shape grammars

basic research into shape grammars

1980-present

In collaboration with George Stiny, Lionel March, Chris Earl, Christian Giraud and Francois Grobler and former students: Rudi Stouffs, Shang-chia Chiou, Kui Yue and Casey Hickerson

course website: http://www.andrew.cmu.edu/course/48-747/

A shape grammar is a system of rewriting shape rules.

A design is generated as a sequence of shapes; each shape in the sequence produces the next shape in the sequence by substituting a part of the shape for another part. The two parts constitute a shape rule. Shapes can be tagged with markers, to deal with functional and other non-spatial features. Markers can be erased and added during design generation. Markers can be specified in the shape rules. Shape rules are usually further classified into stages; in this way, layout generation can be broken down into phases. A shape grammar is developed from a methodological examination of corpora of designs specified by a set of characteristics.

I am best known for my work in shape grammar computation; that is, on computer implementations. In 1981 I wrote the first complete implementation of a shape grammar interpreter (SGI) that could handle emergent shapes, based on a complete and uniform representation of two-dimensional shapes as finite sets of straight lines based on a theory of rational shapes that I hade developed for the implementation. Since then, for nearly 30 years, periodically, with colleagues and students I have revisited the subject.

My early work looked at shape arithmetic and recognition for line and plane shapes in two- and three dimensions. With my former doctoral student Rudi Stouffs, we developed the theory and algorithms for shape arithmetic and recognition for shapes in three dimensions and; developed an algebraic theory of shapes and implemented a toolkit for shape manipulation in C and in Java. More recently, with my student Kui Yue, we looked at implementing parametric shape grammars

The table below summarizes the state-of-the-art.

					Shape problems solved
U₀	U_0,0	U_0,1	U_0,2	U_0,3	arithmetic
U₁		U_1,1	U_1,2	U_1,3	+ recognition
U₂			U_2,2	U_2,3	+ grammar implementation
U₃				U_3,3

Chinese Vernacular Architecture

LUBAN Feng-shui based geomancy calculations for new construction

With my former doctoral student Shang-chia Chiou, we developed shape grammars for vernacular Taiwanese architecture, traditional san-he-yuan houses and temples. A feature of this grammar, quite distinct from conventional shape grammars, is that the grammar did not rely upon a corpus of forms from which shape rules were induced. Instead, the rules were derived purely from an analysis of traditional processes of design and construction based on precepts of feng-shuiand geomancy. The rules were tested out on a number of extant complex vernacular houses.

Example shape rules and 3-D rule based model of a traditional Taiwanese vernacular architecture

Tractable parametric shape grammars

With Kui Yue, we have explored the implementation of a class of tractable parametric shape grammars for which we have developed a paradigm for con-structing viable parametric shape grammar interpreters. Two interpreters were constructed and tested on new shape grammars for Queen Anne Houses and the Baltimore Rowhouse. We have plans to develop interpreters for other grammars.

Possible generated layouts

The Baltimore Rowhouse shape grammar as a tree and as working prototype

Other investigations include theoretical studies on emergence, continuity, computational complexity, and decidability of shape grammar computation.

sponsors

— over the years parts of the work on shape grammars have been supported by various sponsors; these include:
Science and Engineering Research Council (UK); The Open University; European Strategic Programme for Information Technology (ESPRIT); The Japan Research Institute; School of Architecture (Carnegie Mellon), the US Army Corp CERL-ERDC and the Netherlands Organization for Scientific Research (NWO) (support for Rudi Stouffs).

publications

Krishnamurti R (1980) The arithmetic of shapes. Environment and Planning B: Planning and Design, 7, 462-484.

Krishnamurti R (1981) The construction of shapes. Environment and Planning B; Planning and Design, 8, 5-40.

Krishnamurti R (1982) SGI: an interpreter for shape grammars. Technical Report, Centre for Configurational Studies, The Open University, Milton Keynes, UK.

Krishnamurti R (1982) SGI user manual. Technical Report, Centre for Configurational Studies, The Open University, Milton Keynes, UK.

Krishnamurti R and Giraud C (1986) Towards a shape editor: an implementation of a shape generation system. Environment & Planning B: Planning and Design, 13, 391–404

Krishnamurti R (1992) The maximal representation of a shape. Environment & Planning B: Planning and Design, 19, 267– 288

Krishnamurti R (1992) The arithmetic of maximal planes. Environment & Planning B: Planning and Design, 19, 431–464.

Krishnamurti R and Earl CF (1992) Shape recognition in three dimensions. Environment & Planning B: Planning and Design, 19, 585–603

Stouffs R and Krishnamurti R (1993) The complexity of the maximal representation of shapes. Proceedings of the IFIP Workshop on Formal Methods

Krishnamurti R, and Stouffs R (1993) Spatial Grammars: Motivation, Comparison and New Results. In U. Flemming and S. Van Wyk (eds) CAAD Futures’93, pp 57-74, Elsevier Science Publishers BV, Netherlands.

Stouffs R and Krishnamurti R (1994) An Algebraic Approach to Shape Computation (Position Paper), Workshop on Reasoning with Shapes in Design, pp 50-55, Artificial Intelligence in Design’94, Lausanne, Switzerland, August 15-18.

Chiou S-C and R Krishnamurti. The fortunate dimensions of Taiwanese traditional architecture. Environment & Planning B: Planning and Design, 22, 547-562.

Chiou S-C and Krishnamurti R (1995) The Grammar of Taiwanese Traditional Vernacular Dwellings. Environment & Planning B: Planning and Design, 22, 689-720.

Chiou S-C and Krishnamurti R (1995) The Grammatical Basis of Traditional Chinese Architecture, Languages in Design, 1(3), 5-31.

Chiou S-C and Krishnamurti R (1996) Example Taiwanese traditional houses. Environment & Planning B: Planning and Design, 23, 191-216.

Krishnamurti R and Stouffs R (1997) Spatial change: Continuity, Reversibility and Emergent Shapes, Environment & Planning B: Planning and Design, 24(3), 359-384

Chiou S-C and Krishnamurti R (1997) A Grammar of Taiwanese Traditional Temples. CAADRIA 97, pp 297-311, Taiwan, April 17-19.

S-C Chiou and R Krishnamurti. (1997) Unraveling Feng-shui. Environment & Planning B: Planning and Design, 24(4), 549-572.

Krishnamurti R and Stouffs R (2004) The boundary of a shape and its classification. The Journal on Design Research, vol. 4, issue 1, (http://www.inderscience.com/)

Stouffs R and Krishnamurti R (2006) Algorithms for the classification and construction of the boundary of a shape. Journal of Design Research, vol. 6, issue 1, (http://www.inderscience.com/)

Yue K, Hickerson C and Krishnamurti R. (2008) Determining the interior layout of buildings describable by shape grammars. CAADRIA 2008 (eds. W Nakapan, E Mahaek, K Teeraparbwong, and P Nilkaew), pp 117-124, Chiang-Mai: Pimniyom Press, April.

Grobler F, Aksamija A, Kim H, Krishnamurti R, Yue K and Hickerson C (2008) Ontologies and shape grammars: Communication between Knowledge-Based and Generative Systems. Design Computing and Cognition: Proceedings of the Third International Conference on Design Computing and Cognition (eds JS Gero and AK Goel), pp 23-40, Springer.

Yue K and Krishnamurti R (2008) A technique for implementing a computation-friendly shape grammar interpreter. Design Computing and Cognition: Proceedings of the Third International Conference on Design Computing and Cognition (eds JS Gero and AK Goel), pp 61-80, Springer.

Yue K, Krishnamurti R and Grobler F (2009) Computation-friendly shape grammars. Joining languages and cultures and vision. CAAD futures 2009 (eds T Tidafi and T Dorta), pp 757-770, Les Presses de l’Université de Montréal, Canada, June.

Yue K, Krishnamurti R and Grobler F (2010). Guesstimating the interior layout of buildings using a shape grammar to capture building style. Submitted to the ASCE Journal of Computing in Civil Engineering. Revised December 2010.