Visual Structures of Embedded Shapes

Chapter
Part of the KAIST Research Series book series (KAISTRS)

Abstract

Shape computations recognise parts and create new shapes through transformations. These elementary computations can be more than they seem, inducing complicated structures as a result of recognising and transforming parts. This paper introduces, what is perhaps in principle, the simplest case where the structure results from seeing embedded parts. It focusses on lines because, despite their visual simplicity, if a symbolic representation for shapes is assumed, lines embedded in lines can give rise to more complicated structures than might be intuitively expected. With reference to the combinatorial structure of words the paper presents a thorough examination of these structures. It is shown that in the case of a line embedded in a line, the resulting structure is palindromic with parts defined by line segments of two different lengths. This result highlights the disparity between visual and symbolic computation when dealing with shapes—computations that are visually elementary are often symbolically complicated.

Keywords

Shape grammars Shape structure Embedding Visual palindromes 

Notes

Acknowledgements

The authors would like to thank George Stiny for his generosity in ongoing discussions about this particular ‘walk in the park’.

References

  1. 1.
    Prats, M., Lim, S., Jowers, I., Garner, S. W., & Chase, S. C. (2009). Transforming shape in design: Observations from studies of sketching. Design Studies, 30(5), 503–520.CrossRefGoogle Scholar
  2. 2.
    Stiny, G. (2006). Shape: Talking about seeing and doing. Cambridge: MIT Press.Google Scholar
  3. 3.
    Stiny, G. (1996). Useless rules. Environment and Planning B: Planning and Design, 23, 235–237.CrossRefGoogle Scholar
  4. 4.
    Jowers, I., Prats, M., McKay, A., & Garner, S. (2013). Evaluating an eye tracking interface for a two-dimensional sketch editor. Computer-Aided Design, 45, 923–936.CrossRefGoogle Scholar
  5. 5.
    Earl, C. F. (1997). Shape boundaries. Environment and Planning B: Planning and Design, 24, 669–687.CrossRefGoogle Scholar
  6. 6.
    Krishnamurti, R. (1992). The maximal representation of a shape. Environment and Planning B: Planning and Design, 19, 267–288.CrossRefGoogle Scholar
  7. 7.
    Krstic, D. (2005). Shape decompositions and their algebras. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 19, 261–276.CrossRefGoogle Scholar
  8. 8.
    Lothaire, M. (1997). Combinatorics on words (2nd edn.). Cambridge University Press.Google Scholar
  9. 9.
    Lyndon, R. C., & Schützenberger, M. P. (1962). The equation aM = bNcP in a free group. Michigan Mathematical Journal, 9, 289–298.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Design GroupThe Open UniversityMilton KeynesUK

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