# KochSnowflake

VTKExamples/Cxx/Visualization/KochSnowflake

### Description

This demo uses recursion to represent a Koch snowflake fractal. For more information about this fractal, there are many resources on the web: http://en.wikipedia.org/wiki/Koch_snowflake, http://mathworld.wolfram.com/KochSnowflake.html.

Other Languages

See (Python)

### Code

KochSnowflake.cxx

    #include <vtkSmartPointer.h>
    #include <vtkPoints.h>
    #include <vtkMath.h>
    #include <vtkCellArray.h>
    #include <vtkPolyData.h>
    #include <vtkIntArray.h>
    #include <vtkPolyDataMapper.h>
    #include <vtkActor.h>
    #include <vtkRenderer.h>
    #include <vtkRenderWindow.h>
    #include <vtkRenderWindowInteractor.h>
    #include <vtkLookupTable.h>
    #include <vtkTriangle.h>
    #include <vtkPolyLine.h>
    #include <vtkCellData.h>

    # define VTK_CREATE(type, name) \
      vtkSmartPointer<type> name = vtkSmartPointer<type>::New()

    # define LEVEL 6

    /*----------------------------------------------------------------------------*
     *                       Koch Snowflake as vtkPolyLine                        *
     *----------------------------------------------------------------------------*/
    vtkSmartPointer<vtkPolyData> as_polyline(vtkSmartPointer<vtkPoints> points, int level)
    {
      // Use the points from the previous iteration to create the points of the
      // next level. There is an assumption on my part that the curve is traversed
      // in a counterclockwise fashion. If the initial triangle above is written to
      // describe clockwise motion, the points will face inward instead of outward.
      for (int i = 0; i < level; i++)
      {
        // We're going to make the next set of points from the old one and swap
        // them at the end. The vtkSmartPointer will go out of scope and be
        // deleted.
        VTK_CREATE(vtkPoints, temp);
        double v0[3];
        double v1[3];

        // The first point of the previous vtkPoints is the first point of the next vtkPoints.
        points->GetPoint(0, v0);
        temp->InsertNextPoint(v0);

        // Iterate over "edges" in the vtkPoints
        for (int ii = 1; ii < points->GetNumberOfPoints(); ii++)
        {
          points->GetPoint(ii - 1, v0);
          points->GetPoint(ii, v1);
          double t = sqrt(vtkMath::Distance2BetweenPoints(v0, v1));
          double nx = (v1[0] - v0[0])/t; // x-component of edge unit tangent
          double ny = (v1[1] - v0[1])/t; // y-component of edge unit tangent

          v1[0] = v0[0] + nx*t/3.;
          v1[1] = v0[1] + ny*t/3.;
          v1[2] = 0.;
          temp->InsertNextPoint(v1);

          v1[0] = v0[0] + t*(nx/2. + ny*sqrt(3.)/6.);
          v1[1] = v0[1] + t*(ny/2. - nx*sqrt(3.)/6.);
          v1[2] = 0.;
          temp->InsertNextPoint(v1);

          v1[0] = v0[0] + 2./3.*nx*t;
          v1[1] = v0[1] + 2./3.*ny*t;
          v1[2] = 0.;
          temp->InsertNextPoint(v1);

          v1[0] = v0[0] + nx*t;
          v1[1] = v0[1] + ny*t;
          v1[2] = 0.;
          temp->InsertNextPoint(v1);
        }
        points = temp;
      }

      // draw the outline
      VTK_CREATE(vtkCellArray, lines);
      VTK_CREATE(vtkPolyLine, pl);
      pl->GetPointIds()->SetNumberOfIds(points->GetNumberOfPoints());
      for (int i = 0; i < points->GetNumberOfPoints(); i++)
      {
        pl->GetPointIds()->SetId(i, i);
      }
      lines->InsertNextCell(pl);

      // complete the polydata
      VTK_CREATE(vtkPolyData, polydata);
      polydata->SetLines(lines);
      polydata->SetPoints(points);

      return polydata;
    }

    /*----------------------------------------------------------------------------*
     *                Koch Snowflake as collection of vtkTriangles                *
     *----------------------------------------------------------------------------*/
    void as_triangles(int start, int end, vtkCellArray *cells, int level, vtkIntArray *data)
    {
      if (end - start >= 3)
      {
        int stride = (end - start + 1)/4;

        VTK_CREATE(vtkTriangle, triangle);
        triangle->GetPointIds()->SetId(0, start +   stride);
        triangle->GetPointIds()->SetId(1, start + 2*stride);
        triangle->GetPointIds()->SetId(2, start + 3*stride);

        cells->InsertNextCell(triangle);
        data->InsertNextValue(level);

        as_triangles(start,            start +   stride, cells, level + 1, data);
        as_triangles(start +   stride, start + 2*stride, cells, level + 1, data);
        as_triangles(start + 2*stride, start + 3*stride, cells, level + 1, data);
        as_triangles(start + 3*stride, start + 4*stride, cells, level + 1, data);
      }
    }

    /*----------------------------------------------------------------------------*
     *                                Main Method                                 *
     *----------------------------------------------------------------------------*/
    int main(int, char *[]) {

      // Initially, set up the points to be an equilateral triangle. Note that the
      // first point is the same as the last point to make this a closed curve when
      // I create the vtkPolyLine.
      VTK_CREATE(vtkPoints, points);
      for (int i = 0; i < 4; i++) {
        points->InsertNextPoint(cos(2.*vtkMath::Pi()*i/3), sin(2*vtkMath::Pi()*i/3.), 0.);
      }

      vtkSmartPointer<vtkPolyData> outline_pd  = as_polyline(points, LEVEL);
      // You have already gone through the trouble of putting the points in the
      // right places - so "all" you need to do now is to create polygons from the
      // points that are in the vtkPoints.

      // The points that are passed in, have an overlap of the beginning and the end.

      // Set this up for each of the initial sides, then call the recursive function.
      VTK_CREATE(vtkCellArray, triangles);
      int stride = outline_pd->GetPoints()->GetNumberOfPoints()/3;

      // The cell data will allow us to color the triangles based on the level of
      // the iteration of the Koch snowflake.
      VTK_CREATE(vtkIntArray, data);
      data->SetNumberOfComponents(0);
      data->SetName("Iteration Level");

      // This is the starting triangle.
      VTK_CREATE(vtkTriangle, t);
      t->GetPointIds()->SetId(0,        0);
      t->GetPointIds()->SetId(1,   stride);
      t->GetPointIds()->SetId(2, 2*stride);
      triangles->InsertNextCell(t);
      data->InsertNextValue(0);

      as_triangles(       0,   stride, triangles, 1, data);
      as_triangles(  stride, 2*stride, triangles, 1, data);
      as_triangles(2*stride, 3*stride, triangles, 1, data);

      VTK_CREATE(vtkPolyData, triangle_pd);
      triangle_pd->SetPoints(outline_pd->GetPoints());
      triangle_pd->SetPolys(triangles);
      triangle_pd->GetCellData()->SetScalars(data);

      //-----------------//
      // rendering stuff //
      //-----------------//
      VTK_CREATE(vtkPolyDataMapper, outline_mapper);
      outline_mapper->SetInputData(outline_pd);

      VTK_CREATE(vtkLookupTable, lut);
      lut->SetNumberOfTableValues(256);
      lut->SetHueRange(0.6, 0.6);
      lut->SetSaturationRange(0., 1.);
      lut->Build();

      VTK_CREATE(vtkPolyDataMapper, triangle_mapper);
      triangle_mapper->SetInputData(triangle_pd);
      triangle_mapper->SetScalarRange(0.0, LEVEL);
      triangle_mapper->SetLookupTable(lut);

      VTK_CREATE(vtkActor, outline_actor);
      outline_actor->SetMapper(outline_mapper);

      VTK_CREATE(vtkActor, triangle_actor);
      triangle_actor->SetMapper(triangle_mapper);

      VTK_CREATE(vtkRenderer, outline_ren);
      outline_ren->AddActor(outline_actor);
      outline_ren->SetViewport(0.0, 0.0, 0.5, 1.0);

      VTK_CREATE(vtkRenderer, triangle_ren);
      triangle_ren->AddActor(triangle_actor);
      triangle_ren->SetViewport(0.5, 0.0, 1.0, 1.0);
      triangle_ren->SetActiveCamera(outline_ren->GetActiveCamera());

      VTK_CREATE(vtkRenderWindow, renw);
      renw->SetMultiSamples(0);
      renw->AddRenderer(outline_ren);
      renw->AddRenderer(triangle_ren);
      renw->SetSize(800, 400);

      VTK_CREATE(vtkRenderWindowInteractor, iren);
      iren->SetRenderWindow(renw);

      outline_ren->ResetCamera();
      renw->Render();
      iren->Start();

      return EXIT_SUCCESS;
    }

### CMakeLists.txt

    cmake_minimum_required(VERSION 2.8)

    PROJECT(KochSnowflake)

    find_package(VTK REQUIRED)
    include(${VTK_USE_FILE})

    add_executable(KochSnowflake MACOSX_BUNDLE KochSnowflake.cxx )

    target_link_libraries(KochSnowflake ${VTK_LIBRARIES})

### Download and Build KochSnowflake

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

    cd KochSnowflake/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:

    ./KochSnowflake

WINDOWS USERS

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