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KochSnowflake

vtk-examples/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)

Question

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

Code

KochSnowflake.cxx

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

namespace {

constexpr int LEVEL = 6;

/*----------------------------------------------------------------------------*
 *                       Koch Snowflake as vtkPolyLine                        *
 *----------------------------------------------------------------------------*/
vtkSmartPointer<vtkPolyData> as_polyline(vtkSmartPointer<vtkPoints> points,
                                         int level);

/*----------------------------------------------------------------------------*
 *                Koch Snowflake as collection of vtkTriangles                *
 *----------------------------------------------------------------------------*/
void as_triangles(int start, int end, vtkCellArray* cells, int level,
                  vtkIntArray* data);

} // namespace

/*----------------------------------------------------------------------------*
 *                                Main Method                                 *
 *----------------------------------------------------------------------------*/
int main(int, char*[])
{
  vtkNew<vtkNamedColors> colors;

  // 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.
  vtkNew<vtkPoints> points;
  for (int i = 0; i < 4; i++)
  {
    points->InsertNextPoint(cos(2. * vtkMath::Pi() * i / 3),
                            sin(2 * vtkMath::Pi() * i / 3.), 0.);
  }

  auto 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.
  vtkNew<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.
  vtkNew<vtkIntArray> data;
  data->SetNumberOfComponents(0);
  data->SetName("Iteration Level");

  // This is the starting triangle.
  vtkNew<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);

  vtkNew<vtkPolyData> triangle_pd;
  triangle_pd->SetPoints(outline_pd->GetPoints());
  triangle_pd->SetPolys(triangles);
  triangle_pd->GetCellData()->SetScalars(data);

  //-----------------//
  // rendering stuff //
  //-----------------//
  vtkNew<vtkPolyDataMapper> outline_mapper;
  outline_mapper->SetInputData(outline_pd);

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

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

  vtkNew<vtkActor> outline_actor;
  outline_actor->SetMapper(outline_mapper);

  vtkNew<vtkActor> triangle_actor;
  triangle_actor->SetMapper(triangle_mapper);

  vtkNew<vtkRenderer> outline_ren;
  outline_ren->AddActor(outline_actor);
  outline_ren->SetViewport(0.0, 0.0, 0.5, 1.0);
  outline_ren->SetBackground(colors->GetColor3d("CornFlowerBLue").GetData());

  vtkNew<vtkRenderer> triangle_ren;
  triangle_ren->AddActor(triangle_actor);
  triangle_ren->SetViewport(0.5, 0.0, 1.0, 1.0);
  triangle_ren->SetBackground(colors->GetColor3d("MistyRose").GetData());
  triangle_ren->SetActiveCamera(outline_ren->GetActiveCamera());

  vtkNew<vtkRenderWindow> renw;
  renw->SetMultiSamples(0);
  renw->AddRenderer(outline_ren);
  renw->AddRenderer(triangle_ren);
  renw->SetSize(800, 400);
  renw->SetWindowName("KochSnowflake");

  vtkNew<vtkRenderWindowInteractor> iren;
  iren->SetRenderWindow(renw);

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

  return EXIT_SUCCESS;
}

namespace {

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.
    vtkNew<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
  vtkNew<vtkCellArray> lines;
  vtkNew<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
  vtkNew<vtkPolyData> polydata;
  polydata->SetLines(lines);
  polydata->SetPoints(points);

  return polydata;
}

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

    vtkNew<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);
  }
}

} // namespace

CMakeLists.txt

cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

project(KochSnowflake)

find_package(VTK COMPONENTS 
  vtkCommonColor
  vtkCommonCore
  vtkCommonDataModel
  vtkInteractionStyle
  vtkRenderingContextOpenGL2
  vtkRenderingCore
  vtkRenderingFreeType
  vtkRenderingGL2PSOpenGL2
  vtkRenderingOpenGL2
  QUIET
)

if (NOT VTK_FOUND)
  message("Skipping KochSnowflake: ${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(KochSnowflake MACOSX_BUNDLE KochSnowflake.cxx )
  target_link_libraries(KochSnowflake PRIVATE ${VTK_LIBRARIES})
else ()
  # include all components
  add_executable(KochSnowflake MACOSX_BUNDLE KochSnowflake.cxx )
  target_link_libraries(KochSnowflake PRIVATE ${VTK_LIBRARIES})
  # vtk_module_autoinit is needed
  vtk_module_autoinit(
    TARGETS KochSnowflake
    MODULES ${VTK_LIBRARIES}
    )
endif ()

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.