The attached gif gives an example - please excuse the horrible graphics. The 
blue dots are the vertices of the polygon, the black is the original lines, and 
the red shows where the one vertex that would likely be removed during 
simplification would create a new line segment that intersects with the rest of 
the polygon.

Chris

Quoting Martin Davis <mbdavis@VividSolutions.com>:

> I don't have time or the setup right now to generate an example that causes
> this, but I have no doubt that I could produce one.  Anytime a process moves
> line segments (e.g. by deleting points) without a global check about whether
> intersections are created there is the potential to corrupt the topology.
> 
> A polygon with a inward spike (which would not be changed by DP) very close
> to a slightly curved line (which *would* be eliminated by DP) would exhibit
> this kind of failure.
> 
> Martin Davis, Senior Technical Architect
> Vivid Solutions Inc.
> Suite #1A-2328 Government Street   Victoria, B.C.   V8T 5G5
> Phone: (250) 385 6040    Fax: (250) 385 6046
> EMail: mbdavis@vividsolutions.com  Web: www.vividsolutions.com
> 
> 
> > -----Original Message-----
> > From: Matt Lynch [mailto:matt@terraEngine.com]
> > Sent: Thursday, August 28, 2003 3:13 PM
> > To: 'PostGIS Users Discussion'
> > Subject: RE: [postgis-users] How to generalize or simplify a Polygon
> >
> >
> > Hi Christoph,
> >
> > I searched the postings with D-P Algorithm and found the
> > posting on Line
> > Simplification that you mentioned.  I will look into that as it would
> > ideal for me to have it within PostGIS.
> >
> > Does anyone have any more details on the self-intersection
> > problem that
> > was mentioned earlier in the thread?  I haven't been able to come up
> > with a case where I could see a self-intersection generated.
> >
> > Thanks,
> >
> > Matt
> >
> > -----Original Message-----
> > From: postgis-users-bounces@postgis.refractions.net
> > [mailto:postgis-users-bounces@postgis.refractions.net] On Behalf Of
> > Christoph Spoerri
> > Sent: Thursday, August 28, 2003 3:06 PM
> > To: PostGIS Users Discussion
> > Subject: Re: [postgis-users] How to generalize or simplify a Polygon
> >
> >
> > I'm not sure if this was mentioned before, but earlier this
> > summer their
> > was a
> > post on the list by somebody that implemented the D-P
> > algorithm on lines
> > as
> > an extension/function to PostGIS. This may be a good starting point to
> > also
> > simplify polygons (if required).
> >
> > Along this line, I was also think if it would be possible/useful to
> > store the
> > simplified feature within the database. This would then allow the user
> > to
> > specify which 'version' of a spatial dataset should be retrieved. This
> > would
> > provide a similar functionality as is already available for raster
> > datasets
> > where pyramids are used to provide this functionality. What does the
> > rest of
> > you think about this?
> >
> > Christoph
> >
> >
> > On Thursday 28 August 2003 04:29 pm, Martin Davis wrote:
> > > > of self-intersection when you process a polygon. So why
> > not put it
> > > > in as an method that is only a member of LineString /
> > > > MultiLineString class ?
> > >
> > > If we were putting D-P into JTS, that would be one place to put it,
> > > alright.  However, as I said I'd really rather keep JTS focussed on
> > > core algorithms.
> > >
> > > On a philosophical note, adding algorithms as methods to Geometry
> > > objects seems to be encouraged by the OO paradigm, but it's not the
> > > most scalable or flexible way of doing things.  For
> > algorithms such as
> >
> > > D-P which are pretty independent of the internal
> > representation of the
> >
> > > Geometry I think it's nicer to keep them outside the
> > Geometry class in
> >
> > > a separate algorithm class.
> > >
> > > Martin Davis, Senior Technical Architect
> > > Vivid Solutions Inc.
> > > Suite #1A-2328 Government Street   Victoria, B.C.   V8T 5G5
> > > Phone: (250) 385 6040    Fax: (250) 385 6046
> > > EMail: mbdavis@vividsolutions.com  Web: www.vividsolutions.com
> > >
> >
> >
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