A greedy heuristic for axial line placement in collections of convex polygons

Master of Science - ScienceAxial line placement is one step in a method known as space syntax which is used in town planning to analyse architectural structures. This is becoming increasingly important in the quickly growing urban world of today. The field of axial line placement is an area of space syntax that has previously been done manually which is becoming increasingly impractical. Research is underway to automate the process and this research forms a large part of the automation. The general problem of axial line placement has been shown to be NP-complete. For this reason, previous research in this field has been focused on finding special cases where this is not the case or finding heuristics that approximate a solution. The majority of the research conducted has been on the simpler case of axial line placement in configurations of orthogonal rectangles and the only work done with convex polygons has been in the restricted case of deformed urban grids. This document presents research that finds two non-trivial special cases of convex polygons that have polynomial solutions and finds the first heuristic for general configurations of convex polygons

The architectures of seeing and going:or, are cities shaped by bodies or minds? And is there a syntax ofspatial cognition?

In my first paper to this Symposium, it was argued that the human cognitive subjectplayed a key part the shaping and working of the city. The key mechanism was thesynchronisation of diachronically experienced (and usually diachronically created)information into higher order pictures of spatial relations, the guiding form for whichwas an abstracted notion of a grid formed by linearised spaces. This notion wasargued to be both perceptual and conceptual, serving at once as an abstractedrepresentation of the space of the city and as a means of solving problems, such asnavigational problems. In this paper, the question addressed is where the notion ofthe ideal grid comes from, why it has the properties it does, and what it has to dowith the real grids of cities, which are commonly of the 'deformed' or 'interrupted'rather than 'ideal' kinds (Hillier, 1996). The answer, it is proposed, lies in the verynature of complex spaces, defining these as spaces in which objects are placed so asto partially block seeing and going, and, in particular, in certain divergences in thelogics of metric and visual accessibility in such spaces. The real grid, deformed orinterrupted, is, it is argued the practical resolution of these divergent logics, and theideal grid its abstract resolution. In both resolutions, however, the resolution is moreon the terms of the visual than the metric, suggesting that cognitive factors are morepowerful than metric factors in shaping the space of the city. The question is thanraised: do people have or acquire the concept of the grid, perhaps as some kind ofperceptual-conceptual invariance of spatial experience in complex spaces, and dothey use it as a model to interact with complex spatial patterns of the urban kind?This possibility is examined against the background of current opinion in the cognitivesciences

Organized complexity of the urban object

Over a half-century, space syntax has proven resilient as a theory and method for describing and analyzing the built environment from dwellings and complex buildings to cities. The paper briefly discusses resilience as a concept in the built environment and the foundations of space syntax itself. We summarize the body of the theoretical thinking in space syntax – laws of the urban object, generic function, principles of centrality and linearity, the design method of spatio-formal processes, and laws of spatial emergence-convergence – before offering a new hypothesis about laws of spatial conservation and spatial optimization at work in the built environment. The latter builds on Conroy-Dalton’s (2001) ideas about angularity and the conservation of linearity in movement. Both could provide an essential bridge with Carvalho and Penn’s (2004) concept of self-similarity in settlements, which relates to Batty and Longley’s (1994) notions of fractal cities. We argue the hypothesis of conservation-optimization defines the conceptual framework for the progressive and regressive practice of urban planning in settlements. We illustrate this theoretical discussion by demonstrating the resilience or replication of previous space syntax findings, and by drawing on new research about the history, spatial structure, and neighborhood logic of Metropolitan Doha.

An algorithmic definition of the axial map

The fewest-line axial map, often simply referred to as the 'axial map, is one of the primary tools of space syntax. Its natural language definition has allowed researchers to draw consistent maps that present a concise description of architectural space; it has been established that graph measures obtained from the map are useful for the analysis of pedestrian movement patterns and activities related to such movement: for example, the location of services or of crime. However, the definition has proved difficult to translate into formal language by mathematicians and algorithmic implementers alike. This has meant that space syntax has been criticised for a lack of rigour in the definition of one of its fundamental representations. Here we clarify the original definition of the fewest-line axial map and show that it can be implemented algorithmically. We show that the original definition leads to maps similar to those currently drawn by hand, and we demonstrate that the differences between the two may be accounted for in terms of the detail of the algorithm used. We propose that the analytical power of the axial map in empirical studies derives from the efficient representation of key properties of the spatial configuration that it captures

Space is the machine, part three: the laws of the field

Part III of the book, ‘The Laws of the Field’, uses these noted regularities to reconsider the most fundamental question of all in architectural theory: how is the vast field of possible spatial complexes constrained to create those that are actually found as buildings? First, in Chapter Eight, ‘Is architecture an ars combinatoria?’, a general theory of ‘partitioning’ is proposed, in which it is shown that local physical changes in a spatial system always have more or less global configurational effects. It is the laws governing this passage form local physical moves to global spatial effects that are the spatial laws that underlie building. These local-to-global spatial laws are linked to the evolution of real buildings through what will be called ‘generic function’, by which is meant the spatial implications of the most fundamental aspects of human use of space, that is, the fact of occupation and the fact of movement. At this generic level, function imposes restraints on what is spatially viable, and this is responsible for what all buildings have in common as spatial designs. Generic function is the ‘first filter’ between the field of possibility and architectural actuality. The second filter is then the cultural or programmatic requirement of that type of building. The third filter is the idiosyncrasies of structure and expression that then distinguish that building from all others. The passage from the possible to the real passes through these three filters, and without an understanding of each we cannot decipher the form-function relation. Most of all, without a knowledge of generic function and its spatial implications we cannot understand that what all buildings have in common in their spatial structures is already profoundly influenced by human functioning in space. In Chapter 9, ‘The fundamental city’, the theory of generic function and the three filters is applied to cities to show how much of the growth of settlements is governed by these basic laws. A new computer modelling technique of ‘all line analysis’, which begins by conceptualising vacant space as an infinitely dense matrix of lines, containing all possible structures, is used to show how the observable regularities in urban forms from the most local to the most global can be seen to be products of the same underlying processes. A fundamental settlement process is proposed, of which particular cultural types are parameterisations. Finally, it is shown how the fundamental settlement process is essentially realised through a small number of spatial ideas which have an essentially geometrical nature

The sequential development and the consequent urban patterns of Bucharest

The main thrust of this thesis is to investigate the intrinsic morphological and topological properties of an urban layout. The study will be focusing on Bucharest, a city built of distinct historic phases and fragments which is facing the need to adapt to new European standards at the same time defining its identity. Syntactic analysis of a spatial configurational model together with classical comparative methods will be used for a fundamental understanding of the urban system. A two phased analysis will be developed. Revising previous hypothesis, the emergence of the city will be discussed illustrating consistent differences between particular stages of its evolution. The argument will be based on previous studies of configurational differences and similarities between cities, done by Hillier (2001), Karimi (1998) and others under the Space Syntax framework; and on morphological urban analysis of Jacobs (1993) and Panerai et al. (2004). Certain transformation in the city structure that occurred under the socialist regime will be proven to have significant effects on the whole configuration of the system. Considering the representative and functional role of the city centre, a second aim will be to produce an evaluative analysis of the major intervention on the city centre that was implemented in the 1980's as a reflection of the political regime, compared to the contrasting configuration of the old centre. The paper will refer to conjectures relating the socio-economic drive and the different modes of employment of space trying to grasp the logic and reasoning behind the distinct spatial systems and how they function together. As a conclusion the paper aims to illustrate once again the functional implications of spatial modelling decisions and objectively question the future development potential of the current configuration on the background of the present concern for the regeneration of the city

Traditional Arabian Marketplaces in Context: A Comparative Study of Souq Waqif in Doha, Qatar and Souq Mutrah in Muscat, Oman

This study presents a comparison of form and function for two traditional markets within their metropolitan regions on the Arabian Peninsula: Souq Waqif in Doha, State of Qatar, and Souq Mutrah in Muscat, Sultanate of Oman. Rapid urbanization and globalization characterize both cities over the previous half-century. Doha and Muscat possess strong similarities in terms of historical origin as coastal settlements. A clear contrast is topography. Flat terrain characterizes Doha. Mountainous terrain characterizes Muscat. The study will explore the dynamic relationship between urban morphology, land use, and social function to better understand the nature and impact of urban changes on the use and experience of these souqs as public spaces today. The research applies several representational techniques common to morphological research including space syntax. The findings reveal the complex nature of these souqs as traditional markets. Understanding better their form and function in their urban context is an important first step for enhancing them in the futur

Single-crossing orthogonal axial lines in orthogonal rectangles

The axial map of a town is one of the key components of the space syntax method – a tool for analysing urban layout. It is derived by placing the longest and fewest lines, called axial lines, to cross the adjacencies between convex polygons in a convex map of a town. Previous research has shown that placing axial lines to cross the adjacencies between a collection of convex polygons is NP-complete, even when the convex polygons are restricted to rectangles and the axial lines to have orthogonal orientation. In this document, we show that placing orthogonal axial lines in orthogonal rectangles where the adjacencies between the rectangles are restricted to be crossed only once (ALPSC- OLOR) is NP-complete. As a result, we infer the single adjacency crossing version of the general axial line placement problem is NP-complete. The transformation of NPcompleteness of ALP-SC-OLOR is from vertex cover for biconnected planar graphs. A heuristic is then presented that gives a reasonable approximate solution to ALP-SC-OLOR based on a greedy method

A Parametrıc Study On The Behavıour Of Mechanıcally Stabılızed Earth (Mse) Wall Usıng Fınıte Element Method

Mekanik olarak stabilize edilmiş dolgu duvarlar, geleneksel olarak kullanılan ağırlık duvarlarına göre basit yapım teknikleri, estetik açıdan görüm ve maliyet açısından daha iyi çözümler sunar. Bu çalışma güçlendirilmiş istinat duvarlarının analizini sunmaktadır. PLAXIS 2D lisanslı sonlu elemanlar programı kullanılarak mekanik olarak stabilize edilmiş dolgu duvarların mühendislik özellikleri ve bu duvarların davranışında etkili olan çeşitli parametreler incelenmiştir. Donatı uzunluğu, donatı tabakaları arasındaki dikey boşluklar, donatının sertliği, duvar yüksekliği,yüzey elemanlarının kalınlığı, trafik yükünün pozisyonu ve güçlendirilmiş zeminin tipi gibi geometrik parametreler analiz edilmiş ve etkiyen yüklerin donatılar ve duvar deformasyonları üzerinde ki etkileri incelenmiştir.Sonuçlar göstermiştir ki; etkiyen yükler genellikle donatı uzunluğundan, donatı sertliğinden ve yüzey elemanlarını kalınlığından bağımsızdır. Genellikle eksenel kuvvetler, duvar yüksekliğinin, geogrid tabakalar arasında ki dikey boşlukların ve dolgu zeminin içsel sürtünme açısının artmasıyla artış göstermiştir. Duvar deformasyonları genellikle geogrid uzunluklarına bağlı olmakta ve L/H oranı 0.7 olduğunda kabul edilebilir sonuçlar elde edilebilmektedir. Duvar deformasyonları ayrıca, geogrid sertliğinin artışına bağlı olarak azalma eğilimi göstermiştir ve bundan dolayı kullanım için yüksek dayanımlı geogridler önerilmiştir. Bunlara ek olarak, geogrid tabakalar arasında ki dikey boşluklar yatay yöndeki deformasyonlarda da etkili olmuştur ve minimum değer olarak bu dikey boşluklar 0.5 m olarak, mekanik olarak stabilize edilmiş dolgu duvarların tasarımında kullanılabileceği önerilmiştir

Grid configuration and land use: A syntactic study of Porto Alegre (Brazil)

This thesis is about the configuration of the urban grid. Configuration is understood here as a perticalor manner of zirratigement which differentiates the layout of the street grid from one part of the town to another. The problem of how to describe, in objective terms, the diversity of grid configurations that compose naturally evolved urban areas is a central concern in this investigation. This thesis is also about the scrutiny of relationships between grid configuration and the distribution of land use. It is conjectured in this respect that configurational factors given by the spatial nature of the grid may affect the way in which land use is distributed in urban areas. A sample of urban areas - grid configurations and corresponding land use distributions - taken from the city of Porto Alegre (Brazil) is the object to be investigated. The simultaneity and interaction of markedly distinct grid configurations within the same city make of Porto Alegre a case where this research has fertile grounds for development. The investigation is centred on the study of the ieWS of tfio offject The urban grid will be assessed in terms of its internal laws and properties which, in a subsequent step, will be statistically compared with the socio-economic dimension of the urban phenomenon given by the distribution of land use. Notes to the reader The non-technical reader may first refer to chapter 7 which provides a summary of the findings produced out of this i nvestigation. The analytical procedure to be developed during chapters 4, 5 and 6 should be read simultaneously with the observation of the diagrams available from the back cover of this thesis