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[QUIZ] Turtle Graphics (#104)

 
 
Morton Goldberg
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Posts: n/a
 
      12-04-2006
On Dec 3, 2006, at 8:30 PM, Dema wrote:

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


Your solution passes all the unit tests I supplied and is certainly
good enough to reproduce all the sample designs. So you have good
reason to think it's completely correct. However, one of the optional
methods has a problem.

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


This won't work in all four quadrants.

I apologize for not providing tests good enough to detect the
problem. Here is one that will test all four quadrants.

<code>
# Test go, toward, and distance.
# Verify heading measures angles clockwise from north.
def test_coord_cmnds
nne = [100, 173]
@turtle.go nne
x, y = @turtle.xy
assert_equal(nne, [x.round, y.round])
@turtle.home
@turtle.run { pd; face nne; fd 200 }
assert_equal(30, @turtle.heading.round)
assert_equal([[[0, 0], nne]], snap(@turtle.track))
sse = [100, -173]
@turtle.home
@turtle.run { face sse; fd 200 }
assert_equal(150, @turtle.heading.round)
ssw = [-100, -173]
@turtle.home
@turtle.run { face ssw; fd 200 }
assert_equal(210, @turtle.heading.round)
nnw = [-100, 173]
@turtle.home
@turtle.run { face nnw; fd 200 }
assert_equal(330, @turtle.heading.round)
@turtle.home
assert_equal(500, @turtle.dist([400, 300]).round)
end
</code>

Regards, Morton



 
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Hidetoshi NAGAI
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Posts: n/a
 
      12-04-2006
From: Edwin Fine <(E-Mail Removed)>
Subject: Re: tk.rb warning in Turtle Graphics (#104)
Date: Sat, 2 Dec 2006 18:28:44 +0900
Message-ID: <(E-Mail Removed)>
> Well, I found a bizarre and (to me) totally inexplicable way to get rid
> of the warning. This is from the quiz turtle_view.rb file. Adding an
> explicit return value (any value; I used nil) to the draw method gets
> rid of the warning. WTF???


Do you use the method "draw" at the end of callback operation?
If so, the method returns the result to the Tcl/Tk interpreter.
Then, the result (a Ruby's object) is converted to a string.

Usually, an object of TkObject or its subclasses is converted to
its @path value which is a string.
And when pass the string to Tcl/Tk side, @encoding check is required.

nil or a numeric doesn't need @encoding check.
--
Hidetoshi NAGAI ((E-Mail Removed))

 
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Edwin Fine
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Posts: n/a
 
      12-04-2006
Here's my solution. It passes all the unit tests, including the new
ones. I added a further unit test to try to force divide by zero errors
in the atan(y/x) calculation, and to see what happens if there is
"stupid" input, like two consecutive "face [100,0]" commands... hey,
stuff happens...
I must say, this turned out to be a bit more involved than I thought it
would. I kept tripping over the differences between turtle space angles
and "normal" angles.

As noted elsewhere, I also added a "nil" return to the turtle_viewer.rb
view method to eliminate most pesky Tk warnings. Thanks to Hidetoshi
NAGAI for explaining why this does what it does.

<code>
class Turtle
include Math # turtles understand math methods
DEG = Math:I / 180.0

NORTH = 0.0
HOME = [0, 0]

alias run instance_eval

def initialize
self.clear
self.pen_up
end

attr_reader :track, y, :heading

# Place the turtle at [x, y]. The turtle does not draw when it changes
# position.
def xy=(coords)
@xy = validate_coords(coords)
end

# Set the turtle's heading to <degrees>. Heading is measured CLOCKWISE
from NORTH!
def heading=(degrees)
@heading = validate_degrees(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_up = true
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_up = false
end

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

# Is the pen down?
def pen_down?
not self.pen_up?
end

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

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

# Turn right through the angle <degrees>.
def right(degrees)
h = self.heading + validate_degrees(degrees)
self.heading = normalize_degrees(h)
end

# Turn left through the angle <degrees>.
def left(degrees)
h = self.heading - validate_degrees(degrees)
self.heading = normalize_degrees(h)
end

# Move forward by <steps> turtle steps.
def forward(steps)
validate_steps(steps)
normal_radians = to_rad(flip_turtle_and_normal(@heading))
new_pt = [@xy[0] + steps * cos(normal_radians),
@xy[1] + steps * sin(normal_radians)]

add_segment_to_track @xy, new_pt if self.pen_down?
@xy = new_pt
end

# Move backward by <steps> turtle steps.
def back(steps)
validate_steps(steps)

normal_radians = to_rad(flip_turtle_and_normal(@heading))
new_pt = [@xy[0] - steps * cos(normal_radians),
@xy[1] - steps * sin(normal_radians)]

if self.pen_down?
add_segment_to_track @xy, new_pt
end

@xy = new_pt
end

# Move to the given point.
def go(pt)
validate_coords(pt)
add_segment_to_track(self.xy, pt) if self.pen_down?
self.xy = pt
end

# Turn to face the given point.
def toward(pt)
validate_coords(pt)
delta_x = (pt[0] - self.xy[0]).to_f
delta_y = (pt[1] - self.xy[1]).to_f
return if delta_x.zero? and delta_y.zero?

# Handle special cases
case
when delta_x.zero? # North or South
self.heading = delta_y < 0.0 ? 180.0 : 0.0
when delta_y.zero? # East or West
self.heading = delta_x < 0.0 ? 270.0 : 90.0
else
# Calcs are done in non-turtle space so we have to flip afterwards
quadrant_adjustment = if delta_x < 0.0 then 180 elsif delta_y <
0.0 then 360.0 else 0.0 end
self.heading = flip_turtle_and_normal(to_deg(atan(delta_y /
delta_x)) + quadrant_adjustment)
end
end

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

# Validations

def validate_coords(coords)
unless coords.respond_to? :[] and
coords.respond_to? :length and
coords.length == 2 and
coords[0].kind_of? Numeric and
coords[1].kind_of? Numeric
raise(ArgumentError, "Invalid coords #{coords.inspect}, should be
[num, num]")
end
coords
end

def validate_degrees(degrees)
raise(ArgumentError, "Degrees must be numeric") unless
degrees.kind_of? Numeric
normalize_degrees(degrees)
end

def validate_steps(steps)
raise(ArgumentError, "Steps must be numeric") unless steps.kind_of?
Numeric
end

# Normalizations

# Flip between turtle space degrees and "normal" degrees (symmetrical)
def flip_turtle_and_normal(degrees)
(450.0 - degrees) % 360.0
end

# Normalize degrees to interval [0, 360)
def normalize_degrees(degrees)
degrees += 360.0 while degrees < 0.0
degrees % 360.0
end

def add_segment_to_track(start, finish)
@track << [ start, finish ]
end

def to_rad(deg)
deg * DEG
end

def to_deg(rad)
rad / DEG
end
end
</code>

---------------
Here's the extra test case:

<code>
def test_edge_cases
east = [100, 0]
west = [-100, 0]
north = [0, 100]
south = [0, -100]
@turtle.home
assert_equal(0, @turtle.heading.round)
assert_nothing_raised { @turtle.face [0, 0] }
assert_equal(0, @turtle.heading.round)
assert_nothing_raised { @turtle.face north }
assert_equal(0, @turtle.heading.round)
@turtle.face east
assert_nothing_raised { @turtle.face east }
assert_equal(90, @turtle.heading.round)
@turtle.face south
assert_nothing_raised { @turtle.face south }
assert_equal(180, @turtle.heading.round)
@turtle.face west
assert_nothing_raised { @turtle.face west }
assert_equal(270, @turtle.heading.round)
end
</code>

--
Posted via http://www.ruby-forum.com/.

 
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Edwin Fine
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Posts: n/a
 
      12-04-2006
Hidetoshi NAGAI wrote:
> Do you use the method "draw" at the end of callback operation?
> If so, the method returns the result to the Tcl/Tk interpreter.
> Then, the result (a Ruby's object) is converted to a string.
>
> Usually, an object of TkObject or its subclasses is converted to
> its @path value which is a string.
> And when pass the string to Tcl/Tk side, @encoding check is required.
>
> nil or a numeric doesn't need @encoding check.


Thanks for the explanation. This was driving me nuts

--
Posted via http://www.ruby-forum.com/.

 
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Matthew Moss
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      12-04-2006
My solution, which does pass your updated test_coord_cmnds, Morton...



require "matrix"

class Turtle
include Math # turtles understand math methods
DEG = Math:I / 180.0
ORIGIN = [0.0, 0.0]
NORTH = 0.0

attr_accessor :track
alias run instance_eval

def initialize
clear
end

attr_reader y, :heading

# Place the turtle at [x, y]. The turtle does not draw when it changes
# position.
def xy=(pt)
validate_point(pt)
if pen_up?
@xy = pt
else
pen_up
@xy = pt
pen_down
end
@xy
end

# Set the turtle's heading to <degrees>.
def heading=(degrees)
validate_angle(degrees)
@heading = degrees % 360
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
@segment = nil
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
if pen_up?
@segment = [@xy.dup]
@track << @segment
end
end

# Is the pen up?
def pen_up?
not @segment
end

# Is the pen down?
def pen_down?
not pen_up?
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, @heading = ORIGIN, NORTH
end

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

# Turn right through the angle <degrees>.
def right(degrees)
validate_angle(degrees)
self.heading += degrees
end

# Turn left through the angle <degrees>.
def left(degrees)
validate_angle(degrees)
self.heading -= degrees
end

# Move forward by <steps> turtle steps.
def forward(steps)
validate_dist(steps)
go offset(steps)
end

# Move backward by <steps> turtle steps.
def back(steps)
validate_dist(steps)
go offset(-steps)
end

# Move to the given point.
def go(pt)
validate_point(pt)
@xy = pt
@segment << @xy if pen_down?
end

# Turn to face the given point.
def toward(pt)
validate_point(pt)
d = delta(pt)
self.heading = atan2(d[0], d[1]) / DEG
end

# Return the distance between the turtle and the given point.
def distance(pt)
validate_point(pt)
delta(pt).r
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

# Given a heading, build a unit vector in that direction.
def facing
rd = @heading * DEG
Vector[ sin(rd), cos(rd) ]
end

# Offset the current position in the direction of the current
# heading by the specified distance.
def offset(dist)
(Vector[*@xy] + (facing * dist)).to_a
end

# Build a delta vector to the specified point.
def delta(pt)
(Vector[*pt] - Vector[*@xy])
end

def validate_point(pt)
raise ArgumentError unless pt.is_a?(Array)
raise ArgumentError unless pt.size == 2
pt.each { |x| validate_dist(x) }
end

def validate_angle(deg)
raise ArgumentError unless deg.is_a?(Numeric)
end

def validate_dist(dist)
raise ArgumentError unless dist.is_a?(Numeric)
end

private :facing
private ffset
private :delta
private :validate_point
private :validate_angle
private :validate_dist
end

 
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Morton Goldberg
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Posts: n/a
 
      12-04-2006
On Dec 4, 2006, at 7:46 AM, Matthew Moss wrote:

> My solution, which does pass your updated test_coord_cmnds, Morton...


Yes, and it passes all my other unit tests, too. Well done.

Regards, Morton

 
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Morton Goldberg
Guest
Posts: n/a
 
      12-04-2006
Quiz 104 -- Solution
====================

Here is what turtle.rb looked like before I messed with it to produce
Quiz 104.

<code>
# An implementation of Turtle Procedure Notation (TPN) as described in
# H. Abelson & A. diSessa, "Turtle Geometry", MIT Press, 1981.
#
# Turtles navigate by traditional geographic coordinates: X-axis
pointing
# east, Y-axis pointing north, and angles measured clockwise from the
# Y-axis (north) in degrees.

class Turtle
include Math
DEG = Math:I / 180.0
ORIGIN = [0.0, 0.0]

alias run instance_eval
attr_accessor :track
attr_reader y, :heading

def degree
DEG
end

###
# Turtle primitives
###
</code>

I explicitly define a writer for @xy to get the Logo-like argument
checking that I wanted. Also, I decided to maintain @xy as an array
of floats to minimize the accumulation of position errors in long
tracks.

<code>
# Place the turtle at [x, y]. The turtle does not draw when it
changes
# position.
def xy=(coords)
if coords.size != 2
raise(ArgumentError, "turtle needs two coordinates")
end
x, y = coords
must_be_number(x, 'x-coordinate')
must_be_number(y, 'y-coordinate')
@xy = x.to_f, y.to_f
end
</code>

Similarly, I explicitly define a writer for @heading. But it's not
just for argument checking: I also use it to constrain @heading to
the interval [0.0, 360.0).

<code>
# Set the turtle's heading to <degrees>.
def heading=(degrees)
must_be_number(degrees, 'heading')
@heading = degrees.to_f
case
when @heading >= 360.0
@heading -= 360.0 while @heading >= 360.0
when @heading < 0.0
@heading += 360.0 while @heading < 0.0
end
@heading
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 = :up
end
</code>

When the pen goes down, a new track segment must be added. Initially,
the segment contains only a single point. If the pen goes up before
another point is added to the segment, the segment ends up with just
one point. Such singleton segments are skipped when the track is
processed by in the view.

<code>
# 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
@track << [@xy]
end

# Is the pen up?
def pen_up?
@pen == :up
end

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

###
# Turtle commands
###

# Place the turtle at the origin, facing north, with its pen up.
# The turtle does not draw when it goes home.
def home
pen_up
self.xy = ORIGIN
self.heading = 0.0
end

# Home the turtle and empty out it's track.
def clear
home
self.track = []
end

alias initialize clear

# Turn right through the angle <degrees>.
def right(degrees)
must_be_number(degrees, 'turn')
self.heading = heading + degrees.to_f
end

# Turn left through the angle <degrees>.
def left(degrees)
right(-degrees)
end
</code>

This is one of two places in the code where it actually has to do
some trigonometry -- Turtle#toward below is the other.

<code>
# Move forward by <steps> turtle steps.
def forward(steps)
must_be_number(steps, 'distance')
angle = heading * DEG
x, y = xy
self.xy = [x + steps * sin(angle), y + steps * cos(angle)]
track.last << xy if pen_down?
end

# Move backward by <steps> turtle steps.
def back(steps)
forward(-steps)
end

# Move to the given point.
def go(pt)
self.xy = pt
track.last << xy if pen_down?
end
</code>

In Turtle#toward, the expression atan2(y2 - y1, x2 - x1) computes the
slope angle of the line between pt and xy. Math#atan2 is better here
than Math#atan because atan2 handles the four quadrant cases
automatically. Once the slope angle is known, it is easily converted
into a heading.

<code>
# Turn to face the given point.
def toward(pt)
x2, y2 = pt
must_be_number(x2, 'pt.x')
must_be_number(y2, 'pt.y')
x1, y1 = xy
set_h(90.0 - atan2(y2 - y1, x2 - x1) / DEG)
end
</code>

Turtle#distance is easy to implement providing one remembers the
existence of Math#hypot.

<code>
# Return the distance between the turtle and the given point.
def distance(pt)
x2, y2 = pt
must_be_number(x2, 'pt.x')
must_be_number(y2, 'pt.y')
x1, y1 = xy
hypot(x2 - x1, y2 - y1)
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

# Raise an exception if <val> is not a number.
def must_be_number(val, name)
if !val.respond_to?(:to_f)
raise(ArgumentError, "#{name} must be a number")
end
end
end
</code>

Now that you've seen the code, let me discuss some of the
implementation decisions I made.

The first issue I had to deal with was how to reconcile the way
turtles measure angles with the way Ruby/Math measures angles.
Turtles, you recall, (following the conventions of geography/
navigation) measure angles clockwise from north in degrees, while the
Math module (following mathematical conventions) measures angles
counterclockwise from east in radians. Since the Turtle class
includes Math, there are advantages to following mathematical
conventions when maintaining the turtle's orientation internal to the
class, However, influenced by Logo, I chose to use the navigator's
notion of angle and to reconcile turtle angles to Math angles each
time I actually did some trig.

I also considered overriding the trig functions with methods that
would accept angles in degrees as their arguments. In the end, I
decided not to, but I still find myself thinking, from time to time,
that I should go back to the code and do it.

The next issue I settled was: what, if any, argument checking should
I do? I settled on accepting any argument that responds to to_f,
raising ArgumentError for those that don't, and providing Logo-like
error messages. The private method Turtle#must_be_number takes care
of this.

The last major issue was: how should I maintain the turtle's state?
That is, what instance variables should the class have? My choices were:

@xy turtle location
@heading turtle orientation
@pen pen state (up or down)
@track array needed to interface with Ruby/Tk

One last remark. Over the years I have built up a good-sized
collection of Logo turtle graphics programs. One of reasons I wanted
a Ruby turtle graphics capability was to convert this collection to
Ruby. I had the feeling that Ruby would prove to be a better Logo
than Logo. Well, I've performed the conversion and I'm convinced I
was right: the Ruby versions of the Logo programs are simpler, easier
to understand, and often considerably shorter than their Logo
counterparts.

Regards, Morton


 
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Pete Yandell
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Posts: n/a
 
      12-04-2006

On 04/12/2006, at 8:28 PM, Edwin Fine wrote:

> Here's my solution.


Ok, a couple of comments.

First, your home method doesn't raise the pen as it should.

Second, all that flipping between turtle space angles and normal
angles is unnecessary. Just swap the x and y axes when doing the trig
and you'll get the right result.

Third, Ruby has an atan2 method that does most of what you do in your
toward method.

Fourth, your normalize_degrees method is overkill. Try '-10 % 360' in
irb.

Here's my solution:


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

attr_accessor :track
alias run instance_eval

def initialize
clear
end

attr_reader y, :heading

# Place the turtle at [x, y]. The turtle does not draw when it
changes
# position.
def xy=(coords)
raise ArgumentError unless is_point?(coords)
@xy = coords
end

# Set the turtle's heading to <degrees>.
def heading=(degrees)
raise ArgumentError unless degrees.is_a?(Numeric)
@heading = degrees % 360
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_is_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_is_down = true
@track << [@xy]
end

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

# Is the pen down?
def pen_down?
@pen_is_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
@heading = 0.0
@xy = [0.0, 0.0]
@pen_is_down = false
end

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

# Turn right through the angle <degrees>.
def right(degrees)
raise ArgumentError unless degrees.is_a?(Numeric)
@heading += degrees
@heading %= 360
end

# Turn left through the angle <degrees>.
def left(degrees)
right(-degrees)
end

# Move forward by <steps> turtle steps.
def forward(steps)
raise ArgumentError unless steps.is_a?(Numeric)
@xy = [@xy.first + sin(@heading * DEG) * steps, @xy.last + cos
(@heading * DEG) * steps]
@track.last << @xy if @pen_is_down
end

# Move backward by <steps> turtle steps.
def back(steps)
forward(-steps)
end

# Move to the given point.
def go(pt)
raise ArgumentError unless is_point?(pt)
@xy = pt
@track.last << @xy if @pen_is_down
end

# Turn to face the given point.
def toward(pt)
raise ArgumentError unless is_point?(pt)
@heading = (atan2(pt.first - @xy.first, pt.last - @xy.last) /
DEG) % 360
end

# Return the distance between the turtle and the given point.
def distance(pt)
raise ArgumentError unless is_point?(pt)
return sqrt((pt.first - @xy.first) ** 2 + (pt.last - @xy.last)
** 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 is_point?(pt)
pt.is_a?(Array) and pt.length == 2 and pt.first.is_a?(Numeric)
and pt.last.is_a?(Numeric)
end

end


 
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Edwin Fine
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Posts: n/a
 
      12-04-2006
Pete Yandell wrote:
> On 04/12/2006, at 8:28 PM, Edwin Fine wrote:
>
>> Here's my solution.

>
> Ok, a couple of comments.
>
> First, your home method doesn't raise the pen as it should.


You're right. That's what I get for working when too tired... .

>
> Second, all that flipping between turtle space angles and normal
> angles is unnecessary. Just swap the x and y axes when doing the trig
> and you'll get the right result.


I did the x-y swapping in an earlier version of the program, but I feel
the flipping is more intuitive for me. It also makes it easier for me to
see how angles change between turtle space and conventional space.

>
> Third, Ruby has an atan2 method that does most of what you do in your
> toward method.


You learn something new every day!

> Fourth, your normalize_degrees method is overkill. Try '-10 % 360' in
> irb.


Thanks for pointing that out. Language specifics are sometimes quite
subtle. This is why it's good to post to RubyQuiz - I learn to do things
in a better way. Thanks for your feedback.

--
Posted via http://www.ruby-forum.com/.

 
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Morton Goldberg
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      12-04-2006
On Dec 4, 2006, at 2:20 PM, Paul Lutus wrote:

> Morton Goldberg wrote:
>
> / ...
>
>> case
>> when @heading >= 360.0
>> @heading -= 360.0 while @heading >= 360.0

>
> @heading %= 360
>
>> when @heading < 0.0
>> @heading += 360.0 while @heading < 0.0

>
> @heading %= 360 # same solution
>
> In fact, now that I think about it, the entire block:
>
> case
> when @heading >= 360.0
> @heading -= 360.0 while @heading >= 360.0
> when @heading < 0.0
> @heading += 360.0 while @heading < 0.0
> end
>
> can be replaced with:
>
> @heading %= 360


Good catch. I had forgotten that %= existed.

Regards, Morton

 
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