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A Computational Method For Generating Convex Maps Using the Medial Axis Transform
KTH, School of Architecture and the Built Environment (ABE), Architecture, Urban Design. (Spatial Analysis and Design)
KTH, School of Architecture and the Built Environment (ABE), Architecture, Urban Design. (Spatial Analysis and Design)ORCID iD: 0000-0002-7089-4244
2013 (English)In: Proceedings of Ninth International Space Syntax Symposium / [ed] Young Ook Kim, Hoon Tae Park, Kyung Wook Seo, Seoul: Sejong University Press , 2013, 064: 1-064: 11 p.Conference paper, Published paper (Refereed)
Abstract [en]

Convex maps were first introduced by Hillier and Hanson in “The social logic of space”, and have since become a standard diagram of space syntax, particularly in the analysis of interior of buildings. Despite of their extensive use, the computer generation of convex maps turns out to be quite difficult. An  algorithmic description of the process would afford an objective form of reproducing analysis results and the consistent application of the same method on a set of data; unfortunately the original guidelines to draw convex maps by hand have been shown to be impossible to translate into a formal description of the type necessary for a computer program. 

Thus, rather than attempting a translation of the original procedure, we have looked at alternatives methods for producing convex maps in the field of shape analysis. In particular we have studied a set of problems which deal with the decomposition of shapes into simpler parts and their organisation,and which are conceptually related to the convex map. We have accordingly developed a method for subdividing architectural plans into non overlapping, convex partitions that captures their most salient organisational features, based on the medial axis transform, a well known shape descriptor first proposed by H.Blum in 1967.  Our method is based on adding the simpler convex regions defined through the segments and branching points of the medial axis according to different priorities, under the condition that these additions remain convex. 

In space syntax the automatic production of convex spaces has often focused on their instrumentality in the calculation of axial maps, and has not have the convex map as the final objective.The method we have developed, in the other hand, produces convincing convex partitions and maps, which often coincide with those resulting from following the original hand-drown method description. Its results can be used for representing the organisation of spaces at the level of simplicity and abstraction of the original convex partitions proposed by Hillier and Hanson, and to allow the study of their configuration through the application of different graph measures and visualisation techniques.

We have implemented our methods in C++. The effective calculation of the medial axis required the use of robust and reliable computational geometry libraries, and consequently we have based most of our geometric data-structures and algorithms in those provided by CGAL, a well tested and widely used library distributed under GPL/LGPL license. Besides CGAL our tests and demonstration programs also use a number of different libraries, such as Dime, for dxf input and output or Qt, for GUI and interaction.

Place, publisher, year, edition, pages
Seoul: Sejong University Press , 2013. 064: 1-064: 11 p.
Keyword [en]
Building diagrams, Convex Maps, Medial Axis, Convex Partitions, Graphs, Building Analysis, Shape Analysis, Algorithm
National Category
URN: urn:nbn:se:kth:diva-137874ISBN: 978-89-86177-21-3 (print)OAI: diva2:679788
9th International Space Syntax Symposium, Seoul, October 31 - November 3, 2013
EU, FP7, Seventh Framework Programme, 242497

Approved for publication via Diva by Conference Organisers. 

QC 20140103

Available from: 2013-12-16 Created: 2013-12-16 Last updated: 2017-11-29Bibliographically approved
In thesis
1. Program Matters: From Drawing to Code
Open this publication in new window or tab >>Program Matters: From Drawing to Code
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Whether on paper, on site or mediating between both, means for reading and writing geometry have been central to architecture: the use of compasses and rulers, strings, pins, stakes or plumb-lines enabled the analysis and reproduction of congruent figures on different surfaces since antiquity, and from the renaissance onwards, the consistent planar representation of three-dimensional shapes by means of projective geometry. Tacitly through practice, or explicitly encoded in classical geometry, the operational syntaxes of drawing instruments, real or imaginary, have determined the geometric literacies regulating the production and instruction of architecture. But making marks on the surfaces of paper, stone or the ground has recently given way to the fundamentally different sequential operations of computers as the material basis of architectural inscription. Practices which have dominated architecture since antiquity make little sense in its current reading and writing systems. 

This thesis examines technologies of digital inscription in a search for literacies equivalent to those of drawn geometry. It particularly looks at programming as a form of notation in close correspondence with its material basis as a technology, and its effects on architecture. It includes prototypes and experiments, graphics, algorithms and software, together with their descriptions and theoretical analyses. While the artefacts and texts respond to the different forms, styles, interests and objectives specific to the fields and contexts in which they have originated, their fundamental purpose is always to critique and propose ways of writing and reading architecture through programming, the rationale of the research and practice they stem from. 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 102 p.
TRITA-ARK. Akademisk avhandling, ISSN 1402-7461 ; 2017:4
program, algorithm, code, drawing, geometry, notation, score, literacy, writing systems, diagram, formalism, sequence, cybernetics, materiality, research programme, archeological, archive, discourse analysis, practice-based, artefact, bricolage
National Category
Research subject
urn:nbn:se:kth:diva-218462 (URN)978-91-7729-586-0 (ISBN)
Public defence
2018-01-12, F3, Lindstedtsvägen 26, Stockholm, 13:00 (English)
Swedish Research CouncilSwedish Research Council FormasEU, FP7, Seventh Framework Programme

QC 20171129

Available from: 2017-11-29 Created: 2017-11-28 Last updated: 2017-11-29Bibliographically approved

Open Access in DiVA