Class PendulumAnimationDemo < Object

# File ext/tk/sample/demos-en/pendulum.rb, line 53
  def initialize(frame)
    # Create some structural widgets
    @pane = TkPanedWindow.new(frame, :orient=>:horizontal).pack(:fill=>:both, :expand=>true)
#    @pane.add(@lf1 = TkLabelFrame.new(@pane, :text=>'Pendulum Simulation'))
#    @pane.add(@lf2 = TkLabelFrame.new(@pane, :text=>'Phase Space'))
    @lf1 = TkLabelFrame.new(@pane, :text=>'Pendulum Simulation')
    @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

    # 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.to_i, y.to_i)},
              '%x %y')
    btag.bind('B1-Motion', proc{|x, y| showPendulum(x.to_i, y.to_i)}, '%x %y')
    btag.bind('ButtonRelease-1',
              proc{|x, y| showPendulum(x.to_i, y.to_i); @timer.start },
              '%x %y')

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

    @k.bind('Configure', proc{|h, w|
              h = h.to_i
              w = w.to_i
              @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')

    # add
    Tk.update
    @pane.add(@lf1)
    @pane.add(@lf2)

    # init display
    showPendulum

    # animation start
    @timer.start(500)
  end

# File ext/tk/sample/demos-en/pendulum.rb, line 192
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

# File ext/tk/sample/demos-en/pendulum.rb, line 230
def repeat
  # Simulate
  recomputeAngle

  # Update the display
  showPendulum
  showPhase
end

# File ext/tk/sample/demos-en/pendulum.rb, line 150
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

# File ext/tk/sample/demos-en/pendulum.rb, line 170
def showPhase
  unless @psw && @psh
    @psw = @k.width/2
    @psh = @k.height/2
  end
  @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