Analysis and Classification of Public Spaces Using Convex and Solid-Void Models

Abstract

Urban planning and design are increasingly often supported by analytical models of urban space. We present a method of representation for analysis and classification of open urban spaces based on physical measures including three-dimensional data to overcome some observed limitations of two-dimensional methods. Beginning with “convex voids” constructed from 2D plan information and 3D data including topography and building facade heights, we proceed to “solid voids” constructed by aggregation of convex voids. We describe rules for construction of both convex voids and solid voids, including basic forms and their adjustment for perception. For analysis we develop descriptive characteristic values such as enclosure, openness, granularity and connectivity, derived from more basic geometric properties of the void representations. We also show how combinations of these values can be correlated with urban open space typologies, including commonly accepted traditional ones as well as previously unnamed classes of space. Concluding with discussion of some future planned developments in this work, we also propose that such methods can contribute to better understanding of the relations between urban forms and their perception and use, so as to guide urban transformations for improved urban quality.

Appendix: Summary of Measures Extracted from Convex- and Solid-Voids’ Model

Convex-voids’ generation
Convex-voids’ height	cv H	${}_{\mathrm{cv}}H=\left(\Sigma {A}_{\mathrm{f}}\right){\!/\!}{P}_{\mathrm{s}}$	Convex-voids’ height is derived from the average height of surrounding buildings
Corrected convex-voids’ height	cv H c	${}_{\mathrm{c}\mathrm{v}}{H}_{\mathrm{c}}={}_{\mathrm{c}\mathrm{v}}H+{}_{\mathrm{c}\mathrm{v}}H_{\mathrm{adj}}$	Corrected convex-voids’ height is sum of convex-void height with the height adjustment value (cv H adj) which can be positive or negative depending on the characteristics of the surrounding spaces
Convex-voids’ characteristics
Area	cv A
Volume	cv V
Shape
Aspect ratio
Convex-voids properties

Spaciousness/containment	${{}_{\mathrm{cv}}S} {{}_{\mathrm{cv}}C}$	$\begin{array}{lll}{{}_{\mathrm{cv}}S={A}_{\mathrm{g}}/{A}_{\mathrm{fv}}} \\ {{}_{\mathrm{cv}}C={A}_{\mathrm{fv}}/{A}_{\mathrm{g}}}\end{array}$	Spaciousness/containment represents the relation between the area of the convex-void façades and its floor area
Enclosure/openness to vision	cvEV cvOV	$\begin{array}{lll}{_{\mathrm{cv}}\mathrm{E}\mathrm{V}={P}_{\mathrm{e}}{\!/\!}{P_{\mathrm{s}}}_{\mathrm{cv}}}\\ {\mathrm{O}\mathrm{V=1{\hbox{--}}} _{\mathrm{cv}}\mathrm{E}\mathrm{V}}\\ {\left({P}_{\mathrm{ev}}+{P}_{\mathrm{ov}}={P}_{\mathrm{s}}\right)}\end{array}$	Enclosure/openness encodes the proportion of open or closed vs total perimeter
Perceived enclosure/openness to vision	cvEV pcvOVp	$\begin{array}{lll}{{}_{\mathrm{cv}}{\mathrm{OV}}_{\mathrm{p}}=}\\{\left(\Sigma {A}_{\mathrm{fv}}\hbox{--}\ \Sigma {A}_{\mathrm{fv}\mathrm{adj}}\right){\!/\!}\Sigma {A}_{\mathrm{fv}}}\end{array}$	Perceived enclosure/openness is a percentage of a convex-void’s faces that is overlapped by surrounding ones
Enclosure/openness to movement	cvEM cvOM	$\begin{array}{lll}{{}_{\mathrm{cv}}\mathrm{E}\mathrm{M}={P}_{\mathrm{em}}/{P}_{\mathrm{s}}}\\{{}_{\mathrm{cv}}\mathrm{O}\mathrm{M}=1\hbox{--} {}_{\mathrm{cv}}\mathrm{E}\mathrm{M}=}\\{\left({P}_{\mathrm{em}}\hbox{--} {P}_{\mathrm{s}}\right){\!/\!}{P}_{\mathrm{s}}}\end{array}$	Enclosure/openness to movement takes into account obstacles to movement
Solid-voids properties
Number of convex-void particles	sv N		Number of convex-voids that are forming the solid-void
Length of solid-void	sv L		Sum of the lengths of all street segments forming the solid-void
Number of façades within a solid-void	sv N f
Granulation of built structure of solid-void	sv G		Number of façades per hundred metres
Connectivity	svCON		Number of physically permeable routes leading from one solid-void toward other spaces
Perceived connectivity	svCONp		Number of all routes, physically permeable and not permeable, opening from one solid-void toward other spaces
Void connectivity	svVCONp		Number of other solid-voids connecting (or crossing) a solid-void

A _g: Ground area of space

A _f: Areas of buildings’ façades

A _fv: Area of vertical faces of convex-voids

A _fn: Areas of neighbourhoods’ façades

A _fvadj: Area of vertical faces of adjoining convex-voids

_cv H _adj: Height adjustment (=_G H × (3/Sqrt(9 + A _g)))

_G H: Gross height correction value ((A _f − A _fn)/P _s)

L _f: Length (on ground) of façades (excl. 0-height)

P _s: Total perimeter of space

P _ev: Length of perimeter closed to vision (=ΣL _f)

P _ov: Length of perimeter opened to vision

P _em: Length of perimeter closed to movement