This commit was manufactured by cvs2svn to create branch 'ruby_1_8'.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/branches/ruby_1_8@8047 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

ext/tk/sample/demos-en/aniwave.rb

@@ -0,0 +1,115 @@
+#
+# animated wave demo (called by 'widget')
+#
+# based on Tcl/Tk8.5a2 widget demos
+
+# destroy toplevel widget for this demo script
+if defined?($aniwave_demo) && $aniwave_demo
+  $aniwave_demo.destroy 
+  $aniwave_demo = nil
+end
+
+# create toplevel widget
+$aniwave_demo = TkToplevel.new {|w|
+  title("Animated Wave Demonstration")
+  iconname("aniwave")
+  positionWindow(w)
+}
+
+# create label
+msg = TkLabel.new($aniwave_demo) {
+  font $font
+  wraplength '4i'
+  justify 'left'
+  text 'This demonstration contains a canvas widget with a line item inside it. The animation routines work by adjusting the coordinates list of the line.'
+}
+msg.pack('side'=>'top')
+
+# create frame
+TkFrame.new($aniwave_demo) {|frame|
+  TkButton.new(frame) {
+    text 'Dismiss'
+    command proc{
+      tmppath = $aniwave_demo
+      $aniwave_demo = nil
+      tmppath.destroy
+    }
+  }.pack('side'=>'left', 'expand'=>'yes')
+
+  TkButton.new(frame) {
+    text 'See Code'
+    command proc{showCode 'aniwave'}
+  }.pack('side'=>'left', 'expand'=>'yes')
+
+}.pack('side'=>'bottom', 'fill'=>'x', 'pady'=>'2m')
+
+# animated wave
+class AnimatedWaveDemo
+  def initialize(frame, dir=:left)
+    @direction = dir
+
+    # create canvas widget
+    @c = TkCanvas.new(frame, :width=>300, :height=>200, 
+                      :background=>'black')
+    @c.pack(:padx=>10, :pady=>10, :expand=>true)
+
+    # Creates a coordinates list of a wave. 
+    @waveCoords = []
+    @backupCoords = []
+    n = 0
+    (-10..300).step(5){|n| @waveCoords << [n, 100]; @backupCoords << [n, 100] }
+    @waveCoords << [n, 0]; @backupCoords << [n, 0]
+    @waveCoords << [n+5, 200]; @backupCoords << [n+5, 200]
+    @coordsLen = @waveCoords.length
+
+    # Create a smoothed line and arrange for its coordinates to be the
+    # contents of the variable waveCoords.
+    @line = TkcLine.new(@c, @waveCoords, 
+                        :width=>1, :fill=>'green', :smooth=>true)
+
+    # Main animation "loop". 
+    # Theoretically 100 frames-per-second (==10ms between frames)
+    @timer = TkTimer.new(10){ basicMotion; reverser }
+
+    # Arrange for the animation loop to stop when the canvas is deleted
+    @c.bindtags_unshift(TkBindTag.new('Destroy'){ @timer.stop })
+  end
+
+  # Basic motion handler. Given what direction the wave is travelling
+  # in, it advances the y coordinates in the coordinate-list one step in
+  # that direction.
+  def basicMotion
+    @backupCoords, @waveCoords = @waveCoords, @backupCoords
+    (0...@coordsLen).each{|idx|
+      if @direction == :left
+        @waveCoords[idx][1] = @backupCoords[(idx+1 == @coordsLen)? 0: idx+1][1]
+      else
+        @waveCoords[idx][1] = @backupCoords[(idx == 0)? -1: idx-1][1]
+      end
+    }
+    @line.coords(@waveCoords)
+  end
+
+  # Oscillation handler. This detects whether to reverse the direction
+  # of the wave by checking to see if the peak of the wave has moved off
+  # the screen (whose size we know already.)
+  def reverser
+    if @waveCoords[0][1] < 10
+      @direction = :right
+    elsif @waveCoords[-1][1] < 10
+      @direction = :left
+    end
+  end
+
+  # animation control
+  def move
+    @timer.start
+  end
+
+  def stop
+    @timer.stop
+  end
+end
+
+# Start the animation processing
+AnimatedWaveDemo.new($aniwave_demo, :left).move

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

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+#
+# 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)

ext/tk/sample/demos-jp/aniwave.rb

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+#
+# animated wave demo (called by 'widget')
+#
+# based on Tcl/Tk8.5a2 widget demos
+
+# destroy toplevel widget for this demo script
+if defined?($aniwave_demo) && $aniwave_demo
+  $aniwave_demo.destroy 
+  $aniwave_demo = nil
+end
+
+# create toplevel widget
+$aniwave_demo = TkToplevel.new {|w|
+  title("Animated Wave Demonstration")
+  iconname("aniwave")
+  positionWindow(w)
+}
+
+# create label
+msg = TkLabel.new($aniwave_demo) {
+  font $font
+  wraplength '4i'
+  justify 'left'
+  text 'このデモでは、ラインアイテムが一つだけ描かれたキャンバスウィジェットが表示されています。アニメーション処理は、そのラインアイテムの座標値を変更することで実現しています。'
+}
+msg.pack('side'=>'top')
+
+# create frame
+TkFrame.new($aniwave_demo) {|frame|
+  TkButton.new(frame) {
+    #text '了解'
+    text '閉じる'
+    command proc{
+      tmppath = $aniwave_demo
+      $aniwave_demo = nil
+      tmppath.destroy
+    }
+  }.pack('side'=>'left', 'expand'=>'yes')
+
+  TkButton.new(frame) {
+    text 'コード参照'
+    command proc{showCode 'aniwave'}
+  }.pack('side'=>'left', 'expand'=>'yes')
+
+}.pack('side'=>'bottom', 'fill'=>'x', 'pady'=>'2m')
+
+# animated wave
+class AnimatedWaveDemo
+  def initialize(frame, dir=:left)
+    @direction = dir
+
+    # create canvas widget
+    @c = TkCanvas.new(frame, :width=>300, :height=>200, 
+                      :background=>'black')
+    @c.pack(:padx=>10, :pady=>10, :expand=>true)
+
+    # Creates a coordinates list of a wave. 
+    @waveCoords = []
+    @backupCoords = []
+    n = 0
+    (-10..300).step(5){|n| @waveCoords << [n, 100]; @backupCoords << [n, 100] }
+    @waveCoords << [n, 0]; @backupCoords << [n, 0]
+    @waveCoords << [n+5, 200]; @backupCoords << [n+5, 200]
+    @coordsLen = @waveCoords.length
+
+    # Create a smoothed line and arrange for its coordinates to be the
+    # contents of the variable waveCoords.
+    @line = TkcLine.new(@c, @waveCoords, 
+                        :width=>1, :fill=>'green', :smooth=>true)
+
+    # Main animation "loop". 
+    # Theoretically 100 frames-per-second (==10ms between frames)
+    @timer = TkTimer.new(10){ basicMotion; reverser }
+
+    # Arrange for the animation loop to stop when the canvas is deleted
+    @c.bindtags_unshift(TkBindTag.new('Destroy'){ @timer.stop })
+  end
+
+  # Basic motion handler. Given what direction the wave is travelling
+  # in, it advances the y coordinates in the coordinate-list one step in
+  # that direction.
+  def basicMotion
+    @backupCoords, @waveCoords = @waveCoords, @backupCoords
+    (0...@coordsLen).each{|idx|
+      if @direction == :left
+        @waveCoords[idx][1] = @backupCoords[(idx+1 == @coordsLen)? 0: idx+1][1]
+      else
+        @waveCoords[idx][1] = @backupCoords[(idx == 0)? -1: idx-1][1]
+      end
+    }
+    @line.coords(@waveCoords)
+  end
+
+  # Oscillation handler. This detects whether to reverse the direction
+  # of the wave by checking to see if the peak of the wave has moved off
+  # the screen (whose size we know already.)
+  def reverser
+    if @waveCoords[0][1] < 10
+      @direction = :right
+    elsif @waveCoords[-1][1] < 10
+      @direction = :left
+    end
+  end
+
+  # animation control
+  def move
+    @timer.start
+  end
+
+  def stop
+    @timer.stop
+  end
+end
+
+# Start the animation processing
+AnimatedWaveDemo.new($aniwave_demo, :left).move

ext/tk/sample/demos-jp/pendulum.rb

@@ -0,0 +1,224 @@
+#
+# 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 $font
+  wraplength '4i'
+  justify 'left'
+  text 'このデモは、物理系のシミュレーションに関わるようなアニメーション実行するために Ruby/Tk をどのように用いることができるかを示しています。左側のキャンバスは単純な振り子である物理系自体のグラフィカル表現であるのに対し、右側のキャンバスは系の位相空間のグラフ（角速度と角度とをプロットしたもの）になっています。左側のキャンバス上でクリックおよびドラッグを行って振り子の重りの位置を変えてみてください。'
+}
+msg.pack('side'=>'top')
+
+# create frame
+TkFrame.new($pendulum_demo) {|frame|
+  TkButton.new(frame) {
+    #text '了解'
+    text '閉じる'
+    command proc{
+      tmppath = $pendulum_demo
+      $pendulum_demo = nil
+      tmppath.destroy
+    }
+  }.pack('side'=>'left', 'expand'=>'yes')
+
+  TkButton.new(frame) {
+    text 'コード参照'
+    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)

ext/tk/sample/irbtk.rb

@@ -0,0 +1,30 @@
+#!/usr/local/bin/ruby
+#
+#   irbtk.rb - irb with Ruby/Tk
+#
+#   If you want to use 'multi-tk.rb', give option '--multi-tk'.
+#   And if you want to use 'remote-tk.rb', give option '--remote-tk'.
+#   If you want both, you don't need to give both options, because 
+#   'remote-tk.rb' includes 'multi-tk.rb'. 
+#   ( There is no trouble even if you give both options. )
+#
+require 'remote-tk' if ARGV.delete('--remote-tk')
+require 'multi-tk'  if ARGV.delete('--multi-tk')
+
+require "tk"
+module Tk
+  MAINLOOP = Thread.new{ mainloop }
+end
+
+require "irb"
+
+if __FILE__ == $0
+  IRB.start(__FILE__)
+else
+  # check -e option
+  if /^-e$/ =~ $0
+    IRB.start(__FILE__)
+  else
+    IRB.setup(__FILE__)
+  end
+end

ext/tk/tkutil/extconf.rb

@@ -0,0 +1,4 @@
+if compiled?('tk')
+  require 'mkmf'
+  create_makefile('tkutil')
+end