ruby--ruby/ext/tk/sample/demos-en/pendulum.rb

#
# This demonstration illustrates how Tcl/Tk can be used to construct
# simulations of physical systems.
# (called by 'widget')
#
# based on Tcl/Tk8.5a2 widget demos

# destroy toplevel widget for this demo script
if defined?($pendulum_demo) && $pendulum_demo
  $pendulum_demo.destroy 
  $pendulum_demo = nil
end

# create toplevel widget
$pendulum_demo = TkToplevel.new {|w|
  title("Pendulum Animation Demonstration")
  iconname("pendulum")
  positionWindow(w)
}

# create label
msg = TkLabel.new($pendulum_demo) {
  font $font
  wraplength '4i'
  justify 'left'
  text 'This demonstration shows how Ruby/Tk can be used to carry out animations that are linked to simulations of physical systems. In the left canvas is a graphical representation of the physical system itself, a simple pendulum, and in the right canvas is a graph of the phase space of the system, which is a plot of the angle (relative to the vertical) against the angular velocity. The pendulum bob may be repositioned by clicking and dragging anywhere on the left canvas.'
}
msg.pack('side'=>'top')

# create frame
TkFrame.new($pendulum_demo) {|frame|
  TkButton.new(frame) {
    text 'Dismiss'
    command proc{
      tmppath = $pendulum_demo
      $pendulum_demo = nil
      tmppath.destroy
    }
  }.pack('side'=>'left', 'expand'=>'yes')

  TkButton.new(frame) {
    text 'See Code'
    command proc{showCode 'pendulum'}
  }.pack('side'=>'left', 'expand'=>'yes')

}.pack('side'=>'bottom', 'fill'=>'x', 'pady'=>'2m')

# animated wave
class PendulumAnimationDemo
  def initialize(frame)
    # Create some structural widgets
    pane = TkPanedWindow.new(frame).pack(:fill=>:both, :expand=>true)
    pane.add(@lf1 = TkLabelFrame.new(pane, :text=>'Pendulum Simulation'))
    pane.add(@lf2 = TkLabelFrame.new(pane, :text=>'Phase Space'))

    # Create the canvas containing the graphical representation of the
    # simulated system.
    @c = TkCanvas.new(@lf1, :width=>320, :height=>200, :background=>'white', 
                      :borderwidth=>2, :relief=>:sunken)
    TkcText.new(@c, 5, 5, :anchor=>:nw, 
                :text=>'Click to Adjust Bob Start Position')
    # Coordinates of these items don't matter; they will be set properly below
    @plate = TkcLine.new(@c, 0, 25, 320, 25, :width=>2, :fill=>'grey50')
    @rod = TkcLine.new(@c, 1, 1, 1, 1, :width=>3, :fill=>'black')
    @bob = TkcOval.new(@c, 1, 1, 2, 2, 
                       :width=>3, :fill=>'yellow', :outline=>'black')
    TkcOval.new(@c, 155, 20, 165, 30, :fill=>'grey50', :outline=>'')

    # pack
    @c.pack(:fill=>:both, :expand=>true)

    # Create the canvas containing the phase space graph; this consists of
    # a line that gets gradually paler as it ages, which is an extremely
    # effective visual trick.
    @k = TkCanvas.new(@lf2, :width=>320, :height=>200, :background=>'white', 
                      :borderwidth=>2, :relief=>:sunken)
    @y_axis = TkcLine.new(@k, 160, 200, 160, 0, :fill=>'grey75', :arrow=>:last)
    @x_axis = TkcLine.new(@k, 0, 100, 320, 100, :fill=>'grey75', :arrow=>:last)

    @graph = {}
    90.step(0, -10){|i|
      # Coordinates of these items don't matter; 
      # they will be set properly below
      @graph[i] = TkcLine.new(@k, 0, 0, 1, 1, :smooth=>true, :fill=>"grey#{i}")
    }

    # labels
    @label_theta = TkcText.new(@k, 0, 0, :anchor=>:ne, 
                               :text=>'q', :font=>'Symbol 8')
    @label_dtheta = TkcText.new(@k, 0, 0, :anchor=>:ne, 
                               :text=>'dq', :font=>'Symbol 8')

    # pack
    @k.pack(:fill=>:both, :expand=>true)

    # Initialize some variables
    @points = []
    @theta = 45.0
    @dTheta = 0.0
    @length = 150

    # init display
    showPendulum

    # animation loop
    @timer = TkTimer.new(15){ repeat }

    # binding
    @c.bindtags_unshift(btag = TkBindTag.new)
    btag.bind('Destroy'){ @timer.stop }
    btag.bind('1', proc{|x, y| @timer.stop; showPendulum(x, y)}, '%x %y')
    btag.bind('B1-Motion', proc{|x, y| showPendulum(x, y)}, '%x %y')
    btag.bind('ButtonRelease-1', 
              proc{|x, y| showPendulum(x, y); @timer.start }, '%x %y')

    btag.bind('Configure', proc{|w| @plate.coords(0, 25, w, 25)}, '%w')

    @k.bind('Configure', proc{|h, w| 
              @psh = h/2; 
              @psw = w/2
              @x_axis.coords(2, @psh, w-2, @psh)
              @y_axis.coords(@psw, h-2, @psw, 2)
              @label_theta.coords(@psw-4, 6)
              @label_dtheta.coords(w-6, @psh+4)
            }, '%h %w')

    # animation start
    @timer.start(500)
  end

  # This procedure makes the pendulum appear at the correct place on the
  # canvas. If the additional arguments x, y are passed instead of computing 
  # the position of the pendulum from the length of the pendulum rod and its 
  # angle, the length and angle are computed in reverse from the given 
  # location (which is taken to be the centre of the pendulum bob.)
  def showPendulum(x=nil, y=nil)
    if x && y && (x != 160 || y != 25)
      @dTheta = 0.0
      x2 = x - 160
      y2 = y - 25
      @length = Math.hypot(x2, y2)
      @theta = Math.atan2(x2,y2)*180/Math::PI
    else
      angle = @theta*Math::PI/180
      x = 160 + @length*Math.sin(angle)
      y = 25 + @length*Math.cos(angle)
    end

    @rod.coords(160, 25, x, y)
    @bob.coords(x-15, y-15, x+15, y+15)
  end

  # Update the phase-space graph according to the current angle and the
  # rate at which the angle is changing (the first derivative with
  # respect to time.)
  def showPhase
    @points << @theta + @psw << -20*@dTheta + @psh
    if @points.length > 100
      @points = @points[-100..-1]
    end
    (0...100).step(10){|i|
      first = - i
      last = 11 - i
      last = -1 if last >= 0
      next if first > last
      lst = @points[first..last]
      @graph[i].coords(lst) if lst && lst.length >= 4
    }
  end

  # This procedure is the "business" part of the simulation that does
  # simple numerical integration of the formula for a simple rotational
  # pendulum.
  def recomputeAngle
    scaling = 3000.0/@length/@length

    # To estimate the integration accurately, we really need to
    # compute the end-point of our time-step.  But to do *that*, we
    # need to estimate the integration accurately!  So we try this
    # technique, which is inaccurate, but better than doing it in a
    # single step.  What we really want is bound up in the
    # differential equation:
    #       ..             - sin theta
    #      theta + theta = -----------
    #                         length
    # But my math skills are not good enough to solve this!

    # first estimate
    firstDDTheta = -Math.sin(@theta * Math::PI/180) * scaling
    midDTheta = @dTheta + firstDDTheta
    midTheta = @theta + (@dTheta + midDTheta)/2
    # second estimate
    midDDTheta = -Math.sin(midTheta * Math::PI/180) * scaling
    midDTheta = @dTheta + (firstDDTheta + midDDTheta)/2
    midTheta = @theta + (@dTheta + midDTheta)/2
    # Now we do a double-estimate approach for getting the final value
    # first estimate
    midDDTheta = -Math.sin(midTheta * Math::PI/180) * scaling
    lastDTheta = midDTheta + midDDTheta
    lastTheta = midTheta + (midDTheta+ lastDTheta)/2
    # second estimate
    lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling
    lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2
    lastTheta = midTheta + (midDTheta + lastDTheta)/2
    # Now put the values back in our globals
    @dTheta = lastDTheta
    @theta = lastTheta
  end

  # This method ties together the simulation engine and the graphical
  # display code that visualizes it.
  def repeat
    # Simulate
    recomputeAngle

    # Update the display
    showPendulum
    showPhase
  end
end

# Start the animation processing
PendulumAnimationDemo.new($pendulum_demo)