A More Complicated Sierpinski

Here is a more elegant use of the mathematics, the main credit to lazydog for figuring it all out, all I did was translate it to ruby-processing. If you just want to see a boring old sphere, remove the comment in front of the last recursive drawTriangle (in drawTriangle of course). If you want to see more amazing processing opengl apps check out lazydogs blog.


# elegant.rb

class ElegantBall < Processing::App
  load_library :opengl
  attr_reader :start_t

  def setup()
    library_loaded?(:opengl) ? configure_opengl : render_mode(P3D)
    color_mode(RGB, 1)
  end

  def configure_opengl
    render_mode OPENGL
    hint ENABLE_OPENGL_4X_SMOOTH     # optional
    hint DISABLE_OPENGL_ERROR_REPORT # optional
  end

  def draw()
    #background(0.25)
    background(0)
    # Move the origin so that the scene is centered on the screen.
    translate(width/2, height/2, 0.0)
    # Set up the lighting.
    setup_lights
    # Rotate the local coordinate system.
    smooth_rotation(5.0, 6.7, 7.3)
    # Draw the inner object.
    no_stroke()
    fill(smooth_colour(10.0, 12.0, 7.0))
    draw_icosahedron(5, 60.0, false)
    # Rotate the local coordinate system again.
    smooth_rotation(4.5, 3.7, 7.3)
    # Draw the outer object.
    stroke(0.2)
    fill(smooth_colour(6.0, 9.2, 0.7))
    draw_icosahedron(5, 200.0, true)
  end

  def setup_lights
    ambient_light(0.025, 0.025, 0.025)
    directional_light(0.2, 0.2, 0.2, -1, -1, -1)
    spot_light(1.0, 1.0, 1.0, -200, 0, 300, 1, 0, -1, Math::PI/4, 20)
  end

  ##
  # Generate a vector whose components change smoothly over time in the range [ 0, 1 ].
  # Each component uses a Math.sin() function to map the current time in milliseconds somewhere
  # in the range [ 0, 1 ].A 'speed' factor is specified for each component.
  #
  def smooth_vector(s1, s2, s3)
    mills = millis * 0.00003 ## Lazydogs factor
    # mills = millis * 0.0000001 ## worked for me a bit slower!!
    x = 0.5 * Math.sin(mills * s1) + 0.5
    y = 0.5 * Math.sin(mills * s2) + 0.5
    z = 0.5 * Math.sin(mills * s3) + 0.5
    PVector.new(x, y, z)
  end

  ##
  # Generate a colour which smoothly changes over time.
  # The speed of each component is controlled by the parameters s1, s2 and s3.
  #
  def smooth_colour(s1, s2, s3)
    v = smooth_vector(s1, s2, s3)
    color(v.x, v.y, v.z)
  end

  ##
  # Rotate the current coordinate system.
  # Uses smooth_vector() to smoothly animate the rotation.
  #
  def smooth_rotation(s1, s2, s3)
    r1 = smooth_vector(s1, s2, s3)
    rotate_x(2.0 * Math::PI * r1.x)
    rotate_y(2.0 * Math::PI * r1.y)
    rotate_x(2.0 * Math::PI * r1.z)
  end

  ##
  # Draw an icosahedron defined by a radius r and recursive depth d.
  # Geometry data will be saved into dst. If spherical is true then the icosahedron
  # is projected onto the sphere with radius r.
  #
  def draw_icosahedron(depth, r, spherical)
    # Calculate the vertex data for an icosahedron inscribed by a sphere radius 'r'.
    # Use 4 Golden Ratio rectangles as the basis.
    gr = (1.0 + Math.sqrt(5.0)) / 2.0
    h = r / Math.sqrt(1.0 + gr * gr)
    v =
      [
      PVector.new(0, -h, h*gr), PVector.new(0, -h, -h*gr), PVector.new(0, h, -h*gr), PVector.new(0, h, h*gr),
      PVector.new(h, -h*gr, 0), PVector.new(h, h*gr, 0), PVector.new(-h, h*gr, 0), PVector.new(-h, -h*gr, 0),
      PVector.new(-h*gr, 0, h), PVector.new(-h*gr, 0, -h), PVector.new(h*gr, 0, -h), PVector.new(h*gr, 0, h)
    ]

    # Draw the 20 triangular faces of the icosahedron.
    unless spherical then
      r = 0.0
    end

    begin_shape(TRIANGLES)
     
    draw_triangle(depth, r, v[0], v[7],v[4])
    draw_triangle(depth, r, v[0], v[4], v[11])
    draw_triangle(depth, r, v[0], v[11], v[3])
    draw_triangle(depth, r, v[0], v[3], v[8])
    draw_triangle(depth, r, v[0], v[8], v[7])
 
    draw_triangle(depth, r, v[1], v[4], v[7])
    draw_triangle(depth, r, v[1], v[10], v[4])
    draw_triangle(depth, r, v[10], v[11], v[4])
    draw_triangle(depth, r, v[11], v[5], v[10])
    draw_triangle(depth, r, v[5], v[3], v[11])
    draw_triangle(depth, r, v[3], v[6], v[5])
    draw_triangle(depth, r, v[6], v[8], v[3])
    draw_triangle(depth, r, v[8], v[9], v[6])
    draw_triangle(depth, r, v[9], v[7], v[8])
    draw_triangle(depth, r, v[7], v[1], v[9])
 
    draw_triangle(depth, r, v[2], v[1], v[9])
    draw_triangle(depth, r, v[2], v[10], v[1])
    draw_triangle(depth, r, v[2], v[5], v[10])
    draw_triangle(depth, r, v[2], v[6], v[5])
    draw_triangle(depth, r, v[2], v[9], v[6])
   
    end_shape()
  end

  ##
  # Draw a triangle either immediately or subdivide it first.
  # If depth is 1 then draw the triangle otherwise subdivide first.
  #
  def draw_triangle(depth, r, p1, p2, p3)

    if (depth == 1) then
      vertex(p1.x, p1.y, p1.z)
      vertex(p2.x, p2.y, p2.z)
      vertex(p3.x, p3.y, p3.z)
    else
      # Calculate the mid points of this triangle.
      v1 = PVector.mult(PVector.add(p1, p2), 0.5)
      v2 = PVector.mult(PVector.add(p2, p3), 0.5)
      v3 = PVector.mult(PVector.add(p3, p1), 0.5)
    unless (r == 0.0) then
      # Project the verticies out onto the sphere with radius r.
      v1.normalize()
      v1.mult(r)
      v2.normalize()
      v2.mult(r)
      v3.normalize()
      v3.mult(r)
    end
      ## Generate the next level of detail
      depth -= 1
      draw_triangle(depth, r, p1, v1, v3)
      draw_triangle(depth, r, v1, p2, v2)
      draw_triangle(depth, r, v2, p3, v3)
      # Uncomment out the next line to include the central part of the triangle.
      # draw_triangle(depth, r, v1, v2, v3)
    end

  end


end

### Guard against current issues with Linux and opengl with ruby-processing (18 Sept 2009)
if java.lang.System.get_property('os.name') == "Linux" then
  ElegantBall.new(:width => 800, :height => 800, :title => "Elegant Ball", :full_screen => true)
else
  ElegantBall.new(:width => 800, :height => 800, :title => "Elegant Ball", :full_screen => false)
end


Currently there is an issue with resizing on linux with opengl and ruby-processing, so best to specify full screen (NB to run this script you will need ruby-processing follow the link in my blog header to find out how, to run the script:-
"rp5 run elegant_ball.rb". See screenshot of running sketch below:-