Shape grammar
Encyclopedia
Shape grammars in computation are a specific class of production system
s that generate geometric shapes. Typically, Shapes are 2- or 3-dimensional, thus shape grammars are a way to study 2- and 3-dimensional languages. 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. Shape grammars need not be limited to architectural applications, of course. For example, Holliday junctions are two-dimensional structures that appear in applications of molecular genetics. Thus shape grammars have been used in linguistic studies of genetics.
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. Shape grammars differ from Chomsky grammars a major respect: the production rules may be applied serially (as with Chomsky grammars) or in parallel (not allowed in Chomsky grammars), similar to the way "productions" are done in L-Systems.
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 parameter
s 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.
Production system
A production system is a computer program typically used to provide some form of artificial intelligence, which consists primarily of a set of rules about behavior. These rules, termed productions, are a basic representation found useful in automated planning, expert systems and action selection...
s that generate geometric shapes. Typically, Shapes are 2- or 3-dimensional, thus shape grammars are a way to study 2- and 3-dimensional languages. 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
George Stiny
George Stiny is an American design and computation theorist. He co-created the concept of shape grammars.Stiny was educated at MIT and UCLA. He has taught at the University of Sydney, the Royal College of Art , and the Open University. He was faculty at UCLA for fifteen years before joining the...
and James Gips in 1971. Shape grammars need not be limited to architectural applications, of course. For example, Holliday junctions are two-dimensional structures that appear in applications of molecular genetics. Thus shape grammars have been used in linguistic studies of genetics.
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. Shape grammars differ from Chomsky grammars a major respect: the production rules may be applied serially (as with Chomsky grammars) or in parallel (not allowed in Chomsky grammars), similar to the way "productions" are done in L-Systems.
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
Palladian architecture
Palladian architecture is a European style of architecture derived from the designs of the Venetian architect Andrea Palladio . The term "Palladian" normally refers to buildings in a style inspired by Palladio's own work; that which is recognised as Palladian architecture today is an evolution of...
and victorian windows
Victorian house
In the United Kingdom, and former British colonies, a Victorian house generally means any house built during the reign of Queen Victoria...
, and to create novel designs such as for Álvaro Siza Vieira
Álvaro Siza Vieira
Álvaro Joaquim de Melo Siza Vieira, GOSE, GCIH, is a Portuguese architect, born 25 June 1933 in Matosinhos a small coastal town by Porto. He is internationally known as Álvaro Siza .-Life and career:...
'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 parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
s 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. & Gips, J. (1972). Shape grammars and the generative specification of painting and sculpture. In Information Processing 71, pp. 1460–1465. North-Holland Publishing Company. link to article
- Stiny, G. (1980). Introduction to shape and shape grammars. Environment and Planning B: Planning and Design 7(3), 343-351.
- Mitchell, W. (1990). The Logic of Architecture. MIT Press, London.
- Knight, T.W. (1994). Transformations in Design: A Formal Approach to Stylistic Change and Innovation in the Visual Arts. Cambridge University Press.
- Stiny, G. (2006). Shape: Talking about Seeing and Doing. MIT Press, Cambridge, MA.
External links
- www.shapegrammar.org
- Shape Grammar and Style Simulation (list of references)
- Shape grammar implementation: from theory to useable software (overview of recent computational implementation approaches)