A Practical Shape Grammar for Chinese Ice-Ray Lattice Designs

  • Rudi Stouffs
Part of the KAIST Research Series book series (KAISTRS)


Different explications of Stiny’s shape grammar for Chinese ice-ray lattice designs found in literature are explored and their ‘practicality’ is assessed in terms of the number of construction elements included in a representative shape rule and the number of potential matches that the matching algorithm must consider when applying this rule to a representative shape. Alternative explications are suggested that score well with respect to both measures. The exercise is meant to provide insights and requirements for the development of a general shape grammar interpreter, with flexibility and ease of use in mind.


Shape grammar Parametric shape grammar Shape schema grammar Description grammar 



This work received some funding support from Singapore MOE’s AcRF start-up grant, WBS R-295-000-129-133.


  1. 1.
    Stiny, G. (1977). Ice-ray: A note on the generation of Chinese lattice designs. Environment Planning B Planning Design, 4(1), 89–98.CrossRefGoogle Scholar
  2. 2.
    Stiny, G., & Mitchell, W. J. (1980). The grammar of paradise: On the generation of Mughul gardens. Environment Planning B Planning Design, 7(2), 209–226.CrossRefGoogle Scholar
  3. 3.
    Flemming, U. (1987). More than the sum of parts: The grammar of Queen Anne houses. Environment Planning B Planning Design, 14(3), 323–350.CrossRefGoogle Scholar
  4. 4.
    Chiou, S.-C., & Krishnamurti, R. (1995). The grammar of Taiwanese traditional vernacular dwellings. Environment Planning B Planning Design, 22(6), 689–720.CrossRefGoogle Scholar
  5. 5.
    Çağdas, G. (1996). A shape grammar: The language of traditional Turkish houses. Environment Planning B Planning Design, 23(4), 443–464.CrossRefGoogle Scholar
  6. 6.
    Li, A. I. (2001). A shape grammar for teaching the architectural style of the Yingzao fashi. Ph.D. thesis, Department of Architecture, MIT.Google Scholar
  7. 7.
    Şener, S. M., & Görgül, E. (2008). A shape grammar algorithm and educational software to analyze classic Ottoman mosques. A| Z ITU. Journal of the Faculty of Architecture, 5(1), 12–30.Google Scholar
  8. 8.
    Muslimin, R. (2013). Decoding Passura’: Representing the indigenous visual messages underlying traditional icons with descriptive grammar. In R. Stouffs, P. Janssen, S. Roudavski, & B. Tunçer (Eds.), Open systems (pp. 781–790). Hong Kong: CAADRIA.Google Scholar
  9. 9.
    Duarte, J. P. (2001). Customizing mass housing: a discursive grammar for Siza’s Malagueira Houses. Ph.D. thesis, Department of Architecture, MIT.Google Scholar
  10. 10.
    Stiny, G. (1980). An introduction to shape and shape grammars. Environment Planning B Planning Design, 7(3), 343–351.CrossRefGoogle Scholar
  11. 11.
    Woodbury, R. (2016). An introduction to shape schema grammars. Environment Planning B Planning Design, 43(1), 152–183.CrossRefGoogle Scholar
  12. 12.
    Stiny, G., & Mitchell, W. J. (1978). The Palladian grammar. Environment Planning B Planning Design, 5(1), 5–18.CrossRefGoogle Scholar
  13. 13.
    Duarte, J. P. (2005). Towards the mass customization of housing: The grammar of Siza’s houses at Malagueira. Environment Planning B Planning Design, 32(3), 347–380.CrossRefGoogle Scholar
  14. 14.
    Stouffs, R. (2005). Description grammars: A general notation. Environment Planning B Planning Design,
  15. 15.
    Grasl, T., & Economou, A. (2013). From topologies to shapes: Prametric shape grammars implemented by graphs. Environment Planning B Planning Design, 40(5), 905–922.CrossRefGoogle Scholar
  16. 16.
    Strobbe, T., Pauwels, P., Verstraeten, R., De Meyer, R., & Van Campenhout, J. (2015). Toward a visual approach in the exploration of shape grammars. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 29(4), 503–521.CrossRefGoogle Scholar
  17. 17.
    Wortmann, T. (2013). Representing shapes as graphs. MSc thesis, Department of Architecture, MIT.Google Scholar
  18. 18.
    Strobbe, T. (2015). Computer-aided exploration of architectural design spaces: A digital sketchbook. Ph.D thesis, Department of Architecture and Urban Planning, Ghent University.Google Scholar
  19. 19.
    Liew, H. (2004). SGML: A meta-language for shape grammar. Ph.D. thesis, Department of Architecture, MIT.Google Scholar
  20. 20.
    Tapia, M. (1992). Chinese lattice design and parametric shape grammars. The Visual Computer, 9, 47–56.CrossRefGoogle Scholar
  21. 21.
    Stouffs, R., & Wieringa, M. (2006). The generation of Chinese ice-ray lattice structures for 3D facade design. In M. Dulaimi (Ed.), Conference Proceedings of the Joint International Conference on Construction Culture, Innovation and Management (CCIM) (pp. 416–424). Dubai: BUiD.Google Scholar
  22. 22.
    Stiny, G. (1981). A note on the description of designs. Environment Planning B Planning Design, 8(3), 343–351.Google Scholar
  23. 23.
    Stouffs, R. (2005). Description grammars: Precedents revisited. Environment Planning B Planning Design.
  24. 24.
    Brown, K. N., McMahon, C. A., & Sims Williams, J. H. (1996). Describing process plans as the formal semantics of a language of shape. Artificial Intelligence in Engineering, 10(2), 153–169.CrossRefGoogle Scholar
  25. 25.
  26. 26.
    Wortmann, T., & Stouffs, R. Algorithmic complexity of shape grammar implementation. AI EDAM (forthcoming).Google Scholar
  27. 27.
    Stouffs, R., & Hou, D. (2017). The complexity of formulating design(ing) grammars. In A. Fioravanti, & et al. (Eds.), Shock! sharing of computable knowledge! (Vol. 2, pp. 443–452). Brussels: eCAADe.Google Scholar
  28. 28.
    Stouffs, R., & Krishnamurti, R. (2001). Sortal grammars as a framework for exploring grammar formalisms. In M. Burry, S. Datta, A. Dawson, & J. Rollo (Eds.), Mathematics and design 2001 (pp. 261–269). Geelong, Australia: Deakin University.Google Scholar
  29. 29.
    Stouffs, R. (2008). Constructing design representations using a sortal approach. Advanced Engineering Informatics, 22(1), 71–89.CrossRefGoogle Scholar
  30. 30.
    Stouffs, R. (2012). On shape grammars, color grammars and sortal grammars: A sortal grammar interpreter for varying shape grammar formalisms. In H. Achten, J. Pavlicek, J. Hulin, & D. Matejovska (Eds.), Digital physicality (Vol. 1, pp. 479–487). Brussels: eCAADe.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of ArchitectureNational University of SingaporeSingaporeSingapore

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