Jake does have a point with our integration measure.  The edge effect is
very noticeable in VGA (far more than in axial analysis).  In addition,
(or perhaps because of) the low radii of the graphs mean that the
restricting the radius is not the solution.  However, having said this,
it does not mean we should give up on integration.  We can easily weight
the edge of the graph to compensate for the edge effect (i.e., the
equivalent of embedding an analysis zone within an overall map of a city
--- something Space Syntax frequently do with projects within London and
other major cities).  There are also many graph approximation methods
for integration, which can be tweaked to minimise edge effect.

JD> Visibility graphs are very simple to produce because the algorithm
JD> is so simple and unambiguous.

Alan is quite right to point out that we are talking about two levels of
simplicity, but be careful to note that although VGA initially looks
very simple, complexity issues come into play when trying to find an
optimum resolution for integration, as I explained in my talk on Tuesday
(I'm currently writing this work up, so please hold on just for the
mo).  Thus, just like axial analysis, the result of VGA is not
independent of the person who applies it.

AP> Not quite true - we had automatic fewest line mapping in about 
AP> 1985/6 written by Stefan in the pre-Sheep era. The methods worked
AP> very well for organic urban form - Apt, Gassin etc. However as 
AP> soon as one starts to look at systems with higher degrees of 
AP> geometric order it becones difficult to determine single solutions
AP> and additional rules must be added. This leads to greater 
AP> algorithmic complexity - not impossibility - and the difficultry
AP> is mainly about recognising where to start searching for a 
AP> solution.

Not quite true again.  Finding a unique set of fewest lines is actually
what we should class as impossible --- in general, it impossible to come
up with a unique set of maximal convex spaces, so that any computer
algorithm will have to make a human-like judgement if it is to find the
actual set of convex spaces, thus what we are trying to cover in the
first place is a moving target.  Even having taken that into account, it
is then not generally possible to select a unique minimum set of
intersecting lines.  This is not just a case of computational
complexity, but of impossibility (thus, why I suggested visibility graph
analysis in the first place :-)

AP>  however there is a problem with scalability with these - just as 
AP> there is with VGA. For this reason at least fewest line maps look 
AP> set to stay for practical purposes

By contrast, Alan is spot on here.  The axial map is here for a while
yet (and with Sheep's new improvements --- cue Sheep! --- probably a
long time after that too).

As Alan says:

AP> Speaking as one of those who invented VGA I agree with Kayvan.
AP> Fewest line analysis will be around for a long time yet for a 
AP> number of practical as well as methematical reasons.

And also note:

AP> extraction of fewest line maps in his spatialist software, based I
AP> think on e and s partitions. However, I dont know too much about 
AP> how  well these have been found to work (John - update??)

Despite my dire prognostications, so long as we accept an 'artificial
intelligence' selecting lines for us and that we accept that there is no
*the* minimal set, we can still retrieve sets of lines that approximate
what we want, even if the formal definition is very complicated.  So,
yes, I'd be interested in the results too.

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

True, though on reflection, it would still be nice to include axial
lines as a limiting case of VGA (and at the time we found VGA we were
trying to see how we could derive axial lines from isovists).

But, as everyone knows, you don't use Quantum Theory to work out the
tensile stress on a bridge, you still use perhaps the perceptively
greater Newton's Laws.

AP> The point  about space syntax and its analysis in design is that
AP> it lets one be relatively clear in ones discussion of different 
AP> design strategies and in the assessment of their likely impact on
AP> a whole range of social and economic outcomes of design.

This also relates something Julienne has said --- surely we should not
lose sight of the importance of the architect in all of our mathematical
meanderings.  Space Syntax is fantastic in that it gives us new tools to
communicate about how a space operates.  And perhaps Alan and Jake are
both right --- there is here a problem in attacking in space by
straight-forward scientific complexity theory.  Yes, we can release a
set of agents into an environment, and yes we can see what's happening
at an ever more detailed level but we begin to lose the ability to
describe the actions of the agents in a language we understand.

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

With due respect AP, half-invented... well, um, not even half... it
appears we were beaten to it by almost 20 years (and we would have been
blissfully ignorant if we did not have such an assiduous researcher as
Ruth Conroy on our side... did I say on our side?)

Braaksma, J P and Cook, W J, Human orientation in transportation
terminals.  Transportation Engineering Journal, 106(TE2):189-203, March
1980.

Alasdair

-- 
Alasdair Turner   Virtual Reality Centre for the Built Environment
Research Fellow   tel +44 20 7679 1806        fax +44 20 7813 2843
University College London   Gower Street   London   WC1E 6BT    UK


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%