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# ParametricObjectsDemo

VTKEx/Cxx/GeometricObjects/ParametricObjectsDemo

### Description

Demonstrates the Parametric classes added by Andrew Maclean and additional classes added by Tim Meehan. The parametric spline is also included.

Options are provided to:

- Specify a single surface (-s SURFACE_NAME)
- Save the image (-w)
- Color the back-face (-b)
- Add normals (-n)

For example:

    ParametricSurfaces -s RandomHills -w -b -n

Will write out a file called `RandomHills.png` and produce an image with all the options enabled.

    ParametricSurfaces -w

Will write out a file with no other options enabled called `ParametricObjectsDemo.png`.

Note

To really appreciate the complexity of some of these surfaces, select a single surface, and use the options `-b -n`. Also try specifying wireframe ( toggle "w" on the keyboard) and zooming in and out.

Tip

If you color the back face, the three-dimensional orientable surfaces will only show backface coloring inside the surface e.g `ConicSpiral` or `Torus`. For three dimensional non-orientable surfaces; backface coloring is visible because of the twisting used to generate these surfaces e.g `Boy` or `Figure8Klein`.

Cite

See: Parametric Equations for Surfaces, for more information. This paper gives a description of the first fifteen surfaces, including their parametric equations and derivatives. Also provided is an example of how to create your own surface, namely the Figure-8 Torus.

Other languages

See (Python), (CSharp)

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

ParametricObjectsDemo.cxx

    #include <vtkActor.h>
    #include <vtkActor2D.h>
    #include <vtkCamera.h>
    #include <vtkMath.h>
    #include <vtkMinimalStandardRandomSequence.h>
    #include <vtkNamedColors.h>
    #include <vtkParametricFunctionSource.h>
    #include <vtkPoints.h>
    #include <vtkPolyDataMapper.h>
    #include <vtkProperty.h>
    #include <vtkRenderWindow.h>
    #include <vtkRenderWindowInteractor.h>
    #include <vtkRenderer.h>
    #include <vtkSmartPointer.h>
    #include <vtkTextMapper.h>
    #include <vtkTextProperty.h>

    #include <vtkParametricBoy.h>
    #include <vtkParametricConicSpiral.h>
    #include <vtkParametricCrossCap.h>
    #include <vtkParametricDini.h>
    #include <vtkParametricEllipsoid.h>
    #include <vtkParametricEnneper.h>
    #include <vtkParametricFigure8Klein.h>
    #include <vtkParametricKlein.h>
    #include <vtkParametricMobius.h>
    #include <vtkParametricRandomHills.h>
    #include <vtkParametricRoman.h>
    #include <vtkParametricSpline.h>
    #include <vtkParametricSuperEllipsoid.h>
    #include <vtkParametricSuperToroid.h>
    #include <vtkParametricTorus.h>
    // Extra parametric surfaces.
    #include <vtkParametricBohemianDome.h>
    #include <vtkParametricBour.h>
    #include <vtkParametricCatalanMinimal.h>
    #include <vtkParametricHenneberg.h>
    #include <vtkParametricKuen.h>
    #include <vtkParametricPluckerConoid.h>
    #include <vtkParametricPseudosphere.h>

    // For glyphing
    #include <vtkArrowSource.h>
    #include <vtkDataSet.h>
    #include <vtkGlyph3D.h>
    #include <vtkMaskPoints.h>

    // For writing out the image.
    #include <vtkBMPWriter.h>
    #include <vtkImageWriter.h>
    #include <vtkJPEGWriter.h>
    #include <vtkPNGWriter.h>
    #include <vtkPNMWriter.h>
    #include <vtkPostScriptWriter.h>
    #include <vtkTIFFWriter.h>
    #include <vtkWindowToImageFilter.h>

    #include <algorithm>
    #include <array>
    #include <iomanip>
    #include <iostream>
    #include <iterator>
    #include <locale>
    #include <map>
    #include <set>
    #include <sstream>
    #include <string>
    #include <vector>

    namespace {

    // Holds the arguments from the command line as a map.
    // e.g. key = name; value = (true|false,[value_0 ... value_n])
    typedef std::map<std::string, std::pair<bool, std::vector<std::string>>>
        TCmdArgs;

    class CommandLineParser
    {
    public:
      /**
       * @param argvArgs: the command line arguments as a vector of strings.
       * @param optArgs: the non-positional keys and their value.
       * @param optArgsParam: the non-positional keys that have parameters and their
       * value.
       * @param posNum: the expected number of positional variables.
       * @param posNumKName: the name of the positional values.
       */
      CommandLineParser(std::vector<std::string>& argvArgs,
                        std::map<std::string, std::string>& optArgs,
                        std::map<std::string, std::string>& optArgsParam,
                        int posNum = 0, std::string const& posName = "_PKN");

      ~CommandLineParser();

    public:
      /**
       * Parse the parameters from the command line.
       *
       * @return true if the parse was successful, false if unsuccessful.
       */
      bool Parse();

      /**
       * Get the parsed command line arguments.
       *
       * @return The parsed arguments.
       */
      TCmdArgs GetCommandArguments()
      {
        return this->cmdArgs;
      }

      /**
       * @return The error message if Parse() failed.
       */
      std::string GetParseError()
      {
        return this->parseError;
      }

      /**
       * @return The key name used to identify positional arguments.
       */
      std::string getPositionalKeyName()
      {
        return this->posName;
      }

      /**
       * @return A string of the parsed command arguments.
       */
      std::string DisplayCommandArguments();

    private:
      /**
       * Separate the key from the value, e.g -kv -> k v.
       *
       * @return The vector with the keys separated from their value(s).
       */
      std::vector<std::string> SeparateKV();

      /**
       * Find any unknown non-positional keys.
       *
       * @return If unknown keys were found, true is returned.
       */
      bool HasUnknownKeys();

      /**
       * Find any duplicate non-positional keys.
       *
       * @return If duplicate keys were found, true is returned.
       */
      bool HasDuplicateKeys();

      /**
       * Take a map and get the set of values in the map.
       *
       * @param m: The map.
       * @param s: The set of values from the map.
       */
      template <typename K, typename V>
      void GetSetOfValues(std::map<K, V> const& m, std::set<V>& s);

      /**
       * Build a map of aliases for the keys from the key/value pairs.
       *
       * @param m: A map of key, value pairs.
       * @param aliases: A map of aliases keyed by value.
       */
      template <typename K, typename V>
      void FindAliases(std::map<K, V> m,
                       std::map<V, std::pair<std::vector<K>, int>>& aliases);

    private:
      TCmdArgs cmdArgs;
      std::map<std::string, std::pair<std::vector<std::string>, int>> aliases;
      std::vector<std::string> cmdLineVec;
      std::map<std::string, std::string>& optArgs;
      std::map<std::string, std::string>& optArgsParam;
      int posNum;
      std::string posName;
      std::string parseError;
      std::vector<std::string> cl;
    };

    /**
     * Show the command lime parameters.
     *
     * @param fn: The program name.
     */
    std::string ShowUsage(std::string fn);

    /**
     * Create a map of the parametric functions and set some parameters.
     * The first key groups the parametric functions and the
     *   second key is the name of the function.
     *
     * @return The map of functions.
     */
    std::map<int, std::map<std::string, vtkSmartPointer<vtkParametricFunction>>>
    GetParametricFunctions();

    /**
     * Write the render window view to an image file.
     *
     * Image types supported are:
     *  BMP, JPEG, PNM, PNG, PostScript, TIFF.
     * The default parameters are used for all writers, change as needed.
     *
     * @param fileName The file name, if no extension then PNG is assumed.
     * @param renWin The render window.
     * @param rgba Used to set the buffer type.
     *
     */
    void WriteImage(std::string const& fileName, vtkRenderWindow* renWin,
                    bool rgba = true);

    /**
     * Get the centre of the object from the bounding box.
     */
    std::vector<double> GetCentre(const std::vector<double>& bounds);

    /**
     * Calculate the maximum length of side of the bounding box.
     */
    double GetMaximumLength(const std::vector<double>& bounds);

    /**
     * Display the dimensions of the bounding box, maximum diagonal length
     *    and coordinates of the centre.
     *
     * @param name: The name of the object.
     * @param index: The index of the object.
     * @param bounds: The bounding box of the object.
     *
     */
    void DisplayBoundingBoxAndCenter(std::string const& name, int const& index,
                                     std::vector<double> const& bounds);

    } // namespace

    int main(int argc, char* argv[])
    {
      // These two maps need to be filled in by the user.
      // key: Optional arguments such as -f or --foo with no parameters.
      // value: A suitable name. For the keys -f or --foo, the name would be the
      // same e.g f.
      std::map<std::string, std::string> optArgs;
      // key: Optional arguments requiring one or more paramters such as -s fn or
      // --some_file fn. value: A suitable name. For the keys -s or --some_file, the
      // name would be the same e.g s. To handle non-optional arguments we use a
      // special key: _PKN (which can be user defined).
      std::map<std::string, std::string> optArgsParam;

      // Specify key/value pairs for the arguments we want.
      optArgs["-b"] = "b";
      optArgs["-n"] = "n";
      optArgs["-w"] = "w";
      // These are followed by one or more parameters on the command line.
      optArgsParam["-s"] = "s";

      // The command line arguments
      std::vector<std::string> cmdVec;
      for (auto i = 1; i < argc; ++i)
      {
        cmdVec.push_back(argv[i]);
      }

      CommandLineParser clp(cmdVec, optArgs, optArgsParam);
      if (!cmdVec.empty())
      {
        // Usually -h and --help are reserved for help.
        if (std::any_of(cmdVec.begin(), cmdVec.end(), [](const std::string& str) {
              return str.size() > 0 && (str == "-h" || str == "--help");
            }))
        {
          std::cout << ShowUsage(argv[0]) << std::endl;
          return EXIT_SUCCESS;
        }
        if (!clp.Parse())
        {
          std::cerr << clp.GetParseError() << std::endl;
          std::cerr << ShowUsage(argv[0]) << std::endl;
          return EXIT_FAILURE;
        }
      }
      TCmdArgs cmdArgs = clp.GetCommandArguments();
      // std::cout << clp.DisplayCommandArguments() << std::endl;

      std::pair<std::string, int> singleSurface;
      if (cmdArgs["s"].first)
      {
        if (cmdArgs["s"].second.size() > 0)
        {
          singleSurface.first = cmdArgs["s"].second[0];
          singleSurface.second = -1;
        }
        else
        {
          std::cerr << "Surface name is missing." << std::endl;
          return EXIT_FAILURE;
        }
      }

      auto colors = vtkSmartPointer<vtkNamedColors>::New();

      auto rendererSize = 200;
      auto gridColumnDimensions = 5;
      auto gridRowDimensions = 5;

      if (cmdArgs["s"].first)
      {
        rendererSize = 800;
        gridColumnDimensions = 1;
        gridRowDimensions = 1;
      }

      // Create one text property for all
      auto textProperty = vtkSmartPointer<vtkTextProperty>::New();
      textProperty->SetJustificationToCentered();
      textProperty->SetFontSize(rendererSize / 12);
      textProperty->SetColor(colors->GetColor3d("LavenderBlush").GetData());

      // Create a parametric function source, renderer, mapper, and actor
      // for each object
      std::vector<vtkSmartPointer<vtkParametricFunctionSource>> pfnSrcs;
      std::vector<vtkSmartPointer<vtkRenderer>> renderers;
      std::vector<vtkSmartPointer<vtkPolyDataMapper>> mappers;
      std::vector<vtkSmartPointer<vtkActor>> actors;
      std::vector<vtkSmartPointer<vtkTextMapper>> textmappers;
      std::vector<vtkSmartPointer<vtkActor2D>> textactors;

      // Glyph the normals.
      std::vector<vtkSmartPointer<vtkMaskPoints>> maskPts;
      std::vector<vtkSmartPointer<vtkArrowSource>> arrow;
      std::vector<vtkSmartPointer<vtkGlyph3D>> glyph;
      std::vector<vtkSmartPointer<vtkPolyDataMapper>> glyphMapper;
      std::vector<vtkSmartPointer<vtkActor>> glyphActor;

      auto backProperty = vtkSmartPointer<vtkProperty>::New();
      if (cmdArgs["b"].first)
      {
        backProperty->SetColor(colors->GetColor3d("Peru").GetData());
      }

      std::vector<std::vector<double>> boundingBox;

      // Get the parametric functions and build the pipeline
      auto pfn = GetParametricFunctions();

      if (cmdArgs["s"].first)
      {
        // Is the surface name in the map?
        std::vector<bool> surfaceExists;
        for (auto& t : pfn)
        {
          if (t.second.find(cmdArgs["s"].second[0]) == t.second.end())
            surfaceExists.push_back(false);
          else
            surfaceExists.push_back(true);
        }
        if (std::find(std::begin(surfaceExists), std::end(surfaceExists), true) ==
            end(surfaceExists))
        {
          // All entries in surfaceExists are false
          std::cout << "Nonexistent surface: " << cmdArgs["s"].second[0]
                    << std::endl;
          return EXIT_FAILURE;
        }
      }

      // The count of parametric objects
      auto objCount = 0;
      std::vector<std::string> sortedNames;
      for (auto t : pfn)
      {
        for (auto obj : t.second)
        {
          sortedNames.push_back(obj.first);
          if (cmdArgs["s"].first)
          {
            if (obj.first == singleSurface.first)
            {
              singleSurface.second = objCount;
            }
          }
          pfnSrcs.push_back(vtkSmartPointer<vtkParametricFunctionSource>::New());
          pfnSrcs[objCount]->SetParametricFunction(pfn[t.first][obj.first]);
          pfnSrcs[objCount]->SetUResolution(51);
          pfnSrcs[objCount]->SetVResolution(51);
          pfnSrcs[objCount]->SetWResolution(51);
          pfnSrcs[objCount]->Update();

          mappers.push_back(vtkSmartPointer<vtkPolyDataMapper>::New());
          mappers[objCount]->SetInputConnection(pfnSrcs[objCount]->GetOutputPort());

          actors.push_back(vtkSmartPointer<vtkActor>::New());
          actors[objCount]->SetMapper(mappers[objCount]);
          actors[objCount]->GetProperty()->SetColor(
              colors->GetColor3d("NavajoWhite").GetData());
          if (cmdArgs["b"].first)
          {

            actors[objCount]->SetBackfaceProperty(backProperty);
          }

          textmappers.push_back(vtkSmartPointer<vtkTextMapper>::New());
          textmappers[objCount]->SetInput(obj.first.c_str());
          textmappers[objCount]->SetTextProperty(textProperty);

          textactors.push_back(vtkSmartPointer<vtkActor2D>::New());
          textactors[objCount]->SetMapper(textmappers[objCount]);
          textactors[objCount]->SetPosition(rendererSize / 2.0, 8);

          renderers.push_back(vtkSmartPointer<vtkRenderer>::New());

          double bounds[6];
          pfnSrcs[objCount]->GetOutput()->GetBounds(bounds);
          std::vector<double> v(std::begin(bounds), std::end(bounds));
          boundingBox.push_back(v);
          // DisplayBoundingBoxAndCenter(obj.first, objCount, v);

          if (cmdArgs["n"].first)
          {
            // Glyphing
            maskPts.push_back(vtkSmartPointer<vtkMaskPoints>::New());
            maskPts[objCount]->RandomModeOn();
            maskPts[objCount]->SetMaximumNumberOfPoints(150);
            maskPts[objCount]->SetInputConnection(
                pfnSrcs[objCount]->GetOutputPort());

            arrow.push_back(vtkSmartPointer<vtkArrowSource>::New());
            arrow[objCount]->SetTipResolution(16);
            arrow[objCount]->SetTipLength(0.3);
            arrow[objCount]->SetTipRadius(0.1);

            double glyphScale = GetMaximumLength(boundingBox[objCount]);

            glyph.push_back(vtkSmartPointer<vtkGlyph3D>::New());
            glyph[objCount]->SetSourceConnection(arrow[objCount]->GetOutputPort());
            glyph[objCount]->SetInputConnection(maskPts[objCount]->GetOutputPort());
            glyph[objCount]->SetVectorModeToUseNormal();
            glyph[objCount]->SetScaleFactor(glyphScale / 10.0);
            glyph[objCount]->OrientOn();
            glyph[objCount]->Update();

            glyphMapper.push_back(vtkSmartPointer<vtkPolyDataMapper>::New());
            glyphMapper[objCount]->SetInputConnection(
                glyph[objCount]->GetOutputPort());

            glyphActor.push_back(vtkSmartPointer<vtkActor>::New());
            glyphActor[objCount]->SetMapper(glyphMapper[objCount]);
            glyphActor[objCount]->GetProperty()->SetColor(
                colors->GetColor3d("GreenYellow").GetData());
          }
          objCount++;
        }
      }

      // Need a renderer even if there is no actor
      for (auto i = objCount; i < gridColumnDimensions * gridRowDimensions; i++)
      {
        renderers.push_back(vtkSmartPointer<vtkRenderer>::New());
        static_cast<vtkRenderer*>(renderers.back().GetPointer())
            ->SetBackground(colors->GetColor3d("MidnightBlue").GetData());
        sortedNames.push_back("");
      }

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

      for (auto row = 0; row < gridRowDimensions; row++)
      {
        for (auto col = 0; col < gridColumnDimensions; col++)
        {
          // (xmin, ymin, xmax, ymax)
          double viewport[4] = {
              static_cast<double>(col) * rendererSize /
                  (gridColumnDimensions * rendererSize),
              static_cast<double>(gridRowDimensions - (row + 1)) * rendererSize /
                  (gridRowDimensions * rendererSize),
              static_cast<double>(col + 1) * rendererSize /
                  (gridColumnDimensions * rendererSize),
              static_cast<double>(gridRowDimensions - row) * rendererSize /
                  (gridRowDimensions * rendererSize)};
          if (!cmdArgs["s"].first)
          {
            auto index = row * gridColumnDimensions + col;
            renderWindow->AddRenderer(renderers[index]);
            renderers[index]->SetViewport(viewport);
            if (index > objCount - 1)
            {
              continue;
            }
            renderers[index]->AddActor(actors[index]);
            // Normals can only be computed for polygons and triangle strips.
            // The Spline is a line.
            if (cmdArgs["n"].first && sortedNames[index] != "Spline")
            {
              renderers[index]->AddActor(glyphActor[index]);
            }
            renderers[index]->AddActor(textactors[index]);
            renderers[index]->SetBackground(
                colors->GetColor3d("MidnightBlue").GetData());
            renderers[index]->ResetCamera();
            renderers[index]->GetActiveCamera()->Azimuth(30);
            renderers[index]->GetActiveCamera()->Elevation(-30);
            renderers[index]->GetActiveCamera()->Zoom(0.9);
            renderers[index]->ResetCameraClippingRange();
          }

          else
          {
            auto index = singleSurface.second;
            if (index != -1)
            {
              renderWindow->AddRenderer(renderers[index]);
              renderers[index]->SetViewport(viewport);
              renderers[index]->AddActor(actors[index]);
              // Normals can only be computed for polygons and triangle strips.
              // The Spline is a line.
              if (cmdArgs["n"].first && singleSurface.first != "Spline")
              {
                renderers[index]->AddActor(glyphActor[index]);
              }
              renderers[index]->AddActor(textactors[index]);
              renderers[index]->SetBackground(
                  colors->GetColor3d("MidnightBlue").GetData());
              renderers[index]->ResetCamera();
              renderers[index]->GetActiveCamera()->Azimuth(30);
              renderers[index]->GetActiveCamera()->Elevation(-30);
              renderers[index]->GetActiveCamera()->Zoom(0.9);
              renderers[index]->ResetCameraClippingRange();
            }
          }
        }
      }

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

      renderWindow->Render();
      if (cmdArgs["s"].first)
      {
        renderWindow->SetWindowName(singleSurface.first.c_str());
      }
      else
      {
        renderWindow->SetWindowName("ParametricObjectsDemo");
      }
      renderWindow->Render();
      if (cmdArgs["w"].first)
      {
        // -------------------------------
        // Save the image
        // -------------------------------
        if (cmdArgs["s"].first)
        {
          WriteImage(singleSurface.first, renderWindow, false);
        }
        else
        {
          WriteImage("ParametricObjectsDemo", renderWindow, false);
        }
      }

      interactor->Start();

      return EXIT_SUCCESS;
    }

    namespace {

    std::string ShowUsage(std::string fn)
    {
      // Remove the folder (if present) then remove the extension in this order
      // since the folder name may contain perionds.
      auto last_slash_idx = fn.find_last_of("\\/");
      if (std::string::npos != last_slash_idx)
      {
        fn.erase(0, last_slash_idx + 1);
      }
      auto period_idx = fn.rfind('.');
      if (std::string::npos != period_idx)
      {
        fn.erase(period_idx);
      }
      std::ostringstream os;
      os << "\nusage: " << fn << "[-h][-s SURFACE_NAME][-w][-b][-n]\n\n"
         << "Display the parametric surfaces.\n\n"
         << "optional arguments:\n"
         << "  -h                    show this help message and exit\n"
         << "  -s SURFACE_NAME       The name of the surface.\n"
         << "  -w                    Write out the the image.\n"
         << "  -b                    Color the back-face.\n"
         << "  -n                    Display normals.\n"
         << std::endl;
      return os.str();
    }

    std::map<int, std::map<std::string, vtkSmartPointer<vtkParametricFunction>>>
    GetParametricFunctions()
    {
      std::map<int, std::map<std::string, vtkSmartPointer<vtkParametricFunction>>>
          pfn;
      pfn[0]["Boy"] = vtkSmartPointer<vtkParametricBoy>::New();
      pfn[0]["ConicSpiral"] = vtkSmartPointer<vtkParametricConicSpiral>::New();
      pfn[0]["CrossCap"] = vtkSmartPointer<vtkParametricCrossCap>::New();
      pfn[0]["Dini"] = vtkSmartPointer<vtkParametricDini>::New();
      pfn[0]["Ellipsoid"] = vtkSmartPointer<vtkParametricEllipsoid>::New();
      pfn[0]["Enneper"] = vtkSmartPointer<vtkParametricEnneper>::New();
      pfn[0]["Figure8Klein"] = vtkSmartPointer<vtkParametricFigure8Klein>::New();
      pfn[0]["Klein"] = vtkSmartPointer<vtkParametricKlein>::New();
      pfn[0]["Mobius"] = vtkSmartPointer<vtkParametricMobius>::New();
      pfn[0]["RandomHills"] = vtkSmartPointer<vtkParametricRandomHills>::New();
      pfn[0]["Roman"] = vtkSmartPointer<vtkParametricRoman>::New();
      pfn[0]["SuperEllipsoid"] =
          vtkSmartPointer<vtkParametricSuperEllipsoid>::New();
      pfn[0]["SuperToroid"] = vtkSmartPointer<vtkParametricSuperToroid>::New();
      pfn[0]["Torus"] = vtkSmartPointer<vtkParametricTorus>::New();
      pfn[0]["Spline"] = vtkSmartPointer<vtkParametricSpline>::New();
      // Extra parametric surfaces.
      pfn[1]["BohemianDome"] = vtkSmartPointer<vtkParametricBohemianDome>::New();
      pfn[1]["Bour"] = vtkSmartPointer<vtkParametricBour>::New();
      pfn[1]["CatalanMinimal"] =
          vtkSmartPointer<vtkParametricCatalanMinimal>::New();
      pfn[1]["Henneberg"] = vtkSmartPointer<vtkParametricHenneberg>::New();
      pfn[1]["Kuen"] = vtkSmartPointer<vtkParametricKuen>::New();
      pfn[1]["PluckerConoid"] = vtkSmartPointer<vtkParametricPluckerConoid>::New();
      pfn[1]["Pseudosphere"] = vtkSmartPointer<vtkParametricPseudosphere>::New();

      // Now set some parameters.
      static_cast<vtkParametricEllipsoid*>(pfn[0]["Ellipsoid"].GetPointer())
          ->SetXRadius(0.5);
      static_cast<vtkParametricEllipsoid*>(pfn[0]["Ellipsoid"].GetPointer())
          ->SetYRadius(2.0);
      static_cast<vtkParametricMobius*>(pfn[0]["Mobius"].GetPointer())
          ->SetRadius(2.0);
      static_cast<vtkParametricMobius*>(pfn[0]["Mobius"].GetPointer())
          ->SetMinimumV(-0.5);
      static_cast<vtkParametricMobius*>(pfn[0]["Mobius"].GetPointer())
          ->SetMaximumV(0.5);
      static_cast<vtkParametricRandomHills*>(pfn[0]["RandomHills"].GetPointer())
          ->AllowRandomGenerationOn();
      static_cast<vtkParametricRandomHills*>(pfn[0]["RandomHills"].GetPointer())
          ->SetRandomSeed(1);
      static_cast<vtkParametricRandomHills*>(pfn[0]["RandomHills"].GetPointer())
          ->SetNumberOfHills(30);
      static_cast<vtkParametricSuperEllipsoid*>(
          pfn[0]["SuperEllipsoid"].GetPointer())
          ->SetN1(0.5);
      static_cast<vtkParametricSuperEllipsoid*>(
          pfn[0]["SuperEllipsoid"].GetPointer())
          ->SetN2(0.4);
      static_cast<vtkParametricSuperToroid*>(pfn[0]["SuperToroid"].GetPointer())
          ->SetN1(0.5);
      static_cast<vtkParametricSuperToroid*>(pfn[0]["SuperToroid"].GetPointer())
          ->SetN2(3.0);
      // The spline needs points
      auto inputPoints = vtkSmartPointer<vtkPoints>::New();
      auto rng = vtkSmartPointer<vtkMinimalStandardRandomSequence>::New();
      rng->SetSeed(8775070);
      for (auto p = 0; p < 10; p++)
      {
        std::array<double, 3> xyz;
        for (auto& idx : xyz)
        {
          idx = rng->GetRangeValue(-1.0, 1.0);
          rng->Next();
        }
        inputPoints->InsertNextPoint(xyz.data());
      }
      static_cast<vtkParametricSpline*>(pfn[0]["Spline"].GetPointer())
          ->SetPoints(inputPoints);
      // Extra parametric surfaces.
      static_cast<vtkParametricBohemianDome*>(pfn[1]["BohemianDome"].GetPointer())
          ->SetA(5.0);
      static_cast<vtkParametricBohemianDome*>(pfn[1]["BohemianDome"].GetPointer())
          ->SetB(1.0);
      static_cast<vtkParametricBohemianDome*>(pfn[1]["BohemianDome"].GetPointer())
          ->SetC(2.0);
      static_cast<vtkParametricKuen*>(pfn[1]["Kuen"].GetPointer())
          ->SetDeltaV0(0.001);
      return pfn;
    }

    std::vector<double> GetCentre(const std::vector<double>& bounds)
    {
      std::vector<double> centre;
      if (bounds.size() != 6)
      {
        return centre;
      }
      for (unsigned int i = 1; i < bounds.size(); i += 2)
      {
        centre.push_back(bounds[i] - (bounds[i] - bounds[i - 1]) / 2.0);
      }
      return centre;
    }

    double GetMaximumLength(const std::vector<double>& bounds)
    {
      auto maxLen = -1.0;
      if (bounds.size() != 6)
      {
        return maxLen;
      }
      for (auto i = 0; i < int(bounds.size()); i += 2)
      {
        maxLen = std::max(maxLen, std::abs(bounds[i + 1] - bounds[i]));
      }
      return maxLen;
    }

    void DisplayBoundingBoxAndCenter(std::string const& name, int const& index,
                                     std::vector<double> const& bounds)
    {
      if (bounds.size() != 6)
      {
        return;
      }
      auto maxLength = GetMaximumLength(bounds);
      auto centre = GetCentre(bounds);
      std::cout << std::left << std::setw(21) << name << std::right << ": "
                << std::setw(2) << index << "\n"
                << std::left << std::setw(21) << "  Bounds (min, max)"
                << ": x:(" << std::right << std::fixed << std::setw(6)
                << std::setprecision(2) << bounds[0] << ", " << std::setw(6)
                << bounds[1] << ") y:(" << std::setw(6) << bounds[2] << ", "
                << std::setw(6) << bounds[3] << ") z:(" << std::setw(6) << bounds[4]
                << ", " << std::setw(6) << bounds[5] << ")\n"
                << std::left << std::setw(21) << "  Maximum side length"
                << ": " << std::right << std::setw(6) << maxLength << "\n"
                << std::left << std::setw(21) << "  Centre (x, y, z)"
                << ": (" << std::right << std::setw(6) << centre[0] << ", "
                << std::setw(6) << centre[1] << ", " << std::setw(6) << centre[2]
                << ")\n"
                << std::endl;
    }

    void WriteImage(std::string const& fileName, vtkRenderWindow* renWin, bool rgba)
    {
      if (!fileName.empty())
      {
        std::string fn = fileName;
        std::string ext;
        auto found = fn.find_last_of(".");
        if (found == std::string::npos)
        {
          ext = ".png";
          fn += ext;
        }
        else
        {
          ext = fileName.substr(found, fileName.size());
        }
        std::locale loc;
        std::transform(ext.begin(), ext.end(), ext.begin(),
                       [=](char const& c) { return std::tolower(c, loc); });
        auto writer = vtkSmartPointer<vtkImageWriter>::New();
        if (ext == ".bmp")
        {
          writer = vtkSmartPointer<vtkBMPWriter>::New();
        }
        else if (ext == ".jpg")
        {
          writer = vtkSmartPointer<vtkJPEGWriter>::New();
        }
        else if (ext == ".pnm")
        {
          writer = vtkSmartPointer<vtkPNMWriter>::New();
        }
        else if (ext == ".ps")
        {
          if (rgba)
          {
            rgba = false;
          }
          writer = vtkSmartPointer<vtkPostScriptWriter>::New();
        }
        else if (ext == ".tiff")
        {
          writer = vtkSmartPointer<vtkTIFFWriter>::New();
        }
        else
        {
          writer = vtkSmartPointer<vtkPNGWriter>::New();
        }
        auto window_to_image_filter =
            vtkSmartPointer<vtkWindowToImageFilter>::New();
        window_to_image_filter->SetInput(renWin);
        window_to_image_filter->SetScale(1); // image quality
        if (rgba)
        {
          window_to_image_filter->SetInputBufferTypeToRGBA();
        }
        else
        {
          window_to_image_filter->SetInputBufferTypeToRGB();
        }
        // Read from the front buffer.
        window_to_image_filter->ReadFrontBufferOff();
        window_to_image_filter->Update();

        writer->SetFileName(fn.c_str());
        writer->SetInputConnection(window_to_image_filter->GetOutputPort());
        writer->Write();
      }
      else
      {
        std::cerr << "No filename provided." << std::endl;
      }

      return;
    }

    CommandLineParser::CommandLineParser(
        std::vector<std::string>& cmdLineVec,
        std::map<std::string, std::string>& optArgs,
        std::map<std::string, std::string>& optArgsParam, int posNum,
        std::string const& posName)
      : cmdLineVec(cmdLineVec),
        optArgs(optArgs),
        optArgsParam(optArgsParam),
        posNum(posNum),
        posName(posName)
    {
      // Make a set of all the values.
      std::set<std::string> pVals;
      this->GetSetOfValues(this->optArgs, pVals);
      this->GetSetOfValues(this->optArgsParam, pVals);

      // Set the default arguments
      for (auto p : pVals)
      {
        this->cmdArgs[p].first = false;
      }

      // Get the aliases
      this->FindAliases(this->optArgsParam, this->aliases);
      this->FindAliases(this->optArgs, this->aliases);

      cl = this->SeparateKV();
    }

    CommandLineParser::~CommandLineParser() = default;

    std::vector<std::string> CommandLineParser::SeparateKV()
    {
      // For keys with parameters, short commands like -xy need to be split into
      // -x y.
      std::vector<std::string> cl;
      if (!this->optArgsParam.empty())
      {
        for (auto v : this->cmdLineVec)
        {
          auto a = v.substr(0, 2);
          if (this->optArgsParam.count(a) > 0 && v.size() > 2)
          {
            cl.push_back(a);
            cl.push_back(v.substr(2));
          }
          else
          {
            cl.push_back(v);
          }
        }
      }
      return cl;
    }

    bool CommandLineParser::HasUnknownKeys()
    {
      auto hasKV = !this->optArgsParam.empty();
      auto hasNKV = !this->optArgs.empty();
      std::vector<std::string> unknownKeys;
      for (auto v : this->cl)
      {
        if (v[0] == '-' || v.substr(0, 2) == "--")
        {
          if ((hasKV && this->optArgsParam.count(v) > 0) ||
              (hasNKV && this->optArgs.count(v) > 0))
          {
            continue;
          }
          else
          {
            unknownKeys.push_back(v);
          }
        }
      }
      if (unknownKeys.size() > 0)
      {
        std::ostringstream os;
        os << "Unknown parameters found: ";
        std::copy(std::begin(unknownKeys), std::prev(std::end(unknownKeys)),
                  std::ostream_iterator<std::string>(os, ", "));
        os << unknownKeys.back();
        this->parseError = os.str();
        return true;
      }
      return false;
    }

    bool CommandLineParser::HasDuplicateKeys()
    {
      // Look for duplicate non-positional parameters.
      for (auto k : this->optArgsParam)
      {
        auto c = std::count(this->cl.begin(), this->cl.end(), k.first);
        this->aliases[k.second].second += int(c);
      }
      for (auto k : this->optArgs)
      {
        auto c = std::count(this->cl.begin(), this->cl.end(), k.first);
        this->aliases[k.second].second += int(c);
      }
      std::map<std::string, std::vector<std::string>> duplicates;
      for (auto v : this->aliases)
      {
        if (v.second.second > 1)
        {
          duplicates[v.first] = v.second.first;
        }
      }
      if (duplicates.size() > 0)
      {
        std::ostringstream os;
        os << "Duplicated parameters found: ";
        for (auto d : duplicates)
        {
          os << "(";
          std::copy(std::begin(d.second), std::prev(std::end(d.second)),
                    std::ostream_iterator<std::string>(os, ", "));
          os << d.second.back();
          os << ") ";
        }
        // Get rid of trailing spaces
        auto last = os.str().find_last_not_of(' ');
        this->parseError = os.str().substr(0, last + 1);
        return true;
      }
      return false;
    }

    bool CommandLineParser::Parse()
    {
      this->parseError.clear();

      if (!this->cl.empty())
      {
        if (HasUnknownKeys() || HasDuplicateKeys())
        {
          return false;
        }

        std::vector<std::string> positionalArguments;
        for (auto it = this->cl.begin(); it != this->cl.end(); ++it)
        {
          if (!this->optArgs.empty())
          {
            if (this->optArgs.count(*it) > 0)
            {
              this->cmdArgs[this->optArgs[*it]].first = true;
              continue;
            }
          }
          if (!this->optArgsParam.empty())
          {
            if (this->optArgsParam.count(*it) > 0)
            {
              if (std::next(it) != this->cl.end())
              {
                auto key = this->optArgsParam[*it];
                while (std::next(it) != this->cl.end())
                {
                  if ((*std::next(it))[0] == '-')
                  {
                    break;
                  }
                  ++it;

                  std::string fn = *it;
                  if (fn[0] != '-')
                  {
                    if (!this->cmdArgs[key].first)
                    {
                      this->cmdArgs[key].first = true;
                    }
                    this->cmdArgs[key].second.push_back(fn);
                  }
                  else
                  {
                    if (this->cmdArgs[key].second.empty())
                    {
                      std::ostringstream os;
                      os << key << " must be followed by a parameter.";
                      this->parseError = os.str();
                      return false;
                    }
                    else
                    {
                      break;
                    }
                  }
                }
              }
              else
              {
                std::ostringstream os;
                os << *it
                   << " must be followed by a parameter, reached the end of the "
                      "commands.";
                this->parseError = os.str();
                return false;
              }
              continue;
            }
          }
          positionalArguments.push_back(*it);
        }
        if (this->posNum != int(positionalArguments.size()))
        {
          std::ostringstream os;
          os << "Expected " << this->posNum << " positional arguments, got "
             << positionalArguments.size() << " instead.";
          this->parseError = os.str();
          return false;
        }
        if (!positionalArguments.empty())
        {
          this->cmdArgs[this->posName].first = true;
          this->cmdArgs[this->posName].second = positionalArguments;
        }
        else
        {
          this->cmdArgs[this->posName].first = false;
        }
      }
      return true;
    }

    std::string CommandLineParser::DisplayCommandArguments()
    {
      std::vector<std::string> setParameters;
      std::vector<std::string> unSetParameters;
      for (auto k : this->cmdArgs)
      {
        if (this->cmdArgs[k.first].first)
        {
          setParameters.push_back(k.first);
        }
        else
        {
          unSetParameters.push_back(k.first);
        }
      }
      // Sort them
      std::sort(setParameters.begin(), setParameters.end());
      std::sort(unSetParameters.begin(), unSetParameters.end());

      std::ostringstream os;
      if (setParameters.size() > 0)
      {
        os << "Set parameters:" << std::endl;
        for (auto k : setParameters)
        {
          if (this->cmdArgs[k].first)
          {
            os << "  " << k;
            if (!this->cmdArgs[k].second.empty())
            {
              os << ": ";
              std::copy(std::begin(cmdArgs[k].second),
                        std::prev(std::end(cmdArgs[k].second)),
                        std::ostream_iterator<std::string>(os, ", "));
              os << this->cmdArgs[k].second.back();
            }
            os << std::endl;
          }
        }
      }

      if (unSetParameters.size() > 0)
      {
        os << "Unset parameters:" << std::endl;
        for (auto k : unSetParameters)
        {
          if (!this->cmdArgs[k].first)
          {
            os << "  " << k;
            if (!this->cmdArgs[k].second.empty())
            {
              os << ": ";
              std::copy(std::begin(this->cmdArgs[k].second),
                        std::prev(std::end(this->cmdArgs[k].second)),
                        std::ostream_iterator<std::string>(os, ", "));
              os << this->cmdArgs[k].second.back();
            }
            os << std::endl;
          }
        }
      }
      return os.str();
    }

    template <typename K, typename V>
    void CommandLineParser::GetSetOfValues(std::map<K, V> const& m, std::set<V>& s)
    {
      std::for_each(m.begin(), m.end(), [&](const std::pair<const K, V>& element) {
        s.insert(element.second);
      });
    }

    template <typename K, typename V>
    void CommandLineParser::FindAliases(
        std::map<K, V> m, std::map<V, std::pair<std::vector<K>, int>>& aliases)
    {
      std::set<V> values;
      this->GetSetOfValues(m, values);
      for (auto v : values)
      {
        std::vector<K> a;
        for (auto it : m)
        {
          if (it.second == v)
          {
            a.push_back(it.first);
          }
        }
        if (a.size() > 0)
        {
          aliases[v] = std::pair<std::vector<K>, int>(a, 0);
        }
      }
    }

    } // namespace

### CMakeLists.txt

    cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

    project(ParametricObjectsDemo)

    find_package(VTK COMPONENTS
      vtkCommonColor
      vtkCommonComputationalGeometry
      vtkCommonCore
      vtkCommonDataModel
      vtkFiltersCore
      vtkFiltersSources
      vtkIOImage
      vtkInteractionStyle
      vtkRenderingContextOpenGL2
      vtkRenderingCore
      vtkRenderingFreeType
      vtkRenderingGL2PSOpenGL2
      vtkRenderingOpenGL2 QUIET)
    if (NOT VTK_FOUND)
      message("Skipping ParametricObjectsDemo: ${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(ParametricObjectsDemo MACOSX_BUNDLE ParametricObjectsDemo.cxx )
      target_link_libraries(ParametricObjectsDemo PRIVATE ${VTK_LIBRARIES})
    else ()
      # include all components
      add_executable(ParametricObjectsDemo MACOSX_BUNDLE ParametricObjectsDemo.cxx )
      target_link_libraries(ParametricObjectsDemo PRIVATE ${VTK_LIBRARIES})
      # vtk_module_autoinit is needed
      vtk_module_autoinit(
        TARGETS ParametricObjectsDemo
        MODULES ${VTK_LIBRARIES}
        )
    endif ()

### Download and Build ParametricObjectsDemo

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

    cd ParametricObjectsDemo/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:

    ./ParametricObjectsDemo

WINDOWS USERS

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