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Algorithmic complexity of shape grammar implementation

Published online by Cambridge University Press:  09 May 2018

Thomas Wortmann  and
Rudi Stouffs Open the ORCID record for Rudi Stouffs [Opens in a new window]
Thomas Wortmann*
Affiliation:
Singapore University of Technology and Design, Architecture and Sustainable Design, 20 Dover Drive, Singapore 138682, Singapore
Rudi Stouffs
Affiliation:
Department of Architecture, National University of Singapore, 4 Architecture Drive, Singapore 117566, Singapore
*
Author for correspondence: Thomas Wortmann, E-mail: [email protected]
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Abstract

Computer-based shape grammar implementations aim to support creative design exploration by automating rule-application. This paper reviews existing shape grammar implementations in terms of their algorithmic complexity, extends the definition of shape grammars with sets of transformations for rule application, categorizes (parametric and non-parametric) sets of transformations, and analyses these categories in terms of the resulting algorithmic complexity. Specifically, it describes how different sets of transformations admit different numbers of targets (i.e., potential inputs) for rule application. In the non-parametric case, this number is quadratic or cubic, while in the parametric case, it can be non-polynomial, depending on the size of the target shape. The analysis thus yields lower bounds for the algorithmic complexity of shape grammar implementations that hold independently of the employed algorithm or data structure. Based on these bounds, we propose novel matching algorithms for non-parametric and parametric shape grammar implementation and analyze their complexity. The results provide guidance for future, general-purpose shape grammar implementations for design exploration.

Keywords

Shape grammarsshape grammar implementationsalgorithmic complexitytractability
Type
Regular Articles
Information
AI EDAM , Volume 32 , Special Issue 2: Advances in Implemented Shape Grammars: Solutions and Applications , May 2018 , pp. 138 - 146
Copyright
Copyright © Cambridge University Press 2018 

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References

Batz, GV (2006) An Optimization Technique for Subgraph Matching Strategies (Internal Report No. 7). Institut für Programmstrukturen und Datenorganisation, Fakultät für Informatik, Universität Karlsruhe (TH), DE.Google Scholar
Chau, HH, Chen, X, McKay, A and de Pennington, A (2004) Evaluation of a 3D shape grammar implementation. In Gero JS (ed.). Design Computing and Cognition'04. Dordrecht, NL: Springer, pp. 357–376.Google Scholar
Cormen, TH, Leiserson, CE, Rivest, R and Stein, C (2009) Introduction to Algorithms, 3rd edn. Cambridge, MA: MIT Press.Google Scholar
Dorn, F (2010) Planar subgraph isomorphism revisited. In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science.Google Scholar
Duarte, JP (2001) Customizing Mass Housing: A Discursive Grammar for Siza's Malagueira Houses, Ph.D. Dissertation. Boston, MA: Massachusetts Institute of Technology.Google Scholar
Frank, AU (1999) One step up the abstraction ladder: Combining algebras-from functional pieces to a whole. In Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science. London, UK: Springer.Google Scholar
Garey, MR and Johnson, DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. New York, NY, USA: W. H. Freeman & Co.Google Scholar
Gips, J (1999) Computer implementation of shape grammars. NSF/MIT Workshop on Shape Computation.Google Scholar
Grasl, T and Economou, A (2013) From topologies to shapes: parametric shape grammars implemented by graphs. Environment and Planning B: Planning and Design 40(5), 905–922.CrossRefGoogle Scholar
Knight, TW (1989) Color grammars: designing with lines and colors. Environment and Planning B: Planning and Design 16(4), 417–449.Google Scholar
Knight, TW (1993) Color grammars: the representation of form and color in designs. Leonardo 26(2), 117–124.Google Scholar
Krishnamurti, R (1981) The construction of shapes. Environment and Planning B: Planning and Design 8(1), 5–40.Google Scholar
Krishnamurti, R and Stouffs, R (1997) Spatial change: continuity, reversibility, and emergent shapes. Environment and Planning B: Planning and Design 24(3), 359–384.Google Scholar
Kukluk, JP, Holder, LB and Cook, DJ (2004) Algorithm and experiments in testing planar graphs for isomorphism. Journal of Graph Algorithms and Applications 8(2), 313–356.Google Scholar
Mitchell, WJ (1993) A computational view of design creativity. In Gero, JS and Maher, ML (eds). Modeling Creativity and Knowledge-Based Creative Design. Hillsdale, NJ: Lawrence Erlbaum, pp. 25–42.Google Scholar
Sloane, NJA and Arndt, J (eds) (2010) The On-Line Encyclopedia of Integer Sequences. Available online at https://oeis.orgGoogle Scholar
Stiny, G (1977) Ice-ray: a note on the generation of Chinese lattice designs. Environment and Planning B: Planning and Design 4(1), 89–98.Google Scholar
Stiny, G (1980) Introduction to shape and shape grammars. Environment and Planning B 7(3), 343–351.Google Scholar
Stiny, G (1981) A note on the description of designs. Environment and Planning B: Planning and Design 8(3), 257–267.Google Scholar
Stiny, G (1990) What is a design? Environment and Planning B: Planning and Design 17(1), 97–103.Google Scholar
Stiny, G (1992) Weights. Environment & Planning B: Planning and Design 19, 413–430.CrossRefGoogle Scholar
Stiny, G (1994) Shape rules: closure, continuity, and emergence. Environment and Planning B: Planning and Design 21(7), S49–S78.CrossRefGoogle Scholar
Stiny, G (2006). Shape: talking about seeing and doing. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Stiny, G (2011) What rule(s) should I use? Nexus Network Journal 13(1), 15–47.Google Scholar
Stiny, G and Mitchell, WJ (1978 a) Counting palladian plans. Environment and Planning B: Planning and Design 5(2), 189–198.Google Scholar
Stiny, G and Mitchell, WJ (1978 b) The palladian grammar. Environment and Planning B: Planning and Design 5(1), 5–18.Google Scholar
Stouffs, R (2017) A practical shape grammar for Chinese ice-ray lattice designs. In Cultural DNA Workshop: Computational studies on the cultural variation and heredity. Daejeon, KR.Google Scholar
Stouffs, R (2018) Implementation issues of parallel shape grammars. Artificial Intelligence for Engineering Design, Analysis and Manufacturing. doi: 10.1017/S0890060417000270.Google Scholar
Stouffs, R and Krishnamurti, R (2002) Representational flexibility for design. In Gero, JS (ed.). Artificial Intelligence in Design ‘02. Springer Netherlands, pp. 105–128.Google Scholar
Stouffs, R and Krishnamurti, R (2006) Algorithms for classifying and constructing the boundary of a shape. Journal of Design Research 5(1), 54–95.Google Scholar
Strobbe, T, Pauwels, P, Verstraeten, R, De Meyer, R and Van Campenhout, J (2015) Toward a visual approach in the exploration of shape grammars. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 29(04), 503–521.Google Scholar
Tapia, M (1992) Chinese lattice designs and parametric shape grammars. The Visual Computer 9(1), 47–56.CrossRefGoogle Scholar
Tapia, M (1999) A visual implementation of a shape grammar system. Environment and Planning B: Planning and Design 26(1), 59–73.Google Scholar
Trescak, T, Esteva, M and Rodriguez, I (2012) A shape grammar interpreter for rectilinear forms. Computer-Aided Design 44(7), 657–670.Google Scholar
Wortmann, T (2013) Representing Shapes as Graphs, SMArchS Thesis. Cambridge, MA: Massachusetts Institute of Technology.Google Scholar
Yue, K and Krishnamurti, R (2013) Tractable shape grammars. Environment and Planning B: Planning and Design 40(4), 576–594.Google Scholar
Yue, K and Krishnamurti, R (2014) A paradigm for interpreting tractable shape grammars. Environment and Planning B: Planning and Design 41(1), 110–137.Google Scholar