We propose a characterization of axial maps by means of an extension of a local property which has been proved to describe the cell decomposition of the plane induced by line arrangements. This gives a discrete model which is more closely related to axial maps than the usual representation by graphs.
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References
1.
BjörnerALas VergnasMSturmfelsBWhiteNZieglerG, 1993Oriented Matroids, in the Encyclopedia of Mathematics and its Applicationsvolume 46(Cambridge University Press, Cambridge)
2.
BokowskiJSturmfelsB, 1989Computational Synthetic Geometry, in the series Lecture Notes in Mathematicsvolume 1355 (Springer, Heidelberg)
3.
GareyM RJohnsonD S, 1979Computers and Intractability: A Guide to the Theory of NP-Completeness (W H Freeman, San Francisco, CA)
4.
GrünbaumB, 1970, “The importance of being straight”, in Proceedings of the 12th Biannual International Seminar of the Canadian Mathematical Congress Vancouver, Ed. PykeR, (Canadian Mathematical Congress, Montreal) pp 243–254
5.
GrünbaumB, 1972Arrangements and Spreads in the CBMS Regional Conference Series in Mathematicsvolume 10 (American Mathematical Society, Providence, RI)
6.
HillierBHansonJ, 1984The Social Logic of Space (Cambridge University Press, Cambridge)
7.
HillierBHansonJGrahamH, 1987a, “Ideas are in things: An application of the space syntax method to discovering house genotypes”Environment and Planning B: Planning and Design14363–385
8.
HillierBHansonJPeponisJ, 1987b, “Syntactic analysis of settlements”Architecture & Comportement/Architecture & Behaviour3217–232
9.
HillierBHansonJPeponisJHudsonJBurdettR, 1983, “Space syntax: A different urban perspective”The Architects' Journal17847–63
10.
HillierBPenAHansonJGrejewvskiTXuJ, 1993, “Natural movement: Or, configuration and attraction in urban pedestrian movement”Environment and Planning B: Planning and Design2029–66
11.
KrügerM J T, 1989, “On node and axial grid maps, distance measures and related topics”, paper presented at the European Conference on the Representation and Management of Urban Change, Cambridge, September; copy available from the Bartlett School of Architecture, University College London
12.
KrügerM J T, 1990, “Representation and understanding urban maps in pedestrian movement analysis”; copy available from the Bartlett School of Architecture, University College London
13.
PapadimitriouC HSteiglitzK, 1982Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, New York)
