Brasilia, Brazil, 29 March - 3 April 1999
Alan Penn and Alasdair Turner
Virtual Reality Centre for the Built Environment
The Bartlett School of Graduate Studies
(Torrington Place Site)
University College London
Gower Street
London WC1E 6BT
England
tel (44) (0)171 504 5919
fax (44) (0)171 916 1887
email a.penn@ucl.ac.uk
www http://www.vr.ucl.ac.uk/
Space syntax analysis is currently a two stage process. First, a map of
continuous open space is subdivided into a finite number of elements such
as axial lines or convex spaces. In the second stage the axial or convex
map is represented in the form of a discrete graph of connectivity relations
between lines or spaces, and properties of the graph are measured. Empirically,
measures of the mean depth of the graph have been found to predict observed
pedestrian and vehicular flows. However, there are clearly variations
in configurational properties that occur from point to point within open
space or along the length of an axial line and which current methods cannot
represent or quantify. In particular, continuous curving alignments and
variations from segment to segment along the length of an axial line pose
problems for current methods.
Both the problem of continuous curves and the 'segment' problem rest ultimately
on the representation of continuous space by a finite number of discrete
entities. Curves must be approximated by flat surfaces and vertices if
an infinite number of convex spaces are not to be produced. Similarly,
given any 'element' with metric extent, there are clearly going to be
variations from point to point within it that a discrete representation
will be unable to quantify. At the basis of both of these problems is
the question of 'resolution'. What is the smallest deformation of the
boundary that needs to be taken into account and how does one generalise
the boundary to eliminate smaller deformations?
This paper paper proposes a new 'field theory' description of spatial
configuration which replaces the graph representation with a geometrical
transformation of the boundary. The key idea is to replace the justified
depth graph with a geometric and metric representation. The mathematics
of this transformation are developed to allow comparison of 'field depths'
from any point of view in a configuration. An analysis is then carried
out of the distribution of field depths in open space in a sample of experimental
configurations. This analysis suggests that the primary spatial representation
of current syntax, the 'axial line map', may itself be an emergent phenomenon
resulting from a global analysis of the spatial field. The paper concludes
that the discrete elements of conventional syntax methods (axial lines
and convex spaces) arise naturally as a consequence of a lower level field
representation which may be able to unify axial and convex properties
of space within a single description.
_______________________________
_______________________________