From: James Edward Gray II <james@...>
Date: 2006-12-08T05:27:21+09:00
Subject: Re: Turtle Graphics (#104)

On Dec 7, 2006, at 11:15 AM, Edwin Fine wrote:

>>      # 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
>
> I think that you should mention a subtlety here. The calculation of a
> new point is usually
>
> [x,y] = [x_old + dist * cos(theta), y_old + dist * sin(theta)]
>
> Because the turtle geometry is 90 degrees out of phase and rotating in
> the other direction, Pete has flipped the x and y so the new point is
>
> [x,y] = [x_old + dist * sin(theta), y_old + dist * cos(theta)]
>
> Another subtlety is that Pete used atan2, which handles division by  
> zero
> and the ambiguity of which quadrant you are in.
>
> (Well, it was subtle to me!!)

Both terrific points.  Thanks for bringing them up!

James Edward Gray II