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# CurvaturesDemo

VTKEx/Cxx/PolyData/CurvaturesDemo

### Description

How to get the Gaussian and Mean curvatures of a surface.

Two different surfaces are used in this demonstration with each surface coloured according to its Gaussian and Mean curvatures.

- The first surface is a superquadric surface, this demonstrates the use of extra filters that are needed to get a nice smooth surface.

- The second surface is a parametric surface, in this case the surface has already been triangulated so no extra processing is necessary.

In order to get a nice coloured image, a vtkColorTransferFunction has been used to generate a set of colours for the vtkLookupTable tables. We have used a diverging colour space. Because of the symmetry of the ranges selected for the lookup tables, the white colouration represents a midpoint value whilst the blue represents values less than the midopoint value and red represents colours greater than the midpoint value.

In the case of the Random Hills Gaussian curvature surface, this colouration shows the nature of the surface quite nicely. The blue areas are saddle points (negative Gaussian curvature) and the red areas have a positive Gaussian curvature. In the case of the mean curvature the blue colouration is representing negative curvature perpendicular to one of the principal axes.

This example also demonstrates the use of std::vector's and the linking of the elements of the vectors together to form a pipeline.

Other languages

See (Python)

Question

If you have a simple question about this example contact us at VTKExProject If your question is more complex and may require extended discussion, please use the VTK Discourse Forum

### Code

CurvaturesDemo.cxx

    /*
    The purpose of this is to demonstrate how to get the Gaussian and Mean
    curvatures of a surface.

    Two different surfaces are used in this demonstration with each
    surface coloured according to its Gaussian and Mean curvatures.

    The first surface is a superquadric surface, this demonstrates the use
    of extra filters that are needed to get a nice smooth surface.

    The second surface is a parametric surface, in this case the surface
    has already been triangulated so no extra processing is necessary.

    In order to get a nice coloured image, a vtkColorTransferFunction has
    been used to generate a set of colours for the vtkLookUp tables. We
    have used a diverging colour space.  Because of the symmetry of the
    ranges selected for the lookup tables, the white colouration
    represents a midpoint value whilst the blue represents values less
    than the midopoint value and red represents colours greater than the
    midpoint value.

    In the case of the Random Hills Gaussian Curvature surface, this
    colouration shows the nature of the surface quite nicely. The blue
    areas are saddle points (negative Gaussian curvature) and the red
    areas have a positive Gaussian curvature.  In the case of the mean
    curvature the blue colouration is representing negative curvature
    perpendicular to one of the principal axes.

    This example also demonstrates the use of std::vector and the linking
    of the elements of the vector together to form a pipeline.
    */

    #include <vtkActor.h>
    #include <vtkActor2D.h>
    #include <vtkCleanPolyData.h>
    #include <vtkColorTransferFunction.h>
    #include <vtkCurvatures.h>
    #include <vtkLookupTable.h>
    #include <vtkNamedColors.h>
    #include <vtkParametricFunctionSource.h>
    #include <vtkParametricRandomHills.h>
    #include <vtkPolyDataAlgorithm.h>
    #include <vtkPolyDataMapper.h>
    #include <vtkRenderWindow.h>
    #include <vtkRenderWindowInteractor.h>
    #include <vtkRenderer.h>
    #include <vtkSmartPointer.h>
    #include <vtkSuperquadricSource.h>
    #include <vtkTextMapper.h>
    #include <vtkTextProperty.h>
    #include <vtkTransform.h>
    #include <vtkTransformFilter.h>
    #include <vtkTriangleFilter.h>

    #include <array>
    #include <vector>

    int main(int, char* argv[])
    {
      auto colors = vtkSmartPointer<vtkNamedColors>::New();
      // We are going to handle two different sources.
      // The first source is a superquadric source.
      auto torus = vtkSmartPointer<vtkSuperquadricSource>::New();
      torus->SetCenter(0.0, 0.0, 0.0);
      torus->SetScale(1.0, 1.0, 1.0);
      torus->SetPhiResolution(64);
      torus->SetThetaResolution(64);
      torus->SetThetaRoundness(1);
      torus->SetThickness(0.5);
      torus->SetSize(0.5);
      torus->SetToroidal(1);

      // Rotate the torus towards the observer (around the x-axis)
      auto torusT = vtkSmartPointer<vtkTransform>::New();
      torusT->RotateX(55);

      auto torusTF = vtkSmartPointer<vtkTransformFilter>::New();
      torusTF->SetInputConnection(torus->GetOutputPort());
      torusTF->SetTransform(torusT);

      // The quadric is made of strips, so pass it through a triangle filter as
      // the curvature filter only operates on polys
      auto tri = vtkSmartPointer<vtkTriangleFilter>::New();
      tri->SetInputConnection(torusTF->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
      auto cleaner = vtkSmartPointer<vtkCleanPolyData>::New();
      cleaner->SetInputConnection(tri->GetOutputPort());
      cleaner->SetTolerance(0.005);

      // The next source will be a parametric function
      auto rh = vtkSmartPointer<vtkParametricRandomHills>::New();
      auto rhFnSrc = vtkSmartPointer<vtkParametricFunctionSource>::New();
      rhFnSrc->SetParametricFunction(rh);

      // Now we have the sources, lets put them into a vector
      std::vector<vtkSmartPointer<vtkPolyDataAlgorithm>> sources;
      sources.push_back(cleaner);
      sources.push_back(cleaner);
      sources.push_back(rhFnSrc);
      sources.push_back(rhFnSrc);

      // Colour transfer function.
      auto ctf = vtkSmartPointer<vtkColorTransferFunction>::New();
      ctf->SetColorSpaceToDiverging();
      ctf->AddRGBPoint(0.0, colors->GetColor3d("MidnightBlue").GetRed(),
                       colors->GetColor3d("MidnightBlue").GetGreen(),
                       colors->GetColor3d("MidnightBlue").GetBlue());
      ctf->AddRGBPoint(1.0, colors->GetColor3d("DarkOrange").GetRed(),
                       colors->GetColor3d("DarkOrange").GetGreen(),
                       colors->GetColor3d("DarkOrange").GetBlue());

      // Lookup table.
      std::vector<vtkSmartPointer<vtkLookupTable>> luts;
      for (auto idx = 0; idx < sources.size(); ++idx)
      {
        auto lut = vtkSmartPointer<vtkLookupTable>::New();
        lut->SetNumberOfColors(256);
        for (auto i = 0; i < lut->GetNumberOfColors(); ++i)
        {
          std::array<double, 4> color;
          ctf->GetColor(double(i) / lut->GetNumberOfColors(), color.data());
          color[3] = 1.0;
          lut->SetTableValue(i, color.data());
        }
        if (idx == 0)
        {
          lut->SetRange(-10, 10);
        }
        else if (idx == 1)
        {
          lut->SetRange(0, 4);
        }
        else if (idx == 2)
        {
          lut->SetRange(-1, 1);
        }
        else
        {
          lut->SetRange(-1, 1);
        }
        lut->Build();
        luts.push_back(lut);
      }

      std::vector<vtkSmartPointer<vtkCurvatures>> curvatures;
      for (auto idx = 0; idx < sources.size(); ++idx)
      {
        curvatures.push_back(vtkSmartPointer<vtkCurvatures>::New());
        if (idx % 2 == 0)
        {
          curvatures[idx]->SetCurvatureTypeToGaussian();
        }
        else
        {
          curvatures[idx]->SetCurvatureTypeToMean();
        }
      }
      std::vector<vtkSmartPointer<vtkRenderer>> renderers;
      std::vector<vtkSmartPointer<vtkActor>> actors;
      std::vector<vtkSmartPointer<vtkPolyDataMapper>> mappers;
      std::vector<vtkSmartPointer<vtkTextMapper>> textmappers;
      std::vector<vtkSmartPointer<vtkActor2D>> textactors;
      for (auto idx = 0; idx < sources.size(); ++idx)
      {
        mappers.push_back(vtkSmartPointer<vtkPolyDataMapper>::New());
        actors.push_back(vtkSmartPointer<vtkActor>::New());
        textmappers.push_back(vtkSmartPointer<vtkTextMapper>::New());
        textactors.push_back(vtkSmartPointer<vtkActor2D>::New());
        renderers.push_back(vtkSmartPointer<vtkRenderer>::New());
      }

      // Create a common text property.
      auto textProperty = vtkSmartPointer<vtkTextProperty>::New();
      textProperty->SetFontSize(24);
      textProperty->SetJustificationToCentered();

      std::vector<std::string> names;
      names.push_back("Torus - Gaussian Curvature");
      names.push_back("Torus - Mean Curvature");
      names.push_back("Random Hills - Gaussian Curvature");
      names.push_back("Random Hills - Mean Curvature");
      // Link the pipeline together.
      for (auto idx = 0; idx < sources.size(); ++idx)
      {
        curvatures[idx]->SetInputConnection(sources[idx]->GetOutputPort());

        mappers[idx]->SetInputConnection(curvatures[idx]->GetOutputPort());
        mappers[idx]->SetLookupTable(luts[idx]);
        mappers[idx]->SetUseLookupTableScalarRange(1);

        actors[idx]->SetMapper(mappers[idx]);

        textmappers[idx]->SetInput(names[idx].c_str());
        textmappers[idx]->SetTextProperty(textProperty);

        textactors[idx]->SetMapper(textmappers[idx]);
        textactors[idx]->SetPosition(250, 16);
      }

      // Create the RenderWindow
      //
      auto rendererSize = 512;
      auto gridDimensions = 2;

      auto renderWindow = vtkSmartPointer<vtkRenderWindow>::New();
      renderWindow->SetSize(rendererSize * gridDimensions,
                            rendererSize * gridDimensions);

      // Add and position the renders to the render window.
      for (auto row = 0; row < gridDimensions; ++row)
      {
        for (auto col = 0; col < gridDimensions; ++col)
        {
          auto idx = row * gridDimensions + col;
          renderers[idx]->SetViewport(
              double(col) / gridDimensions,
              double(gridDimensions - (row + 1)) / gridDimensions,
              double(col + 1) / gridDimensions,
              double(gridDimensions - row) / gridDimensions);
          renderWindow->AddRenderer(renderers[idx]);

          renderers[idx]->AddActor(actors[idx]);
          renderers[idx]->AddActor(textactors[idx]);
          renderers[idx]->SetBackground(
              colors->GetColor3d("CornflowerBlue").GetData());
        }
      }

      auto interactor = vtkSmartPointer<vtkRenderWindowInteractor>::New();
      interactor->SetRenderWindow(renderWindow);

      renderWindow->Render();

      interactor->Start();

      return EXIT_SUCCESS;
    }

### CMakeLists.txt

    cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

    project(CurvaturesDemo)

    find_package(VTK COMPONENTS
      vtkvtkCommonColor
      vtkvtkCommonComputationalGeometry
      vtkvtkCommonCore
      vtkvtkCommonExecutionModel
      vtkvtkCommonTransforms
      vtkvtkFiltersCore
      vtkvtkFiltersGeneral
      vtkvtkFiltersSources
      vtkvtkInteractionStyle
      vtkvtkRenderingContextOpenGL2
      vtkvtkRenderingCore
      vtkvtkRenderingFreeType
      vtkvtkRenderingGL2PSOpenGL2
      vtkvtkRenderingOpenGL2 QUIET)
    if (NOT VTK_FOUND)
      message("Skipping CurvaturesDemo: ${VTK_NOT_FOUND_MESSAGE}")
      return ()
    endif()
    message (STATUS "VTK_VERSION: ${VTK_VERSION}")
    if (VTK_VERSION VERSION_LESS "8.90.0")
      # old system
      include(${VTK_USE_FILE})
      add_executable(CurvaturesDemo MACOSX_BUNDLE CurvaturesDemo.cxx )
      target_link_libraries(CurvaturesDemo PRIVATE ${VTK_LIBRARIES})
    else ()
      # include all components
      add_executable(CurvaturesDemo MACOSX_BUNDLE CurvaturesDemo.cxx )
      target_link_libraries(CurvaturesDemo PRIVATE ${VTK_LIBRARIES})
      # vtk_module_autoinit is needed
      vtk_module_autoinit(
        TARGETS CurvaturesDemo
        MODULES ${VTK_LIBRARIES}
        )
    endif ()

### Download and Build CurvaturesDemo

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

    cd CurvaturesDemo/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:

    ./CurvaturesDemo

WINDOWS USERS

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