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Stefan Fina Patterns of Urban Sprawl Geographical Analysis
Functional triangle (FT)
The second indicator introduced to measure the dispersion of urban functions is called the Functional
Triangle (FT). Like DI it is based on an adaptation of point pattern analysis with average nearest
neighbors. The difference, however, is that it does not measure distances between all urban entities,
but differentiates between their function. The concept goes back to theories about urban planning and
land use change that describe a low neighborhood mix of land uses as a typical outcome of urban
sprawl (see background section). The idea is to analyze the minimum distance between the main
origins and destinations that most households need to travel to in daily activities, forth and back.
Essentially, the indicator adopts methods from transport modeling and replaces qualitative inputs
(usually derived from household surveys) with highly generalized proxies for trip purpose, trip rates,
and origin-destination matrices:
- Trip purposes cover residence to business (industrial, retail, warehousing), residence to public
services location (schools, administration, recreation), and business to public services.
- Trip rates are replaced by feature weightings of residential units, i.e. number of households or
number of people.
- Detailed origin-destination matrices are replaced by nearest neighbor trip chains, starting with
residential entities.
The minimum distance is the closest triangle that can be formed between the trip purpose functions in
the existing configuration of urban entities (see Fig. 2). This is not to say that closest connections are
the most relevant ones in reality or that this approach could capture actual interactions. Its aim is to
give an average indication about the compactness or dispersion of urban functions, and from that
perspective distance is certainly a crucial evaluator. In other words, people in areas with shorter
average FT distances are likely to have to travel less for their daily activities than in areas with long
average distances.
Ideally, a road network is used for distance calculations, as roads usually reflect the geographical
conditions in an area (topography, waterways, etc.) and give more meaningful distances for
calculations. Fig. 2 shows examples of typical travel paths for FT: Example 1 is a dense urban center