Planarity and Street Network Representation in Urban Form Analysis

TL;DR

This paper investigates the three-dimensional complexity of urban street networks, quantifies their nonplanarity, and introduces new indicators to assess how planar models may misrepresent real-world connectivity and infrastructure.

Contribution

It develops two novel metrics, the Spatial Planarity Ratio and Edge Length Ratio, to measure and analyze the nonplanarity of street networks across multiple cities.

Findings

Some street networks are approximately planar.

Planar models can significantly misrepresent connectivity and street lengths.

Nonplanarity varies within cities and impacts urban analysis.

Abstract

Models of street networks underlie research in urban travel behavior, accessibility, design patterns, and morphology. These models are commonly defined as planar, meaning they can be represented in two dimensions without any underpasses or overpasses. However, real-world urban street networks exist in three-dimensional space and frequently feature grade separation such as bridges and tunnels: planar simplifications can be useful but they also impact the results of real-world street network analysis. This study measures the nonplanarity of drivable and walkable street networks in the centers of 50 cities worldwide, then examines the variation of nonplanarity across a single city. It develops two new indicators - the Spatial Planarity Ratio and the Edge Length Ratio - to measure planarity and describe infrastructure and urbanization. While some street networks are approximately planar, we empirically quantify how planar models can inconsistently but drastically misrepresent intersection density, street lengths, routing, and connectivity.