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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)
|
