I was very encouraged to see some response to the issue of Visibility Graph
Analysis (VGA) on the mailbase (see
http://www.mailbase.ac.uk/lists/spacesyntax/2000-04/thread.html). Open
debate like this is valuable if we are to progress the techniques for
representation available to spatial analysis, especially as there are some
major areas of disagreement about them.
Firstly, the use of the term 'isovist integration' as a synonym for
visibility graph analysis is misleading for the important reasons that the
technique of VGA is neither based on isovists nor on the measure of
integration. Visibility graphs are composed of intervisible point pairings
(not visual fields). The set of intervisible points can be used as a
connectivity matrix and this can be the basis for many interesting graph
measures, of which integration is one. But integration is not really useful
unless complete systems are being processed because the result that it
gives is so heavily influenced by edge effect. The article by Alasdair
Turner, Maria Doxa et al. 'From isovists to Visibility Graphs' explains in
more detail why the misnomer 'isovist integration' was first used and for
historical reasons and why VGA is now considered a more appropriate
descriptor (see http://www.vr.ucl.ac.uk/vga).
The other main source of confusion is on the difference between axial maps
and visibility graphs. Kayvan argued that visibility graphs are very
complicated whereas the virtues of axial maps are "the simplicity of the
model and its inherent compatibility with the way the space is used by
people". I would argue that, on the contrary, a 'fewest line' axial map is
actually a far more unknown and complicated thing than you might initially
expect; more complex than a visibility graph and in some senses a more
limited description of space that is actually derived from VGA.
Although we may not always be very conscious of it, just because axial maps
are not drawn by a computer it does not mean that they are somehow simpler
than visibility graphs. On the contrary, the opposite is true: axial maps
must be drawn by people because they are hard and the steps required
(finding the 'fewest' and 'longest' lines) are quite mathematically
complex. Fewest by what criteria? Longest of what set? This is why nobody
has yet produced a computer program to carry out the arduous task of
drawing the fewest line axial map. Visibility graphs are very simple to
produce because the algorithm is so simple and unambiguous. The only limit
is on the size of the representation because the technique generates so
much more information- but this is a practical not a theoretical limit and
advances in computer technology suggest that this is no longer such an issue.
One of the uses of visibility graphs could be to provide a basis to
automatically calculate different kinds of 'fewest line' axial maps. VGA
can be used to define clusters of intervisible points (which is one
definition of a 'convex space') from these clusters of points it is quite
easy to find the two furthest apart in metric terms. The parameters of
clustering coefficient and minimum length of line could also be tweaked to
explore different versions of the fewest line map. Although this would by
no means solve all of the computational complexity involved in trying to
create a fewest line map (John Peponis has written at length about some of
the other problems involved) it would at least be one approach to trying to
automate the production of axial maps that are completely clear,
unambiguous and repeatable because the whole 'thought process' required to
make them would be specified in the computer program.
This may clarify the fact that although Kayvan believes VGA "is based on
multidirectional visual fields… without bringing into consideration the
factor of linearity and linear orientation", lines of sight are actually
the basis of visibility graphs too. The simplest property of VGA is whether
two points in an environment can see each other. 'Isovists' are actually a
higher order property derived from visibility graphs. So the lines of sight
that an axial map tries to describe are contained within VGA.
I do not understand Kayvan's assertion that the "Axial map (before
analysis) creates a new representation of the space by approximating
two-dimensional space into one-dimensional components, whereas IIA
represents the space by an unlimited … number of dimensionless components".
This just isn't true. An axial map is described by two dimensional lines
(x,y co-ordinate pairs). The components of a simple visibility graph are
two dimensional points (x,y co-ordinate points). Two intervisible points in
VGA make a line of sight and each point holds information about which other
points it can see, or in other words what possible lines of sight are
available to it. So there is nothing as strange as 'dimensionless
components' or 'one dimensional spaces' in either representation- we are
talking about ways of capturing lines of sight in both cases.
It is also wrong to assert that an axial map allows you to retrieve
descriptions of 'urban blocks' and 'ringiness'. Axial maps do not
accurately describe either urban blocks or ringiness because they
necessarily create many fake rings and fake blocks: if anyone has ever
tried to represent a bit of town containing an open space or a curving
street with axial lines they will know that all sorts of trivial blocks or
rings are created by overlapping and crossing lines. A simple figure
ground representation can tell you much more about the morphological
characteristics of urban blocks, if that is what you are trying to measure.
Nobody would argue that spatial analysis should be reduced to one single
technique, and I don't know who Kayvan is debating with when he says "it is
much too soon to say that one single method of analysis can solve all our
problems". However, all these representation techniques are only
interesting in so far as they are useful in informing us about the world
and helping us tackle specific real world problems like simulating the
effect that a change to the environment will have on pedestrian movement
patterns. And specific problems should be tackled with specific techniques:
the best ones available at any point in time.
Surely it is not a goal of the research programme just to keep accumulating
alternative methods? There must be progress. Rather than use "a combination
of all possible and relevant methods", the "best" approach should be the
subject of vigorous debate- we should be constantly refining the criteria,
tests and specification for which techniques are the best.
It is right of Kayvan to point out that "spatial analysis, especially when
it is to be applied in design… should be accompanied by a lot of research
and experience. The results of spatial analysis, if they are not handled
properly, can be misleading". I agree with this completely because design
itself is not a science. There is a huge difference between undertaking an
accurate analysis of space and knowing what to do with that analysis either
in developing social policy, developing a property or developing an
architectural design. These activities are about experience and judgement
because they involve weighing up the costs and benefits of different and
sometimes opposing considerations (of which spatial configuration is only
one). Let us be clear that although spatial analysis can inform one aspect
of these considerations, in itself it has nothing to do with design which
is quite a different pursuit. Spatial analysis is not a science of design
and it never will be.
I agree with the idea that "What we have to create in parallel with
developing new analytical ideas and tools, is to enhance our overall
'vision' of space, society and design". In this spirit we should strive to
always make our techniques the servants of the big problems that our
research programme is aimed at. In terms of a vision of space, I hope that
we can keep in mind what these representations are for, namely to
understand how environments influence the way that people use them. Without
serving that purpose the representations are just works of art.
Einstein once said; "No fairer destiny could be allotted to any physical
theory than that it should itself point out the way to introducing a more
comprehensive theory in which it lives on as a limiting case". I believe
that visibility graph analysis is, in this sense, a real descendent of the
axial map representation of space.
Jake
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Dr. Jake Desyllas
Partner
Intelligent Space
1 Torriano Mews
London NW5 2RZ
phone: 020 7267 7392
fax: 020 7428 0782
email [log in to unmask]
http://www.intelligentspace.com
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