From: Dema <demetriusnunes@...>
Date: 2006-12-04T10:30:05+09:00
Subject: Re: Turtle Graphics (#104)

Here is my straight-to-the-point answer:

class Turtle
   include Math # turtles understand math methods
   DEG = Math::PI / 180.0

   attr_accessor :track
   alias run instance_eval

   def initialize
     clear
   end

   attr_reader :xy, :heading

   # Place the turtle at [x, y]. The turtle does not draw when it
changes
   # position.
   def xy=(coords)
   	 raise ArgumentError if !coords.is_a?(Array) ||
   	                        coords.size != 2 ||
   	                        coords.any? { |c| !c.is_a?(Numeric) }
   	 @xy = coords
   end

   # Set the turtle's heading to <degrees>.
   def heading=(degrees)
   	 raise ArgumentError if !degrees.is_a?(Numeric)
   	 set_heading(degrees)
   end

   # Raise the turtle's pen. If the pen is up, the turtle will not
draw;
   # i.e., it will cease to lay a track until a pen_down command is
given.
   def pen_up
   	 @pen_down = false
   end

   # Lower the turtle's pen. If the pen is down, the turtle will draw;
   # i.e., it will lay a track until a pen_up command is given.
   def pen_down
   	 @pen_down = true
   end

   # Is the pen up?
   def pen_up?
   	 !@pen_down
   end

   # Is the pen down?
   def pen_down?
   	 @pen_down
   end

   # Places the turtle at the origin, facing north, with its pen up.
   # The turtle does not draw when it goes home.
   def home
   	 pen_up
   	 @xy = [0,0]
   	 @heading = 0
   end

   # Homes the turtle and empties out it's track.
   def clear
   	 home
   	 @track = []
   end

   # Turn right through the angle <degrees>.
   def right(degrees)
     set_heading(@heading + degrees)
   end

   # Turn left through the angle <degrees>.
   def left(degrees)
     set_heading(@heading - degrees)
   end

   # Move forward by <steps> turtle steps.
   def forward(steps)
     dx, dy = calc_delta(steps)
     go [ @xy[0] + dx, @xy[1] + dy ]
   end

   # Move backward by <steps> turtle steps.
   def back(steps)
     dx, dy = calc_delta(steps)
     go [ @xy[0] - dx, @xy[1] - dy ]
   end

   # Move to the given point.
   def go(pt)
     track << [ @xy, pt ] if pen_down?
     @xy = pt
   end

   # Turn to face the given point.
   def toward(pt)
     @heading = atan(pt[0].to_f / pt[1].to_f) / DEG
   end

   # Return the distance between the turtle and the given point.
   def distance(pt)
     sqrt((@xy[0] - pt[0]) ** 2 + (@xy[1] - pt[1]) ** 2)
   end

   # Traditional abbreviations for turtle commands.
   alias fd forward
   alias bk back
   alias rt right
   alias lt left
   alias pu pen_up
   alias pd pen_down
   alias pu? pen_up?
   alias pd? pen_down?
   alias set_h heading=
   alias set_xy xy=
   alias face toward
   alias dist distance

   private
   def set_heading(degrees)
     @heading = degrees % 360
   end

   def calc_delta(steps)
     [ sin(heading * DEG) * steps,
       cos(heading * DEG) * steps ]
   end
end

Ruby Quiz wrote:
> The three rules of Ruby Quiz:
>
> 1.  Please do not post any solutions or spoiler discussion for this quiz until
> 48 hours have passed from the time on this message.
>
> 2.  Support Ruby Quiz by submitting ideas as often as you can:
>
> http://www.rubyquiz.com/
>
> 3.  Enjoy!
>
> Suggestion:  A [QUIZ] in the subject of emails about the problem helps everyone
> on Ruby Talk follow the discussion.  Please reply to the original quiz message,
> if you can.
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
>
> by Morton Goldberg
>
> [Editor's Note:  You can download the files for this quiz at:
>
> 	http://rubyquiz.com/turtle.zip
>
> --JEG2]
>
> 	Turtle Graphics
> 	===============
>
> Turtle graphics is a form of computer graphics based on the ideas of turtle
> geometry, a formulation of local (coordinate-free) geometry. As a brief
> introduction to turtle graphics, I quote from [1]:
>
> 	Imagine that you have control of a little creature called a turtle
> 	that exists in a mathematical plane or, better yet, on a computer
> 	display screen. The turtle can respond to a few simple commands:
> 	FORWARD moves the turtle in the direction it is facing some
> 	number of units. RIGHT rotates it clockwise in its place some
> 	number of degrees. BACK and LEFT cause the opposite movements. ...
> 	The turtle can leave a trace of the places it has been: [its
> 	movements] can cause lines to appear on the screen. This is
> 	controlled by the commands PENUP and PENDOWN. When the pen is
> 	down, the turtle draws lines.
>
> For example, the turtle commands to draw a square, 100 units on a side, can be
> written (in a Ruby-ized form) as:
>
> 	pen_down
> 	4.times { forward 100; right 90 }
>
> For more information, see [2] and [3].
>
> This quiz is a bit different from most. If the usual Ruby quiz can be likened to
> an essay exam, this one is a fill-in-the-blanks test. I'm supplying you with a
> complete turtle graphics package, except -- to give you something to do -- I've
> removed the method bodies from the key file, lib/turtle.rb. Your job is to
> repair the damage I've done and make the package work again.
>
> 	Turtle Commands
> 	===============
>
> There are quite a few turtle commands, but that doesn't mean you have to write a
> lot of code to solve this quiz. Most of the commands can be implemented in a
> couple of lines. It took me a lot longer to write a description of the commands
> than it did for me to implement and test all of them.
>
> I use the following format to describe turtle commands:
>
> 	long_name | short_name <arg>
> 	   description ...
> 	   Example: ...
>
> All turtle commands take either one argument or none, and not all turtle
> commands have both a long name and a short name.
>
> 	Required Commands
> 	-----------------
>
> These commands are required in the sense that they are needed to reproduce the
> sample designs. Actually, you could get away without implementing 'back' and
> 'left', but implementing them is far easier than trying to write turtle code
> without them.
>
> 	pen_up | pu
> 	   Raises the turtle's pen. The turtle doesn't draw (lay down a visible
> 	   track) when its pen is up.
>
> 	pen_down | pd
> 	   Lowers the turtle's pen. The turtle draws (lays down a visible track)
> 	   when its pen is down.
>
> 	forward | fd <distance>
> 	   Moves the turtle forwards in the direction it is facing.
> 	   Example: forward(100) advances the turtle by 100 steps.
>
> 	back | bk <distance>
> 	   Moves the turtle backwards along its line of motion.
> 	   back <distance> == forward -<distance>
> 	   Example: back(100) backs up the turtle by 100 steps.
>
> 	right | rt <angle>
> 	   Turns the turtle clockwise by <angle> degrees.
> 	   Example: right(90) turns the turtle clockwise by a right angle.
>
> 	left | lt <angle>
> 	   Turns the turtle counterclockwise by <angle> degrees.
> 	   left  <angle> == right -<angle>
> 	   Example: left(45) turns the turtle counterclockwise by 45 degrees.
>
> 	Traditional Commands
> 	--------------------
>
> These commands are not needed to reproduce any of the sample designs, but they
> are found in all implementations of turtle graphics that I know of.
>
> 	home
> 	   Places the turtle at the origin, facing north, with its pen up. The
> 	   turtle does not draw when it goes home.
>
> 	clear
> 	   Homes the turtle and empties out it's track. Sending a turtle a clear
> 	   message essentially reinitializes it.
>
> 	xy
> 	   Reports the turtle's location.
> 	   Example: Suppose the turtle is 10 turtle steps north and 15 turtle steps
> 	   west of the origin, then xy will return [-15.0, 10.0].
>
> 	set_xy | xy= <point>
> 	   Places the turtle at <point>. The turtle does not draw when this command
> 	   is executed, not even if its pen is down. Returns <point>.
> 	   Example: Suppose the turtle is at [10.0, 20.0], then self.xy = [50, 80]
> 	   moves the turtle to [50.0, 80.0], but no line will drawn between the [10,
> 	   20] and [50, 80].
>
> 	heading
> 	   Reports the direction in which the turtle is facing. Heading is measured
> 	   in degrees, clockwise from north.
> 	   Example: Suppose the turtle is at the origin facing the point [100, 200],
> 	   then heading will return 26.565 (approximately).
>
> 	heading= | set_h <angle>
> 	   Sets the turtle's heading to <angle>. <angle> should be given in degrees,
> 	   measured clockwise from north. Returns <angle>.
> 	   Example: After self.heading = 135 (or set_h(135) which is easier to
> 	   write), the turtle will be facing southeast.
>
> 	pen_up? | pu?
> 	   Reports true if the turtle's pen is up and false otherwise.
>
> 	pen_down? | pd?
> 	   Reports true if the turtle's pen is down and false otherwise.
>
> 	Optional Commands
> 	-----------------
>
> These commands are only found in some implementations of turtle graphics. When
> they are implemented, they make the turtle capable of doing global (coordinate)
> geometry in addition to local (coordinate-free) geometry.
>
> I used one of these commands, go, to draw the mandala design (see
> designs/mandala.tiff and samples/mandala.rb). If you choose not to implement the
> optional commands, you might try writing a turtle program for drawing the
> mandala design without using go. But, believe me, it is much easier to implement
> go than to write such a program.
>
> 	go <point>
> 	   Moves the turtle to <point>.
> 	   Example: Suppose the turtle is home (at the origin facing north). After
> 	   go([100, 200]), the turtle will be located at [100.0, 200.0] but will
> 	   still be facing north. If its pen was down, it will have drawn a line
> 	   from [0, 0] to [100, 200].
>
> 	toward | face <point>
> 	   Turns the turtle to face <point>.
> 	   Example: Suppose the turtle is at the origin. After toward([100, 200]),
> 	   its heading will be 26.565 (approximately).
>
> 	distance | dist <point>
> 	   Reports the distance between the turtle and <point>.
> 	   Example: Suppose the turtle is at the origin, then distance([400, 300])
> 	   will return 500.0 (approximately).
>
> 	Interfacing to the Turtle Graphics Viewer
> 	=========================================
>
> Implementing turtle graphics without being able to view what the turtle draws
> isn't much fun, so I'm providing a simple turtle graphics viewer. To interface
> with the viewer, turtle instances must respond to the message track by returning
> an array which the viewer can use to generate a line drawing.
>
> The viewer expects the array returned by track to take the following form:
>
> 	track   ::= [segment, segment, ...]  # drawing data
> 	segment ::= [point, point, ...]      # points to be joined by line segments
> 	point   ::= [x, y]                   # pair of floats
>
> 	Example: [[[0.0, 0.0], [200.0, 200.0]], [[200.0, 0.0], [0.0, 200.0]]]
>
> This represents an X located in the upper-right quadrant of the viewer; i.e.,
> two line segments, one running from the center of the viewer up to its
> upper-right corner and the other running from the center of the top edge down to
> the center of the right edge.
>
> [Editor's Note:  I added a script to dump your turtle graphics output to PPM
> image files, for those that don't have TK up and running.  It works identically
> to Morton's turtle_viewer.rb, save that it writes output to a PPM image file in
> the current directory.  For example, to output the included tree image, use
> `ruby turtle_ppm_writer.rb samples/tree.rb`.  --JEG2]
>
> 	Unit Tests
> 	==========
>
> I'm including the unit tests which I developed to test turtle commands. For the
> purposes of the quiz, you can ignore tests/turtle_view_test.rb. But I hope you
> will find the other test suite, tests/turtle_test.rb, helpful. It tests every
> one of the turtle commands described above as well as argument checking by the
> commands. Don't hesitate to modify any of the unit tests to meet the needs of
> your quiz solution.
>
> 	References
> 	==========
>
> 	[1] Abelson, H. & A. diSessa, "Turtle Geometry", MIT Press, 1981.
> 	[2] Harvey, B., "Computer Science Logo Style", Chapter 10.
> 	    http://www.cs.berkeley.edu/~bh/pdf/v1ch10.pdf
> 	[3] Wikipedia, http://en.wikipedia.org/wiki/LOGO_programming_language