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Re: [Phys-l] zero width?



On 10/15/2007 05:24 PM, Michael Porter wrote:

Okay, just to play devil's advocate here, how are you defining the
boundary? Chalk is made of atoms and atoms don't have a well-defined
edge.

That's a reasonable question; satanic advocacy not required.

Step 1: Atoms do have reasonably well-defined centers. Define
the edge as halfway between where "this" row of atom-centers is
and where the "next" row would be.

http://www.av8n.com/physics/atom-intro.htm#fig-st3153c1

Step 2a: For a chalk region that is intended to be convex,
take the convex hull of the atoms as "the" region.

Step 2b: More generally, you can define some sort of
smoothing spline. The smoothing parameter must be large
compared to atoms and small compared to the detail you
are trying to depict ... which are usually non-conflicting
requirements, non-conflicting by a wide margin.