedFontSizeOn();
  if (desiredSurface == "Plane")
  {
    scalarBarElev->SetNumberOfLabels(1);
  }
  else
  {
    scalarBarElev->SetNumberOfLabels(5);
  }
  scalarBarElev->SetMaximumWidthInPixels(windowWidth / 8);
  scalarBarElev->SetMaximumHeightInPixels(windowHeight / 3);
  // scalarBarElev->SetBarRatio(scalarBarElev->GetBarRatio() * 0.5);
  scalarBarElev->SetPosition(0.85, 0.4);

  // ------------------------------------------------------------
  // Create the RenderWindow, Renderer and Interactor
  // ------------------------------------------------------------
  vtkNew<vtkRenderer> ren;
  vtkNew<vtkRenderWindow> renWin;
  vtkNew<vtkRenderWindowInteractor> iren;
  vtkNew<vtkInteractorStyleTrackballCamera> style;
  iren->SetInteractorStyle(style);

  renWin->AddRenderer(ren);
  // Important: The interactor must be set prior to enabling the widget.
  iren->SetRenderWindow(renWin);
#ifdef HAS_COW
  vtkNew<vtkCameraOrientationWidget> camOrientManipulator;
  camOrientManipulator->SetParentRenderer(ren);
  // Enable the widget.
  camOrientManipulator->On();
#endif

  // add actors
  ren->AddViewProp(srcActor);
  ren->AddViewProp(edgeActor);
  ren->AddViewProp(glyphActor);
  ren->AddActor2D(scalarBar);
  ren->AddActor2D(scalarBarElev);

  ren->SetBackground(colors->GetColor3d("ParaViewBkg").GetData());
  renWin->SetSize(windowWidth, windowHeight);
  renWin->SetWindowName("CurvatureBandsWithGlyphs");

  if (desiredSurface == "RandomHills")
  {
    auto camera = ren->GetActiveCamera();
    camera->SetPosition(10.9299, 59.1505, 24.9823);
    camera->SetFocalPoint(2.21692, 7.97545, 7.75135);
    camera->SetViewUp(-0.230136, 0.345504, -0.909761);
    camera->SetDistance(54.6966);
    camera->SetClippingRange(36.3006, 77.9852);
    renWin->Render();
  }

  iren->Start();

  return EXIT_SUCCESS;
}

namespace {

void AdjustEdgeCurvatures(vtkPolyData* source, std::string const& curvatureName,
                          double const& epsilon)
{
  auto PointNeighbourhood =
      [&source](vtkIdType const& pId) -> std::set<vtkIdType> {
    // Extract the topological neighbors for point pId. In two steps:
    //  1) source->GetPointCells(pId, cellIds)
    //  2) source->GetCellPoints(cellId, cellPointIds) for all cellId in cellIds
    vtkNew<vtkIdList> cellIds;
    source->GetPointCells(pId, cellIds);
    std::set<vtkIdType> neighbours;
    for (vtkIdType i = 0; i < cellIds->GetNumberOfIds(); ++i)
    {
      auto cellId = cellIds->GetId(i);
      vtkNew<vtkIdList> cellPointIds;
      source->GetCellPoints(cellId, cellPointIds);
      for (vtkIdType j = 0; j < cellPointIds->GetNumberOfIds(); ++j)
      {
        neighbours.insert(cellPointIds->GetId(j));
      }
    }
    return neighbours;
  };

  auto ComputeDistance = [&source](vtkIdType const& ptIdA,
                                   vtkIdType const& ptIdB) {
    std::array<double, 3> ptA{0.0, 0.0, 0.0};
    std::array<double, 3> ptB{0.0, 0.0, 0.0};
    std::array<double, 3> ptC{0.0, 0.0, 0.0};
    source->GetPoint(ptIdA, ptA.data());
    source->GetPoint(ptIdB, ptB.data());
    std::transform(std::begin(ptA), std::end(ptA), std::begin(ptB),
                   std::begin(ptC), std::minus<double>());
    // Calculate the norm.
    auto result = std::sqrt(std::inner_product(std::begin(ptC), std::end(ptC),
                                               std::begin(ptC), 0.0));
    return result;
  };

  source->GetPointData()->SetActiveScalars(curvatureName.c_str());
  // Curvature as a vector.
  auto array = source->GetPointData()->GetAbstractArray(curvatureName.c_str());
  std::vector<double> curvatures;
  for (vtkIdType i = 0; i < source->GetNumberOfPoints(); ++i)
  {
    curvatures.push_back(array->GetVariantValue(i).ToDouble());
  }

  // Get the boundary point IDs.
  std::string name = "Ids";
#ifdef USE_USE_GENERATE_IDS
  vtkNew<vtkGenerateIds> idFilter;
#else
  vtkNew<vtkIdFilter> idFilter;
#endif
  idFilter->SetInputData(source);
  idFilter->SetPointIds(true);
  idFilter->SetCellIds(false);
  idFilter->SetPointIdsArrayName(name.c_str());
  idFilter->SetCellIdsArrayName(name.c_str());
  idFilter->Update();

  vtkNew<vtkFeatureEdges> edges;

  edges->SetInputConnection(idFilter->GetOutputPort());
  edges->BoundaryEdgesOn();
  edges->ManifoldEdgesOff();
  edges->NonManifoldEdgesOff();
  edges->FeatureEdgesOff();
  edges->Update();

  auto edgeAarray =
      edges->GetOutput()->GetPointData()->GetAbstractArray(name.c_str());
  std::vector<vtkIdType> boundaryIds;
  for (vtkIdType i = 0; i < edges->GetOutput()->GetNumberOfPoints(); ++i)
  {
    boundaryIds.push_back(edgeAarray->GetVariantValue(i).ToInt());
  }
  // Remove duplicate Ids.
  std::set<vtkIdType> pIdsSet(boundaryIds.begin(), boundaryIds.end());
  for (auto const pId : boundaryIds)
  {
    auto pIdsNeighbors = PointNeighbourhood(pId);
    std::set<vtkIdType> pIdsNeighborsInterior;
    std::set_difference(
        pIdsNeighbors.begin(), pIdsNeighbors.end(), pIdsSet.begin(),
        pIdsSet.end(),
        std::inserter(pIdsNeighborsInterior, pIdsNeighborsInterior.begin()));
    // Compute distances and extract curvature values.
    std::vector<double> curvs;
    std::vector<double> dists;
    for (auto const pIdN : pIdsNeighborsInterior)
    {
      curvs.push_back(curvatures[pIdN]);
      dists.push_back(ComputeDistance(pIdN, pId));
    }
    std::vector<vtkIdType> nonZeroDistIds;
    for (size_t i = 0; i < dists.size(); ++i)
    {
      if (dists[i] > 0)
      {
        nonZeroDistIds.push_back(i);
      }
    }
    std::vector<double> curvsNonZero;
    std::vector<double> distsNonZero;
    for (auto const i : nonZeroDistIds)
    {
      curvsNonZero.push_back(curvs[i]);
      distsNonZero.push_back(dists[i]);
    }
    // Iterate over the edge points and compute the curvature as the weighted
    // average of the neighbours.
    auto countInvalid = 0;
    auto newCurv = 0.0;
    if (curvsNonZero.size() > 0)
    {
      std::vector<double> weights;
      double sum = 0.0;
      for (auto const d : distsNonZero)
      {
        sum += 1.0 / d;
        weights.push_back(1.0 / d);
      }
      for (size_t i = 0; i < weights.size(); ++i)
      {
        weights[i] = weights[i] / sum;
      }
      newCurv = std::inner_product(curvsNonZero.begin(), curvsNonZero.end(),
                                   weights.begin(), 0.0);
    }
    else
    {
      // Corner case.
      // countInvalid += 1;
      // Assuming the curvature of the point is planar.
      newCurv = 0.0;
    }
    // Set the new curvature value.
    curvatures[pId] = newCurv;
  }

  // Set small values to zero.
  if (epsilon != 0.0)
  {
    auto eps = std::abs(epsilon);
    for (size_t i = 0; i < curvatures.size(); ++i)
    {
      if (std::abs(curvatures[i]) < eps)
      {
        curvatures[i] = 0.0;
      }
    }
  }

  if (static_cast<size_t>(source->GetNumberOfPoints()) != curvatures.size())
  {
    std::string s = curvatureName;
    s += ":\nCannot add the adjusted curvatures to the source.\n";
    s += " The number of points in source does not equal the\n";
    s += " number of point ids in the adjusted curvature array.";
    std::cerr << s << std::endl;
    return;
  }
  vtkNew<vtkDoubleArray> adjustedCurvatures;
  adjustedCurvatures->SetName(curvatureName.c_str());
  for (auto curvature : curvatures)
  {
    adjustedCurvatures->InsertNextTuple1(curvature);
  }
  source->GetPointData()->AddArray(adjustedCurvatures);
  source->GetPointData()->SetActiveScalars(curvatureName.c_str());
}

void ConstrainCurvatures(vtkPolyData* source, std::string const& curvatureName,
                         double const& lowerBound, double const& upperBound)
{
  std::array<double, 2> bounds{0.0, 0.0};
  if (lowerBound < upperBound)
  {
    bounds[0] = lowerBound;
    bounds[1] = upperBound;
  }
  else
  {
    bounds[0] = upperBound;
    bounds[1] = lowerBound;
  }

  source->GetPointData()->SetActiveScalars(curvatureName.c_str());
  // Curvature as a vector.
  auto array = source->GetPointData()->GetAbstractArray(curvatureName.c_str());
  std::vector<double> curvatures;
  for (vtkIdType i = 0; i < source->GetNumberOfPoints(); ++i)
  {
    curvatures.push_back(array->GetVariantValue(i).ToDouble());
  }
  //  Set upper and lower bounds.
  for (size_t i = 0; i < curvatures.size(); ++i)
  {
    if (curvatures[i] < bounds[0])
    {
      curvatures[i] = bounds[0];
    }
    else
    {
      if (curvatures[i] > bounds[1])
      {
        curvatures[i] = bounds[1];
      }
    }
  }
  vtkNew<vtkDoubleArray> adjustedCurvatures;
  for (auto curvature : curvatures)
  {
    adjustedCurvatures->InsertNextTuple1(curvature);
  }
  adjustedCurvatures->SetName(curvatureName.c_str());
  source->GetPointData()->RemoveArray(curvatureName.c_str());
  source->GetPointData()->AddArray(adjustedCurvatures);
  source->GetPointData()->SetActiveScalars(curvatureName.c_str());
}

vtkSmartPointer<vtkPolyData> GetElevations(vtkPolyData* src)
{
  double bounds[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
  src->GetBounds(bounds);
  if (std::abs(bounds[2]) < 1.0e-8 && std::abs(bounds[3]) < 1.0e-8)
  {
    bounds[3] = bounds[2] + 1;
  }
  vtkNew<vtkElevationFilter> elevFilter;
  elevFilter->SetInputData(src);
  elevFilter->SetLowPoint(0, bounds[2], 0);
  elevFilter->SetHighPoint(0, bounds[3], 0);
  elevFilter->SetScalarRange(bounds[2], bounds[3]);
  elevFilter->Update();

  return elevFilter->GetPolyDataOutput();
}

vtkSmartPointer<vtkPolyData> GetHills()
{
  // Create four hills on a plane.
  // This will have regions of negative, zero and positive Gsaussian curvatures.

  auto xRes = 50;
  auto yRes = 50;
  auto xMin = -5.0;
  auto xMax = 5.0;
  auto dx = (xMax - xMin) / (xRes - 1.0);
  auto yMin = -5.0;
  auto yMax = 5.0;
  auto dy = (yMax - yMin) / (xRes - 1.0);

  // Make a grid.
  vtkNew<vtkPoints> points;
  for (auto i = 0; i < xRes; ++i)
  {
    auto x = xMin + i * dx;
    for (auto j = 0; j < yRes; ++j)
    {
      auto y = yMin + j * dy;
      points->InsertNextPoint(x, y, 0);
    }
  }

  // Add the grid points to a polydata object.
  vtkNew<vtkPolyData> plane;
  plane->SetPoints(points);

  // Triangulate the grid.
  vtkNew<vtkDelaunay2D> delaunay;
  delaunay->SetInputData(plane);
  delaunay->Update();

  auto polydata = delaunay->GetOutput();

  vtkNew<vtkDoubleArray> elevation;
  elevation->SetNumberOfTuples(points->GetNumberOfPoints());

  //  We define the parameters for the hills here.
  // [[0: x0, 1: y0, 2: x variance, 3: y variance, 4: amplitude]...]
  std::vector<std::array<double, 5>> hd{{-2.5, -2.5, 2.5, 6.5, 3.5},
                                        {2.5, 2.5, 2.5, 2.5, 2},
                                        {5.0, -2.5, 1.5, 1.5, 2.5},
                                        {-5.0, 5, 2.5, 3.0, 3}};
  std::array<double, 2> xx{0.0, 0.0};
  for (auto i = 0; i < points->GetNumberOfPoints(); ++i)
  {
    auto x = polydata->GetPoint(i);
    for (size_t j = 0; j < hd.size(); ++j)
    {
      xx[0] = std::pow(x[0] - hd[j][0] / hd[j][2], 2.0);
      xx[1] = std::pow(x[1] - hd[j][1] / hd[j][3], 2.0);
      x[2] += hd[j][4] * std::exp(-(xx[0] + xx[1]) / 2.0);
    }
    polydata->GetPoints()->SetPoint(i, x);
    elevation->SetValue(i, x[2]);
  }

  vtkNew<vtkFloatArray> textures;
  textures->SetNumberOfComponents(2);
  textures->SetNumberOfTuples(2 * polydata->GetNumberOfPoints());
  textures->SetName("Textures");

  for (auto i = 0; i < xRes; ++i)
  {
    float tc[2];
    tc[0] = i / (xRes - 1.0);
    for (auto j = 0; j < yRes; ++j)
    {
      // tc[1] = 1.0 - j / (yRes - 1.0);
      tc[1] = j / (yRes - 1.0);
      textures->SetTuple(static_cast<vtkIdType>(i) * yRes + j, tc);
    }
  }

  polydata->GetPointData()->SetScalars(elevation);
  polydata->GetPointData()->GetScalars()->SetName("Elevation");
  polydata->GetPointData()->SetTCoords(textures);

  vtkNew<vtkPolyDataNormals> normals;
  normals->SetInputData(polydata);
  normals->SetInputData(polydata);
  normals->SetFeatureAngle(30);
  normals->SplittingOff();

  vtkNew<vtkTransform> tr1;
  tr1->RotateX(-90);

  vtkNew<vtkTransformPolyDataFilter> tf1;
  tf1->SetInputConnection(normals->GetOutputPort());
  tf1->SetTransform(tr1);
  tf1->Update();

  return tf1->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetParametricHills()
{
  vtkNew<vtkParametricRandomHills> fn;
  fn->AllowRandomGenerationOn();
  fn->SetRandomSeed(1);
  fn->SetNumberOfHills(30);

  vtkNew<vtkParametricFunctionSource> source;
  source->SetParametricFunction(fn);
  source->SetUResolution(50);
  source->SetVResolution(50);
  source->SetScalarModeToZ();
  source->Update();

  // Name the arrays (not needed in VTK 6.2+ for vtkParametricFunctionSource).
  // source->GetOutput()->GetPointData()->GetNormals()->SetName("Normals");
  // source->GetOutput()->GetPointData()->GetScalars()->SetName("Scalars");
  // Rename the scalars to "Elevation" since we are using the Z-scalars as
  // elevations.
  source->GetOutput()->GetPointData()->GetScalars()->SetName("Elevation");

  vtkNew<vtkTransform> transform;
  transform->Translate(0.0, 5.0, 15.0);
  transform->RotateX(-90.0);
  vtkNew<vtkTransformPolyDataFilter> transformFilter;
  transformFilter->SetInputConnection(source->GetOutputPort());
  transformFilter->SetTransform(transform);
  transformFilter->Update();

  return transformFilter->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetParametricTorus()
{
  vtkNew<vtkParametricTorus> fn;
  fn->SetRingRadius(5);
  fn->SetCrossSectionRadius(2);

  vtkNew<vtkParametricFunctionSource> source;
  source->SetParametricFunction(fn);
  source->SetUResolution(50);
  source->SetVResolution(50);
  source->SetScalarModeToZ();
  source->Update();

  // Name the arrays (not needed in VTK 6.2+ for vtkParametricFunctionSource).
  // source->GetOutput()->GetPointData()->GetNormals()->SetName("Normals");
  // source->GetOutput()->GetPointData()->GetScalars()->SetName("Scalars");
  // Rename the scalars to "Elevation" since we are using the Z-scalars as
  // elevations.
  source->GetOutput()->GetPointData()->GetScalars()->SetName("Elevation");

  vtkNew<vtkTransform> transform;
  transform->RotateX(-90.0);
  vtkNew<vtkTransformPolyDataFilter> transformFilter;
  transformFilter->SetInputConnection(source->GetOutputPort());
  transformFilter->SetTransform(transform);
  transformFilter->Update();

  return transformFilter->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetPlane()
{
  vtkNew<vtkPlaneSource> source;
  source->SetOrigin(-10.0, -10.0, 0.0);
  source->SetPoint2(-10.0, 10.0, 0.0);
  source->SetPoint1(10.0, -10.0, 0.0);
  source->SetXResolution(20);
  source->SetYResolution(20);
  source->Update();

  vtkNew<vtkTransform> transform;
  transform->Translate(0.0, 0.0, 0.0);
  transform->RotateX(-90.0);
  vtkNew<vtkTransformPolyDataFilter> transformFilter;
  transformFilter->SetInputConnection(source->GetOutputPort());
  transformFilter->SetTransform(transform);
  transformFilter->Update();

  // We have a m x n array of quadrilaterals arranged as a regular tiling in a
  // plane. So pass it through a triangle filter since the curvature filter only
  // operates on polys.
  vtkNew<vtkTriangleFilter> tri;
  tri->SetInputConnection(transformFilter->GetOutputPort());

  // Pass it though a CleanPolyDataFilter and merge any points which
  // are coincident, or very close
  vtkNew<vtkCleanPolyData> cleaner;
  cleaner->SetInputConnection(tri->GetOutputPort());
  cleaner->SetTolerance(0.005);
  cleaner->Update();

  return cleaner->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetSphere()
{
  vtkNew<vtkSphereSource> source;
  source->SetCenter(0.0, 0.0, 0.0);
  source->SetRadius(10.0);
  source->SetThetaResolution(32);
  source->SetPhiResolution(32);
  source->Update();

  return source->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetTorus()
{
  vtkNew<vtkSuperquadricSource> source;
  source->SetCenter(0.0, 0.0, 0.0);
  source->SetCenter(1.0, 1.0, 1.0);
  source->SetPhiResolution(64);
  source->SetThetaResolution(64);
  source->SetThetaRoundness(1);
  source->SetThickness(0.5);
  source->SetSize(10);
  source->SetToroidal(1);
  source->Update();

  // The quadric is made of strips, so pass it through a triangle filter as
  // the curvature filter only operates on polys
  vtkNew<vtkTriangleFilter> tri;
  tri->SetInputConnection(source->GetOutputPort());

  // The quadric has nasty discontinuities from the way the edges are generated
  // so let's pass it though a CleanPolyDataFilter and merge any points which
  // are coincident, or very close
  vtkNew<vtkCleanPolyData> cleaner;
  cleaner->SetInputConnection(tri->GetOutputPort());
  cleaner->SetTolerance(0.005);
  cleaner->Update();

  return cleaner->GetOutput();
}

vtkSmartPointer<vtkPolyData> GetSource(std::string const& source)
{
  std::string surface = source;
  std::transform(surface.begin(), surface.end(), surface.begin(),
                 [](unsigned char c) { return std::tolower(c); });
  std::map<std::string, int> available_surfaces = {
      {"hills", 0},       {"parametrictorus", 1}, {"plane", 2},
      {"randomhills", 3}, {"sphere", 4},          {"torus", 5}};
  if (available_surfaces.find(surface) == available_surfaces.end())
  {
    std::cout << "The surface is not available." << std::endl;
    std::cout << "Using RandomHills instead." << std::endl;
    surface = "randomhills";
  }
  switch (available_surfaces[surface])
  {
  case 0:
    return GetHills();
    break;
  case 1:
    return GetParametricTorus();
    break;
  case 2:
    return GetElevations(GetPlane());
    break;
  case 3:
    return GetParametricHills();
    break;
  case 4:
    return GetElevations(GetSphere());
    break;
  case 5:
    return GetElevations(GetTorus());
    break;
  }
  return GetParametricHills();
}

vtkSmartPointer<vtkColorSeries> GetColorSeries()
{

  vtkNew<vtkColorSeries> colorSeries;
  // Select a color scheme.
  int colorSeriesEnum;
  // colorSeriesEnum = colorSeries->BREWER_DIVERGING_BROWN_BLUE_GREEN_9;
  // colorSeriesEnum = colorSeries->BREWER_DIVERGING_SPECTRAL_10;
  // colorSeriesEnum = colorSeries->BREWER_DIVERGING_SPECTRAL_3;
  // colorSeriesEnum = colorSeries->BREWER_DIVERGING_PURPLE_ORANGE_9;
  // colorSeriesEnum = colorSeries->BREWER_SEQUENTIAL_BLUE_PURPLE_9;
  // colorSeriesEnum = colorSeries->BREWER_SEQUENTIAL_BLUE_GREEN_9;
  colorSeriesEnum = colorSeries->BREWER_QUALITATIVE_SET3;
  // colorSeriesEnum = colorSeries->CITRUS;
  colorSeries->SetColorScheme(colorSeriesEnum);
  return colorSeries;
}

vtkSmartPointer<vtkLookupTable> GetCategoricalLUT()
{
  vtkSmartPointer<vtkColorSeries> colorSeries = GetColorSeries();
  // Make the lookup table.
  vtkNew<vtkLookupTable> lut;
  colorSeries->BuildLookupTable(lut, vtkColorSeries::CATEGORICAL);
  lut->SetNanColor(0, 0, 0, 1);

  return lut;
}

vtkSmartPointer<vtkLookupTable> GetOrdinaLUT()
{
  vtkSmartPointer<vtkColorSeries> colorSeries = GetColorSeries();
  // Make the lookup table.
  vtkNew<vtkLookupTable> lut;
  colorSeries->BuildLookupTable(lut, vtkColorSeries::ORDINAL);
  lut->SetNanColor(0, 0, 0, 1);

  return lut;
}

// clang-format off
/**
 * See: [Diverging Color Maps for Scientific Visualization](https://www.kennethmoreland.com/color-maps/)
 *
 *                   start point         midPoint            end point
 * cool to warm:     0.230, 0.299, 0.754 0.865, 0.865, 0.865 0.706, 0.016, 0.150
 * purple to orange: 0.436, 0.308, 0.631 0.865, 0.865, 0.865 0.759, 0.334, 0.046
 * green to purple:  0.085, 0.532, 0.201 0.865, 0.865, 0.865 0.436, 0.308, 0.631
 * blue to brown:    0.217, 0.525, 0.910 0.865, 0.865, 0.865 0.677, 0.492, 0.093
 * green to red:     0.085, 0.532, 0.201 0.865, 0.865, 0.865 0.758, 0.214, 0.233
 *
 */
// clang-format on
vtkSmartPointer<vtkLookupTable> GetDivergingLUT()
{

  vtkNew<vtkColorTransferFunction> ctf;
  ctf->SetColorSpaceToDiverging();
  ctf->AddRGBPoint(0.0, 0.085, 0.532, 0.201);
  ctf->AddRGBPoint(0.5, 0.865, 0.865, 0.865);
  ctf->AddRGBPoint(1.0, 0.758, 0.214, 0.233);

  auto tableSize = 256;
  vtkNew<vtkLookupTable> lut;
  lut->SetNumberOfTableValues(tableSize);
  lut->Build();

  for (auto i = 0; i < lut->GetNumberOfColors(); ++i)
  {
    std::array<double, 3> rgb;
    ctf->GetColor(static_cast<double>(i) / lut->GetNumberOfColors(),
                  rgb.data());
    std::array<double, 4> rgba{0.0, 0.0, 0.0, 1.0};
    std::copy(std::begin(rgb), std::end(rgb), std::begin(rgba));
    lut->SetTableValue(static_cast<vtkIdType>(i), rgba.data());
  }

  return lut;
}

vtkSmartPointer<vtkLookupTable> ReverseLUT(vtkLookupTable* lut)
{
  // First do a deep copy just to get the whole structure
  // and then reverse the colors and annotations.
  vtkNew<vtkLookupTable> lutr;
  lutr->DeepCopy(lut);
  vtkIdType t = lut->GetNumberOfTableValues() - 1;
  for (vtkIdType i = t; i >= 0; --i)
  {
    std::array<double, 3> rgb{0.0, 0.0, 0.0};
    std::array<double, 4> rgba{0.0, 0.0, 0.0, 1.0};
    lut->GetColor(i, rgb.data());
    std::copy(std::begin(rgb), std::end(rgb), std::begin(rgba));
    rgba[3] = lut->GetOpacity(i);
    lutr->SetTableValue(t - i, rgba.data());
  }
  t = lut->GetNumberOfAnnotatedValues() - 1;
  for (vtkIdType i = t; i >= 0; --i)
  {
    lutr->SetAnnotation(t - i, lut->GetAnnotation(i));
  }

  return lutr;
}

vtkNew<vtkGlyph3D> GetGlyphs(vtkPolyData* src, double const& scaleFactor,
                             bool const& reverseNormals)
{
  // Sometimes the contouring algorithm can create a volume whose gradient
  // vector and ordering of polygon(using the right hand rule) are
  // inconsistent. vtkReverseSense cures this problem.
  vtkNew<vtkReverseSense> reverse;
  vtkNew<vtkMaskPoints> maskPts;
  maskPts->SetOnRatio(5);
  maskPts->RandomModeOn();
  if (reverseNormals)
  {
    reverse->SetInputData(src);
    reverse->ReverseCellsOn();
    reverse->ReverseNormalsOn();
    maskPts->SetInputConnection(reverse->GetOutputPort());
  }
  else
  {
    maskPts->SetInputData(src);
  }

  // Source for the glyph filter
  vtkNew<vtkArrowSource> arrow;
  arrow->SetTipResolution(16);
  arrow->SetTipLength(0.3);
  arrow->SetTipRadius(0.1);

  vtkNew<vtkGlyph3D> glyph;
  glyph->SetSourceConnection(arrow->GetOutputPort());
  glyph->SetInputConnection(maskPts->GetOutputPort());
  glyph->SetVectorModeToUseNormal();
  glyph->SetScaleFactor(scaleFactor);
  glyph->SetColorModeToColorByVector();
  glyph->SetScaleModeToScaleByVector();
  glyph->OrientOn();
  glyph->Update();

  return glyph;
}

std::map<int, std::vector<double>> GetBands(double const dR[2],
                                            int const& numberOfBands,
                                            int const& precision,
                                            bool const& nearestInteger)
{
  auto prec = abs(precision);
  prec = (prec > 14) ? 14 : prec;

  auto RoundOff = [&prec](const double& x) {
    auto pow_10 = std::pow(10.0, prec);
    return std::round(x * pow_10) / pow_10;
  };

  std::map<int, std::vector<double>> bands;
  if ((dR[1] < dR[0]) || (numberOfBands <= 0))
  {
    return bands;
  }
  double x[2];
  for (int i = 0; i < 2; ++i)
  {
    x[i] = dR[i];
  }
  if (nearestInteger)
  {
    x[0] = std::floor(x[0]);
    x[1] = std::ceil(x[1]);
  }
  double dx = (x[1] - x[0]) / static_cast<double>(numberOfBands);
  std::vector<double> b;
  b.push_back(x[0]);
  b.push_back(x[0] + dx / 2.0);
  b.push_back(x[0] + dx);
  for (int i = 0; i < numberOfBands; ++i)
  {
    if (i == 0)
    {
      for (std::vector<double>::iterator p = b.begin(); p != b.end(); ++p)
      {
        *p = RoundOff(*p);
      }
      b[0] = x[0];
    }
    bands[i] = b;
    for (std::vector<double>::iterator p = b.begin(); p != b.end(); ++p)
    {
      *p = RoundOff(*p + dx);
    }
  }
  return bands;
}

std::map<int, std::vector<double>>
GetCustomBands(double const dR[2], int const& numberOfBands,
               std::vector<std::array<double, 2>> const& myBands)
{
  std::map<int, std::vector<double>> bands;
  if ((dR[1] < dR[0]) || (numberOfBands <= 0))
  {
    return bands;
  }

  std::vector<std::array<double, 2>> x;
  std::copy(myBands.begin(), myBands.end(), std::back_inserter(x));

  // Determine the index of the range minimum and range maximum.
  int idxMin = 0;
  for (auto idx = 0; idx < static_cast<int>(myBands.size()); ++idx)
  {
    if (dR[0] < myBands[idx][1] && dR[0] >= myBands[idx][0])
    {
      idxMin = idx;
      break;
    }
  }
  int idxMax = static_cast<int>(myBands.size()) - 1;
  for (int idx = static_cast<int>(myBands.size()) - 1; idx >= 0; --idx)
  {
    if (dR[1] < myBands[idx][1] && dR[1] >= myBands[idx][0])
    {
      idxMax = static_cast<int>(idx);
      break;
    }
  }

  // Set the minimum to match the range minimum.
  x[idxMin][0] = dR[0];
  x[idxMax][1] = dR[1];
  for (int i = idxMin; i < idxMax + 1; ++i)
  {
    std::vector<double> b(3);
    b[0] = x[i][0];
    b[1] = x[i][0] + (x[i][1] - x[i][0]) / 2.0;
    b[2] = x[i][1];
    bands[i] = b;
  }
  return bands;
}

std::map<int, std::vector<double>> GetIntegralBands(double const dR[2])
{
  if (dR[1] < dR[0])
  {
    std::map<int, std::vector<double>> bands;
    return bands;
  }
  double x[2];
  for (int i = 0; i < 2; ++i)
  {
    x[i] = dR[i];
  }
  x[0] = std::floor(x[0]);
  x[1] = std::ceil(x[1]);
  int numberOfBands = static_cast<int>(std::abs(x[1]) + std::abs(x[0]));
  return GetBands(x, numberOfBands, false);
}

std::map<int, int> GetFrequencies(std::map<int, std::vector<double>>& bands,
                                  vtkPolyData* src)
{
  std::map<int, int> freq;
  for (auto i = 0; i < static_cast<int>(bands.size()); ++i)
  {
    freq[i] = 0;
  }
  vtkIdType tuples = src->GetPointData()->GetScalars()->GetNumberOfTuples();
  for (int i = 0; i < tuples; ++i)
  {
    const double* x = src->GetPointData()->GetScalars()->GetTuple(i);
    for (auto j = 0; j < static_cast<int>(bands.size()); ++j)
    {
      if (*x <= bands[j][2])
      {
        freq[j] = freq[j] + 1;
        break;
      }
    }
  }
  return freq;
}

void AdjustFrequencyRanges(std::map<int, std::vector<double>>& bands,
                           std::map<int, int>& freq)
{
  // Get the indices of the first and last non-zero elements.
  auto first = 0;
  for (auto i = 0; i < static_cast<int>(freq.size()); ++i)
  {
    if (freq[i] != 0)
    {
      first = i;
      break;
    }
  }
  std::vector<int> keys;
  for (std::map<int, int>::iterator it = freq.begin(); it != freq.end(); ++it)
  {
    keys.push_back(it->first);
  }
  std::reverse(keys.begin(), keys.end());
  auto last = keys[0];
  for (size_t i = 0; i < keys.size(); ++i)
  {
    if (freq[keys[i]] != 0)
    {
      last = keys[i];
      break;
    }
  }
  // Now adjust the ranges.
  std::map<int, int>::iterator freqItr;
  freqItr = freq.find(first);
  freq.erase(freq.begin(), freqItr);
  freqItr = ++freq.find(last);
  freq.erase(freqItr, freq.end());
  std::map<int, std::vector<double>>::iterator bandItr;
  bandItr = bands.find(first);
  bands.erase(bands.begin(), bandItr);
  bandItr = ++bands.find(last);
  bands.erase(bandItr, bands.end());
  // Reindex freq and bands.
  std::map<int, int> adjFreq;
  int idx = 0;
  for (auto p : freq)
  {
    adjFreq[idx] = p.second;
    ++idx;
  }
  std::map<int, std::vector<double>> adjBands;
  idx = 0;
  for (auto const& p : bands)
  {
    adjBands[idx] = p.second;
    ++idx;
  }
  bands = adjBands;
  freq = adjFreq;
}

void PrintBandsFrequencies(std::map<int, std::vector<double>> const& bands,
                           std::map<int, int>& freq, int const& precision)
{
  auto prec = abs(precision);
  prec = (prec > 14) ? 14 : prec;

  if (bands.size() != freq.size())
  {
    std::cout << "Bands and frequencies must be the same size." << std::endl;
    return;
  }
  std::ostringstream os;
  os << "Bands & Frequencies:\n";
  size_t idx = 0;
  auto total = 0;
  auto width = prec + 6;
  for (std::map<int, std::vector<double>>::const_iterator p = bands.begin();
       p != bands.end(); ++p)
  {
    total += freq[p->first];
    for (std::vector<double>::const_iterator q = p->second.begin();
         q != p->second.end(); ++q)
    {
      if (q == p->second.begin())
      {
        os << std::setw(4) << idx << " [";
      }
      if (q == std::prev(p->second.end()))
      {
        os << std::fixed << std::setw(width) << std::setprecision(prec) << *q
           << "]: " << std::setw(8) << freq[p->first] << "\n";
      }
      else
      {
        os << std::fixed << std::setw(width) << std::setprecision(prec) << *q
           << ", ";
      }
    }
    ++idx;
  }
  width = 3 * width + 13;
  os << std::left << std::setw(width) << "Total" << std::right << std::setw(8)
     << total << std::endl;
  std::cout << os.str() << endl;
}

} // namespace

CMakeLists.txt

cmake_minimum_required(VERSION 3.12 FATAL_ERROR)

project(CurvatureBandsWithGlyphs)

find_package(VTK COMPONENTS 
  CommonColor
  CommonComputationalGeometry
  CommonCore
  CommonDataModel
  CommonTransforms
  FiltersCore
  FiltersGeneral
  FiltersModeling
  FiltersSources
  InteractionStyle
  InteractionWidgets
  RenderingAnnotation
  RenderingContextOpenGL2
  RenderingCore
  RenderingFreeType
  RenderingGL2PSOpenGL2
  RenderingOpenGL2
)

if (NOT VTK_FOUND)
  message(FATAL_ERROR "CurvatureBandsWithGlyphs: Unable to find the VTK build folder.")
endif()

# Prevent a "command line is too long" failure in Windows.
set(CMAKE_NINJA_FORCE_RESPONSE_FILE "ON" CACHE BOOL "Force Ninja to use response files.")
add_executable(CurvatureBandsWithGlyphs MACOSX_BUNDLE CurvatureBandsWithGlyphs.cxx )
  target_link_libraries(CurvatureBandsWithGlyphs PRIVATE ${VTK_LIBRARIES}
)
# vtk_module_autoinit is needed
vtk_module_autoinit(
  TARGETS CurvatureBandsWithGlyphs
  MODULES ${VTK_LIBRARIES}
)

Download and Build CurvatureBandsWithGlyphs

Click here to download CurvatureBandsWithGlyphs and its CMakeLists.txt file. Once the tarball CurvatureBandsWithGlyphs.tar has been downloaded and extracted,

cd CurvatureBandsWithGlyphs/build

If VTK is installed:

cmake ..

If VTK is not installed but compiled on your system, you will need to specify the path to your VTK build:

cmake -DVTK_DIR:PATH=/home/me/vtk_build ..

Build the project:

make

and run it:

./CurvatureBandsWithGlyphs

WINDOWS USERS

Be sure to add the VTK bin directory to your path. This will resolve the VTK dll's at run time.