convexity for discrete set of points...

[Longin Jan Latecki]

Hi,

The term Michael Aupetit defines is called digital convexity.
There are a few definitions of digital convexity,
which are not necessarily equivalent.
I can recommend two older references:

Rosenfeld, A., Kim, C.E., 
How a Digital Computer Can Tell Whether a Line is Straight,
AMM(89), 1982, pp. 230-235.

Kim, C.E., and Rosenfeld, A., 
Digital Straight Lines and Convexity of Digital Regions,
PAMI(4), No. 2, March 1982, pp. 149-153.

With best regards, 
Longin Jan

***
Dr. Longin Jan Latecki
Department of Applied Mathematics
University of Hamburg
Bundesstr. 55, 20146 Hamburg, Germany
Email: latecki at math.uni-hamburg.de 
http://www.math.uni-hamburg.de/home/latecki/
Phone: ++49 40 428385156 or ++49 40 822273241 
Fax: ++49 40 42838 5117



Michael Aupetit wrote:

To: "compgeom-discuss at research.bell-labs.com" 
<compgeom-discuss at research.bell-labs.com>, aupetit at eerie.site-eerie.ema.fr 
Subject: convexity for discrete set of points... 
From: aupetit <Michael.Aupetit at site-eerie.ema.fr> 
Date: Thu, 08 Feb 2001 10:32:36 +0100 


Hello,

I'm a PhD student from France. I'd like to know if it exists a
"correct" name for the following property:

considering a set S of a finite number N of points in R^d and
an indicator value 0 or 1 associated to them which indicates
if the points are part or not of a particular set X. (X subset of S)

If any point of X is inside the convex hull of X,
then I would like to say that X is "convex".

And if it exists at least one point in S which is not in X but
which is in the convex hull of X, I would like to say that
X is not "convex".

I'm not sure I can use the term "convex" for that property.
Does it already exist a well suited term for that?

Thank you for your help

Michael Aupetit

0 0 0 0 0         0 0 0 0 0
0 1 1 1 0         0 1 1 1 0
0 1 1 1 0         0 1 0 1 0
0 1 1 1 0         0 1 1 1 0
0 0 0 0 0         0 0 0 0 0

"convex"  - "non convex" ?




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