please see message 1926 with art
&or topozone for original
& no time to tell you who i am now
later
m
--- In BoundaryPoint@y..., "granthutchison" <granthutchison@b...>
wrote:
> Michael:
> > but if you were rationalizing some place like palm springs or the
> > salton sea rezzies in this way
> > where the apparent border cross singluarities actually come by
the
> > dozens & scores in continuous grids
> > you would quickly get stuck retracing your own route
> > & couldnt even complete your tour & accounting
>
> OK, who are you and what have you done with the real Michael
Donner?!
> I can't believe you keep using practicality as an argument in this,
> given your usual brisk opposition to all practicality.
>
> And, actually, I reckon I *can* do a just this sort of tour.
> What you're talking about is a modification of something called an
> Euler Tour - in a net of linked points and lines ("vertices"
> and "edges", in the jargon) it's possible to make a tour visiting
> each edge only once and then returning to your starting point, if
and
> only if all the vertices are of even degree (ie form the meeting
> point of an even number of edges).
> This is exactly the state of affairs in a set of linked bi-entity
> quadripoints - each vertex is the meeting point for four edges.
> The reason I say "a modification" of the standard Euler Tour is
> because my edges are "directed" -I'm only allowed to traverse them
in
> one direction. But each vertex is of in-degree 2 and out-degree 2:
> two edges leading in, two edges leading out, so I can never get
> trapped at a vertex. Some slight handwaving and scribbling makes me
> think that with this specific set-up I can still do an Euler Tour,
> but I really haven't seen a definitive statement in a maths
reference
> to back that up.
> But by way of experiment, what I *have* just done is to use
something
> called the Fleury algorithm to plot an Euler Tour of the edges of
the
> white squares on a chessboard, visiting all 49 vertices twice each,
> passing along every edge only once, *never* performing a border
> cross, *and* always travelling in a clockwise direction relative
the
> white square (so meeting my own self-imposed criteria, too). And I
> can do this with a chess-board with an odd number of squares on a
> side, as well.
> So I think with a decent map and some planning, I'd have a fighting
> chance of getting around your quadripoint sea(s). Do you have a
good
> map you could scan and send me?
>
> Grant