Shapes, structures and shape grammar implementation

Shape grammars are a generative formalism in which dynamic changes to shape structure plays a vital role. Such changes support ambiguity and emergence, and as a result shape grammars are often used as the basis for proposed developments in supporting shape exploration in computer-aided design. However, the general implementation of shape grammars remains an unsolved problem, and a common solution is to adopt a fixed structure. This paper explores the consequences of assuming a fixed structure, via analysis of a simple shape grammar, often used as a benchmark problem to illustrate advances in shape grammar implementation. With reference to the combinatorics of words, it is proved that adopting a finite fixed structure limits the capability of a shape grammar. The paper concludes with a discussion exploring the implication of this result for shape grammar implementation and for design descriptions in CAD.

[1]  Scott Curland Chase,et al.  Transforming shape in design: observations from studies of sketching , 2009 .

[2]  Ramesh Krishnamurti,et al.  A Paradigm for Interpreting Tractable Shape Grammars , 2014 .

[3]  John Stark,et al.  Product lifecycle management : 21st century paradigm for product realisation , 2005 .

[4]  Aristides A. G. Requicha,et al.  Representaiton of Rigid Solid Objects , 1980, CAD Advanced Course.

[5]  Ian F. C. Smith,et al.  Engineering Informatics – Fundamentals of Computer-Aided Engineering , 2013 .

[6]  G. Stiny.  Shape Rules: Closure, Continuity, and Emergence , 1994 .

[7]  Manuela Ruiz-Montiel,et al.  Layered shape grammars , 2014, Comput. Aided Des..

[8]  Jose Encarnacao.  Computer Aided Design Modelling, Systems Engineering, CAD-Systems , 1980, Lecture Notes in Computer Science.

[9]  Jin Yan,et al.  The impact of 3D CAD interfaces on user ideation: A comparative analysis using SketchUp and Silhouette Modeler , 2016 .

[10]  H. Wilf,et al.  Uniqueness theorems for periodic functions , 1965 .

[11]  Marc Esteva,et al.  A shape grammar interpreter for rectilinear forms , 2012, Comput. Aided Des..

[12]  George Stiny,et al.  Shapes are Individuals , 1982 .

[13]  Ivan E. Sutherland,et al.  Sketchpad a Man-Machine Graphical Communication System , 1899, Outstanding Dissertations in the Computer Sciences.

[14]  Ramesh Krishnamurti,et al.  The Construction of Shapes , 1981 .

[15]  M. Lothaire.  Combinatorics on words, Second Edition , 1997 .

[16]  Sivam Krish,et al.  A practical generative design method , 2011, Comput. Aided Des..

[17]  George Stiny.  Computational Foundations of Architectural Design , 1986 .

[18]  T W Knight,et al.  Shape Grammars: Six Types , 1999 .

[19]  M. Lothaire,et al.  Combinatorics on words: Frontmatter , 1997 .

[20]  Djordje Krstic.  From Shape Computations to Shape Decompositions , 2017 .

[21]  Rudi Stouffs,et al.  Algorithmic complexity of shape grammar implementation , 2018, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[22]  Steve Garner,et al.  Evaluating an eye tracking interface for a two-dimensional sketch editor , 2013, Comput. Aided Des..

[23]  Fernando López-Romero,et al.  Fuzzy shape grammars , 2015, Progress in Artificial Intelligence.

[24]  George Stiny,et al.  Pictorial and Formal Aspects of Shape and Shape Grammars , 1975 .

[25]  Iestyn Jowers,et al.  Shape Computations Without Compositions , 2017 .

[26]  Thomas Grasl,et al.  From Topologies to Shapes: Parametric Shape Grammars Implemented by Graphs , 2013 .

[27]  M. Schützenberger,et al.  The equation $a^M=b^Nc^P$ in a free group. , 1962 .

[28]  M Tapia,et al.  A Visual Implementation of a Shape Grammar System , 1999 .

[29]  George Stiny,et al.  Shape: Talking about Seeing and Doing , 2006 .

[30]  Bryan Lawson,et al.  Sketches of thought , 1997 .

[31]  Pieter Pauwels,et al.  AI EDAM special issue: advances in implemented shape grammars: solutions and applications , 2018, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[32]  Nelson Goodman,et al.  The calculus of individuals and its uses , 1940, Journal of Symbolic Logic.