Spatial relations and shape grammars are defined. A spatial relation is specified by a finite number of shapes arranged in a certain way. A shape grammar provides for the recursive generation of arrangements of shapes in terms of given spatial relations. The possible spatial relations between two edge-connected polygons are characterised. The use of these spatial relations to define shape grammars generating distinct languages of shapes is discussed. The construction of shape grammars to generate infinite languages of shapes containing a given shape made up of polygons is also considered.
Get full access to this article
View all access options for this article.
References
1.
AckermanJ S, 1962“A theory of style” in Aesthetic Inquiry Eds BeardsleyM CSchuellerH M (Dickenson, Belmont, Calif.)
2.
ChomskyN, 1963“Formal properties of grammars” in Handbook of Mathematical Psychology, Volume II Eds LuceR DBushR R (John Wiley, New York)
3.
DurandJ N L, 1823–1831Précis des Leçons d'Architecture3 volumes (École Royale Polytechnique, Paris)
4.
FranklP, 1914Principles of Architectural History (MIT Press, Cambridge, Mass.)
5.
FuK S, 1974Syntactic Methods in Pattern Recognition (Academic Press, New York)
6.
GipsJ, 1975Shape Grammars and Their Uses (Birkhauser Verlag, Basel, Switzerland). Also PhD dissertation, Computer Science Department, Stanford University, Stanford, Calif.
7.
GuadetJ, 1902Éléments et Théories de l'Architecture (Paris)
8.
MarchLMatelaR, 1974“The animals of architecture: Some census results on N-omino populations for N = 6, 7, 8”Environment and Planning B1193–216
9.
MinskyM, 1967Computation: Finite and Infinite (Prentice-Hall, Englewood Cliffs, NJ)
10.
MitchellW J, 1973“Vitruvius computatus” in Proceedings, LUBFS Conference on Models and Systems in Architecture and Building (Medical and Technical Press, Lancaster)
11.
MitchellW JDillonR L, 1972“A polyomino assembly procedure for architectural floor planning” in Proceedings of the EDRA3/AR 8 ConferenceSchool of Architecture and Urban Planning, University of California, Los Angeles
12.
RittleH, 1968“Theories of cell configurations” in Emerging Methods in Environmental Design and Planning Ed. MooreG (MIT Press, Cambridge, Mass.)
13.
StinyG, 1975Pictorial and Formal Aspects of Shape and Shape Grammars (Birkhauser Verlag, Basel, Switzerland). Also PhD dissertation, System Science Department, University of California, Los Angeles
14.
StinyG, in press “Generating and measuring aesthetic forms” in Handbook of Perception, Volume X Eds CarteretteE CFriedmanM P (Academic Press, New York)
15.
StinyGGipsJ, 1972“Shape grammars and the generative specification of painting and sculpture” in Information Processing 71 Ed. FreimanC V (North-Holland, Amsterdam)
16.
SummersonJ, 1963The Classical Language of Architecture (MIT Press, Cambridge, Mass)
