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