Re: representing patterns and structures
phayes@cs.uiuc.edu (Pat Hayes)
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Date: Fri, 18 Nov 1994 17:59:26 -0600
To: brayman@zuben.ca.boeing.com (Bill Brayman), cg@cs.umn.edu,
srkb@cs.umbc.edu
From: phayes@cs.uiuc.edu (Pat Hayes)
Subject: Re: representing patterns and structures
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At 9:40 AM 11/18/94 -0800, Bill Brayman wrote:
>Here is a modeling question in the spirit of brainstorming (I wonder
>why there isn't more of this among us).
>
>Suppose you have a sheet of metal with holes in it, or a table with
>marbles on it, or a row of pickets in a fence, inch marks on a ruler,
>telephone poles on the road, etc.
>
>What constructs would one use to say that objects are grouped, that
>they are evenly spaced, that they reside in a region of an object, that
>they form a shape such as a gentle curve, or a matrix?
>
> fence pickets are spaced 3 inches apart
> the marbles were arranged in a circle
>
>The dictionary says that a row is a group of objects that are next to
>one another. How would one model "next to one another?"
>
>
>It seems that there should be some way to represent patterns or
>structures without having identify every point to point
>interelationship among elements of the pattern.
Yes. Consider 'the marbles were arranged in a square." This could mean
arranged like this
*********
* *
* *
* *
* *
* *
*********
or like this:
*********
*********
*********
*********
*********
*********
The first case is most analogous to "..were arranged in a circle" , which
suggests that the relevant concept here is that of a curve of some kind, ie
an essentially onedimensional path, probably fairly smooth by mathematical
standards. Now, to say that some marbles (say) are arranged along such a
curve means that the curve passes through each one exactly once, and we
could define 'through' as meaning in one side and out the other, and define
'side' to mean that part of the surface which is closest to another thing
in the set. This gives a global characterisation of the main shape that
they all lie on, but a local one of what it means for them to lie on it.
The need for some local care is to avoid cases like saying that
* *
* *
lie on a circle. Even though thats geometrically possible, these
intuitively form a square, and that can be accounted for by this criterion
for what a 'side' of one of the objects is.
Things are next to one another, now, if they lie on (using above criteria)
a straight line (or at any rate a very smooth curve, so we don't allow
corners inside one of the objects, as in the above square.)
There have to be snags with this. Please shoot it down.
Pat Hayes
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