Some guys down here in CASA have shown me some correspondence about
isovists and isovist fields and the idea of visibility graphs. I have some
points.

1. The geneology: let's try and get this right for a change. The notion of
visibility graphs is part and parcel of the enormous literature on shortest
routes. In fact in the book I have to hand - Berg et al (1996)
Computational Geometry (Springer, Berlin) - there is an entire chapter (Ch
15) entitled Visibility Graphs: Finding the Shortest Route. The idea and
terminology of a visibility graph goes back to the 1960s and possibly even
before. E. F. Moore wrote a paper on shortest paths in a maze in 1957 and I
think that visibility graphs are mentioned in the book by Claude Berge
(1960) Theory of Graphs which is an English translation of the French. So
trying to say who invented them/it is probably not useful. They emerged .....

2. The problem with the visibility graph is that it is an analytic device
used in computing isovists by ray tracing type methods, and not really a
representational concept. It is useful in that there are some properties of
space that it picks up but it is also inefficient in that large areas of
space are very similar, and these have to be represented in the same way as
areas of space which show great heterogeneity. My own feeling is that there
needs to be quite a lot of work done in trying to simplify such graphs and
one obvious strategy would be to follow the sorts of methods used in
mainstream cartography which involve hierarchical nestings such as
quadtrees. I suspect such things already exist in graph theory.

3. The reason why I do not consider visibility graphs to be anything more
than a tool is that isovist fields are one of the few concepts in built
environment that are truly fields in the sense in which fields in physics
exist. This is because the level of their discreteness is so fine that it
is not relevant and we can to all intents and purpose treat such fields as
continuous. The fact we can sweep out such a field from any point at which
we are standing by rotating ourselves around the clock and sensing
everything we see at a very very fine level of resolution (to the level at
which the eye senses) suggests that we should be able to use conventional
mathematics ie calculus to define such fields. Visibility graphs does not
follow this approach.

However again within the shortest routes literature, there are some very
interesting papers written from the mid 1980s onwards about shortest routes
to all and any point which uses ideas from wavelets - ie waves that move
out from a vatnage point. The nice thing about this work is that such waves
are then altered by obstacles and by other waves that crish into them from
other vatnage points. Seems like this is a very interesting area that could
be used to develop continuous maths of isovist fields which could lead to
some interesting operational methods which would go beyond visibility
graphs. The papers that I have seen are by Mitchell, J. B. and one source
is his chapter on Shortest Routes in the Handbook of Discrete and
Computational Geometry edited by J. O'Rourke - dont have detailed reference
at hand.

4. Finally and much closer to home, Geoff Hyman (DoT/DETR) and Shlomo Angel
(AIT) in their book Urban Fields (1976, Pion) basically developed shortest
routes without networks based on continuous spatial interaction models and
this work was done in the late 1960s when they were at Centre for
Environmental Studies, a stones throw from UCL. They appealed to Hugyen's
Theory of Light and these ideas go back to the 1700's. My first PhD
student, Ray Wyatt, wrote his PhD on 'Shortest Routes Without Networks'
(Reading University Geography Dept 1975) and he has a working paper on
this: see R. Wyatt (1974) Shortest Rputes without Networks (Reading
Geographical Papers, No 6).


Mike Batty
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