In response to Jake:

> 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).

I agree that we should standardise on VGA - I think I suggested it in the
first place - but terminology tends to have a life of its own and 'isovist
integration' slips off the tongue better so this may be a hard battle.....
However, just to clarify, 'intervisible point pairings' _do_ describe
isovists, and integration (or at least mean depth) has been found so far to
be the best predictive measure of the VG so far as movement is concerned.

> 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.

Radius integration seems to avoid edge effect so far as we can work out.

> 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.

The point here is that there are two forms of 'simplicity' being talked
about. In terms of the simplicity of actually making and computing 'by hand'
the fewest line map wins hands down. In terms of algorithmic simplicity VGA
wins.

> 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.

Not quite true - we had automatic fewest line mapping in about 1985/6
written by Stefan in the pre-Sheep era. The methods worked very well for
organic urban form - Apt, Gassin etc. However as soon as one starts to look
at systems with higher degrees of geometric order it becones difficult to
determine single solutions and additional rules must be added. This leads to
greater algorithmic complexity - not impossibility - and the difficultry is
mainly about recognising where to start searching for a solution. This is
somthing that people are particularly good at. The result so far as
automation was concerned lay with the all line map, however there is a
problem with scalability with these - just as there is with VGA. For this
reason at least fewest line maps look set to stay for practical purposes
(ie. for answering design questions) for a while yet as the crucial issue
seems to be about being able to analyse a large enough area rather than a
small area at a high resolution. The edge effect that Jake notes is only a
problem because the areas being analysed are too small.
More recently John Peponis has developed some methods for autmated
extraction of fewest line maps in his spatialist software, based I think on
e and s partitions. However, I dont know too much about how well these have
been found to work (John - update??)

> 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.


> 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.

One needs to be very carful to be clear when starting on discussions of
numbers of dimensions involved in this kind of maths. Kayvan's point refers
to the dimensionality of the particular element not the composition of these
elements into a configuration. In this sense points are dimension 0, lines
dimension 1 and convex spaces dimension 2. That is they are extended in 0, 1
and 2 dimensions respectively. Of course spatial configurations considered
as plans are two dimensional in this sense and so are the individual
elements of these configurations - hence Jake's confusion. Of course it gets
far more confusing when one considers the dimensionality of graphs and there
are several approaches to defining this - I won't go into these here.

>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.

At one level that is true, however the point about figure grounds is that
they dont give much in the way of measures (just a number of blocks or
average area for example). Axial maps go further than this giving measures
of ringiness in terms of line link ratio etc. See the Social Logic for a
description.

> 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".

I suspect that this is KK's reaction to what came over as a bit of an
'overclaim' on behalf of VGA by you, Jake, in the email that started this
thread. Speaking as one of those who invented VGA I agree with Kayvan.
Fewest line analysis will be around for a long time yet for a number of
practical as well as methematical reasons.

> 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.

Well the history of Space Syntax analysis suggests that we accumulate a lot
of alternative methods, VGA is just one of the latest, and what sorts out
those that survive is their ability to throw light on practical and
theoretical problems and empirical data.

>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.

Well, this is a bit of a nonsequitur - of course few would hold that spatial
analysis is the only thing that matters, but space and the way it is
configured is pretty fundamental to architectural design at least. The point
about space syntax and its analysis in design is that it lets one be
relatively clear in ones discussion of different design strategies and in
the assessment of their likely impact on a whole range of social and
economic outcomes of design.

> I believe that visibility graph analysis is, in this sense, a real
descendent of the
> axial map representation of space.

Of course it is Jake - that is why I invented it !

Alan




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