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Article #229

Re: aspect ratio (was: LOGO riddle/task/something to think about)

#229
From: Brian Harvey
Date: Wed, 07 Oct 1992 04:22
35 lines
1939 bytes
When I tried [PD FD 4 PU FD 1] the problem I found wasn't about aspect
ratio (although later I had those problems too).  Rather, it was a
fencepost problem.

Suppose that one turtle step equals one pixel.  What happens when you
say FORWARD 1 with the pen down?  Answer: *two* pixels are turned on.
The turtle used to be at, let's say, [0 0].  After moving forward one
step, it's now at [0 1] (supposing it's facing up).  That makes two
pixels that are part of its one step.  If you say FD 100 then the 100
steps include 101 pixels.

(If that seems strange, think about FORWARD 0, which turns on one pixel
in most versions of Logo, namely the one where the turtle is.)

So, if we start at the origin and do PD FD 4 PU FD 1 then the sequence
of events is

1.  No pixels on, turtle at [0 0].
2.  Turtle moves to [0 4], turning on the five pixels at
		[0 0], [0 1], [0 2], [0 3], [0 4]
3.  Pen up.
4.  Turtle moves one step, not changing what's on the screen since
		the pen's up, ending up at [0 5].

Now if we repeat the same steps, five more pixels will be turned
on, from [0 5] to [0 9].  There is no gap!  Every pixel along the
way was turned on.

If there is no aspect ratio problem, the sequence
	REPEAT 18 [PD FD 3 PU FD 2]
should make four-on, one-off dotted lines.

If you *do* have an aspect ratio problem, you'll know it because
the dottedness comes out uneven because of roundoff errors in
convering turtle steps to pixel steps.
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References: <1992Oct7.002753.14062@discus.technion.ac.il>

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Path: arc1-ca.pugleaf.net!sparky!uunet!sun-barr!ames!agate!anarres.CS.Berkeley.EDU!bh
From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: comp.lang.logo
Subject: Re: aspect ratio (was: LOGO riddle/task/something to think about)
Date: 7 Oct 1992 04:22:27 GMT
Organization: University of California at Berkeley
Lines: 35
Message-ID: <1atom3INNng6@agate.berkeley.edu>
References: <1992Oct7.002753.14062@discus.technion.ac.il>
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