Shape grammar

Shape grammars in computation are a specific class of production systems that generate geometric shapes. With shape grammars, forms can be created that are not stored in the computer previously. Shape grammars have been studied in particular in computer-aided architectural design, as they provide a formalism to create new designs. The foundation of shape grammars in architectural design have been defined in a seminal article by George Stiny and James Gips in 1971.

Definition

A shape grammar consists of shape rules and a generation engine that selects and processes rules. A shape rule defines how an existing (part of a) shape can be transformed. A shape rule consists of two parts separated by an arrow pointing from left to right. The part left of the arrow is termed the Left-Hand Side (LHS). It depicts a condition in terms of a shape and a marker. The part right of the arrow is termed the Right-Hand Side (RHS). It depicts how the LHS shape should be transformed and where the marker is positioned. The marker helps to locate and orient the new shape.

A shape grammar minimally consists of three shape rules: a start rule, at least one transformation rule, and a termination rule. The start rule is necessary to start the shape generation process. The termination rule is necessary to make the shape generation process stop. The simplest way to stop the process is by a shape rule that removes the marker.

A shape grammar system additionally has a working area where the created geometry is displayed. The generation engine checks the existing created geometry for conditions that match the LHS of the shape rules. Shape rules with matching LHS are eligible for use. If no rule applies, but a termination rule also has not been applied, then the production stops but the system keeps running (an undesirable state). If more than one rule applies, the generation engine has to choose which rule to apply. Applying a rule is usually termed firing the rule.

Shape grammars have been used to study historical architecture such as palladian villas and victorian windows, and to create novel designs such as for Álvaro Siza Vieira's Malagueira housing project (work by dr. José Duarte at MIT). Shape grammars are most useful when confined to a small, well-defined generation problem such as housing layouts, and structure refinement. Because shape rules typically are defined on small shapes, a shape grammar can quickly contain a lot of rules. The palladian villas shape grammar presented by William Mitchell (1990) for example contains 69 rules, that are fired throughout eight stages.

Parametric shape grammars are an advanced form of shape grammars. The new shape in the RHS of the shape rule is defined by parameters so that it can take into account more of the context of the already existing shapes. This typically affects internal proportions of the new shape so that a greater variety of forms can be created. In this way, attempts are made to make shape grammars respond to structural conditions, for example the width of beams in roof structures which depends on span.

Despite their popularity and applicability in academic circles, shape grammars have not found widespread use in generic Computer Aided Design applications.

Literature

• Stiny, G. and Gips, J. (1971). Shape grammars and the generative specification of painting and sculpture. IFIP Congress 1971. North Holland Publishing Co.link to article
• Mitchell, W. (1990). The Logic of Architecture. MIT Press, London.
• Duarte, J. (2000). Customizing mass housing: a discursive grammar for Siza's Malagueira houses. PhD-Thesis. Faculty of Architecture, Massachusetts Institute of Technology.
• Stiny, G. (2006). Shape: Talking about Seeing and Doing. MIT Press, Cambridge, MA.

See also

• L-system
• Graph rewriting

External links

• Shape Grammar and Style Simulation (list of references)
• Shape grammar implementation: from theory to useable software (overview of recent computational implementation approaches)