# KochSnowflake

VTKExamples/Python/Visualization/KochSnowflake

### Description

This script draws a Koch snowflake using the VTK. The general idea is to exercise some of the components of a vtkPolyData to produce something interesting rather than a boring old cube. Not that I have anything against cubes. There is also a C++ version of this example: KochSnowflake.

### Code

KochSnowflake.py

    #!/usr/bin/env python
    #------------------------------------------------------------------------------#
    #                                   Imports                                    #
    #------------------------------------------------------------------------------#
    from math import pi, cos, sin, sqrt
    import vtk

    LEVEL = 6

    #------------------------------------------------------------------------------#
    #                        Koch Snowflake as vtkPolyLine                         #
    #------------------------------------------------------------------------------#
    def as_polyline(points, 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 i in range(level):
        temp = vtk.vtkPoints()
        # The first point of the previous vtkPoints is the first point of the next vtkPoints.
        temp.InsertNextPoint(*points.GetPoint(0))

        # Iterate over "edges" in the vtkPoints
        for i in range(1, points.GetNumberOfPoints()):
          x0, y0, z0 = points.GetPoint(i - 1)
          x1, y1, z1 = points.GetPoint(i)
          t = sqrt((x1 - x0)**2 + (y1 - y0)**2)
          nx = (x1 - x0)/t # x-component of edge unit tangent
          ny = (y1 - y0)/t # y-component of edge unit tangent

          # the points describing the Koch snowflake edge
          temp.InsertNextPoint(x0 + nx*t/3, y0 + ny*t/3, 0.)
          temp.InsertNextPoint(x0 + nx*t/2 + ny*t*sqrt(3)/6, y0 + ny*t/2 - nx*t*sqrt(3)/6, 0.)
          temp.InsertNextPoint(x0 + nx*2*t/3, y0 + ny*2*t/3, 0.)
          temp.InsertNextPoint(x0 + nx*t, y0 + ny*t, 0.)

        points = temp

      # draw the outline
      lines = vtk.vtkCellArray()
      pl = vtk.vtkPolyLine()
      pl.GetPointIds().SetNumberOfIds(points.GetNumberOfPoints())
      for i in range(points.GetNumberOfPoints()):
        pl.GetPointIds().SetId(i, i)
      lines.InsertNextCell(pl)

      # complete the polydata
      polydata = vtk.vtkPolyData()
      polydata.SetLines(lines)
      polydata.SetPoints(points)

      return polydata

    #------------------------------------------------------------------------------#
    #                 Koch Snowflake as collection of vtkTriangles                 #
    #------------------------------------------------------------------------------#
    def as_triangles(indices, cellarray, level, data):
      if len(indices) >= 3:
        stride = len(indices)//4
        indices.append(indices[-1] + 1)

        triangle = vtk.vtkTriangle()
        triangle.GetPointIds().SetId(0, indices[ stride])
        triangle.GetPointIds().SetId(1, indices[2*stride])
        triangle.GetPointIds().SetId(2, indices[3*stride])

        cellarray.InsertNextCell(triangle)
        data.InsertNextValue(level)

        as_triangles(indices[       0:   stride], cellarray, level + 1, data)
        as_triangles(indices[  stride: 2*stride], cellarray, level + 1, data)
        as_triangles(indices[2*stride: 3*stride], cellarray, level + 1, data)
        as_triangles(indices[3*stride:       -1], cellarray, level + 1, data)

    #------------------------------------------------------------------------------#
    #                                 Main Method                                  #
    #------------------------------------------------------------------------------#
    if __name__ == "__main__":
      # 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.
      points = vtk.vtkPoints()
      for i in range(4):
        points.InsertNextPoint(cos(2.*pi*i/3), sin(2*pi*i/3.), 0.)

      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 todo 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. For this next trick, I will need a list of the indices in the
      # vtkPoints. They're consecutive, so thats pretty straightforward.

      indices = [i for i in range(outline_pd.GetPoints().GetNumberOfPoints() + 1)]
      triangles   = vtk.vtkCellArray()

      # Set this up for each of the initial sides, then call the recursive function.
      stride = (len(indices) - 1)//3

      # The cell data will allow us to color the triangles based on the level of
      # the iteration of the Koch snowflake.
      data = vtk.vtkIntArray()
      data.SetNumberOfComponents(0)
      data.SetName("Iteration Level")

      # This is the starting triangle.
      t = vtk.vtkTriangle()
      t.GetPointIds().SetId(0,        0)
      t.GetPointIds().SetId(1,   stride)
      t.GetPointIds().SetId(2, 2*stride)
      triangles.InsertNextCell(t)
      data.InsertNextValue(0)

      as_triangles(indices[       0:   stride + 1], triangles, 1, data)
      as_triangles(indices[  stride: 2*stride + 1], triangles, 1, data)
      as_triangles(indices[2*stride:           -1], triangles, 1, data)

      triangle_pd = vtk.vtkPolyData()
      triangle_pd.SetPoints(outline_pd.GetPoints())
      triangle_pd.SetPolys(triangles)
      triangle_pd.GetCellData().SetScalars(data)

      #-----------------#
      # rendering stuff #
      #-----------------#
      outline_mapper = vtk.vtkPolyDataMapper()
      outline_mapper.SetInputData(outline_pd)

      lut = vtk.vtkLookupTable()
      lut.SetNumberOfTableValues(256)
      lut.SetHueRange(0.6, 0.6)
      lut.SetSaturationRange(0., 1.)
      lut.Build()

      triangle_mapper = vtk.vtkPolyDataMapper()
      triangle_mapper.SetInputData(triangle_pd)
      triangle_mapper.SetScalarRange(0.0, LEVEL)
      triangle_mapper.SetLookupTable(lut)

      outline_actor = vtk.vtkActor()
      outline_actor.SetMapper(outline_mapper)

      triangle_actor = vtk.vtkActor()
      triangle_actor.SetMapper(triangle_mapper)

      outline_ren = vtk.vtkRenderer()
      outline_ren.AddActor(outline_actor)
      outline_ren.SetViewport(0.0, 0.0, 0.5, 1.0)

      triangle_ren = vtk.vtkRenderer()
      triangle_ren.AddActor(triangle_actor)
      triangle_ren.SetViewport(0.5, 0.0, 1.0, 1.0)
      triangle_ren.SetActiveCamera(outline_ren.GetActiveCamera())

      renw = vtk.vtkRenderWindow()
      renw.AddRenderer(outline_ren)
      renw.AddRenderer(triangle_ren)
      renw.SetSize(800, 400)

      iren = vtk.vtkRenderWindowInteractor()
      iren.SetRenderWindow(renw)

      outline_ren.ResetCamera()
      renw.Render()
      iren.Start()