Abstract
This is a third paper in a series on shape decompositions, which are seen here as a means to grasp computations with shapes. That is, decompositions that arise in computations with shapes and may serve to explain them are investigated. Due to certain isomorphisms, computations with discrete and topological decompositions are carried out in parallel with shape computations thus providing insights into the latter. In particular, discrete decompositions grasp the transition of intuitive spatial computations envisioned by the designers into symbolic ones that could be carried out by a computer. Some counting has been done showing that even simple spatial computations require a great many symbols in order to be turned into the symbolic ones. It is interesting to explore the converse: turning complex symbolic computations with vast numbers of symbols into the simpler spatial ones with shapes. This may prove promising in tackling big data problems.
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References
Hoffman D, Singh M (1997) Salience of visual parts. Cognition 63:29–78
Knight TW (1994) Transformations in design: a formal approach to stylistic change and innovation in visual arts. Cambridge University Press, Cambridge
Krstic D (1996) Decompositions of shapes. Ph.D. thesis UCLA
Krstic D (2004) Computing with analyzed shapes. In: Gero JS (ed) Design computing and cognition’04. Springer, Berlin, pp 397–416
Krstic D (2005) Shape decompositions and their algebras. AIEDAM 19:261–276
Krstic D (2008) Approximating shapes with topologies. In: Gero JS, Goel AK (eds) Design computing and cognition’08. Springer, Berlin, pp 81–100
Krstic D (2010) Approximating shapes with hierarchies and topologies. AIEDAM 24:259–276
Krstic D (2014) Algebras of shapes revisited. In: Gero JS (ed) Design computing and cognition ’12. Springer, Berlin, pp 361–376
Stiny G (1980) Kindergarten grammars: designing with Frobel’s building gifts. Environ Plan B 7:251–343
Stiny G (1982) Spatial relations and grammars. Environ Plan B 9:113–114
Stiny G (1991) The algebras of design. Res Eng Design 2:171–181
Stiny G (1992) Weights. Environ Plan B 19:413–430
Stiny G (1994) Shape rules: closure, continuity, and emergence. Environ Plan B 21:S49–S78
Stiny G (2006) Shape: talking about seeing and doing. The MIT Press, Cambridge
Stiny G, Gips J (1972) Shape grammars and the generative specification of painting and sculpture. In: Freiman CV (ed) Information processing 71. North-Holland, Amsterdam, pp 1460–1465
Stouffs R, Krishnamurti R (2004) Data views, data recognition and design rules. In: Gero JS (ed) Design computing and cognition’04. Springer, Berlin, pp 219–238
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Krstic, D. (2017). From Shape Computations to Shape Decompositions. In: Gero, J. (eds) Design Computing and Cognition '16. Springer, Cham. https://doi.org/10.1007/978-3-319-44989-0_14
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DOI: https://doi.org/10.1007/978-3-319-44989-0_14
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