Stochastic Isovist Fields

When isovist analysis is applied to a plan in its totality (rather than to individual locations of special interest), one issue to be resolved by appropriate convention is the identification of “all points” from which isovists will be drawn. The nature of space is such that the actual number of possible points is infinite.

In conventional approaches (such as UCL’s ‘Depthmap’ programme), an square tessellation of samples is adopted. Such a method establishes ‘all points’ as having a uniform and orthogonal grid spacing. The resolution of such a spacing is defined by the user and has implications for the complexity of analysis calculation required and the detail of mapping ultimately produced. In order for a mapping to be ‘complete’, all points need to be analysed and so even for small contiguous spaces a large amount of time is taken up by calculation.


Here we propose an alternative approach. Isovists are continually generated based on a stochastic location sampling as shown in this hypothetical ‘T’ block layout (filmed at 1/10th actual speed):

The inherent geometric properties of these isovists (such as area) can be recorded directly back to all spatial points contained within each isovist. When this is done successively, for multiple different isovists, and the values accumulated at the points of isovist overlap, coherent quantitative spatial fields can be rapidly formed:


Since calculation is continual and ongoing, developing results can be immediately observed by the user. The ‘resolution’ of the quantitative spatial fields produced is greater than that achieved by standard approaches; providing values at the level of each pixel of the plan imported, rather than for arbitrary ‘cellular’ spatial divisions. It can provide a much finer differentiation of spatial partitioning for a series of differing spatio-geometric fields.

An extended taxonomy of spatial fields produced in this method for a series of hypothetical layouts can be found here.

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The work described above was supported by the UCL Space Group EPSRC platform grant EP/G02619X/1 (P7726), in the context of a research project on Dynamic Three Dimensional Space Syntax Modelling directed by Sophia Psarra at UCL.

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