c  o  n  t  e  n  t  s

r e s e a r c h

C o n s t r u c t i n g   D e s i g n   C o n c e p t s :   A Computational Approach to the Synthesis of Architectural Form Kotsopoulos S, Ph.D. Dissertation, Massachusetts Institute of Technology, 2005

V.     A Studio Exercise in Rule Based Composition              3.1 THE DIGITAL INTERPRETER                                                                            A shape grammar interpreter (Liew 2003) is used for the digital part of the exercise.  The interpreter, written in       VisualLISP, uses a scripting language based on LISP to describe a rule.  Each rule has four parts: left-hand       schema, right-hand schema, transformation mapping, and variable mapping.  A vector description format       (Nagakura 1995) is used to describe the geometry and variables of a schema. The transformation mapping       determines any transformation changes between the left-hand schema and the right-hand schema. The variable       mappings define a relationship between the parameters of both schemata. A schema is composed of two parts,       the geometry and the constraints on the geometry variables. The geometry of a schema is described using a       series of vector displacements.  Each vector has 3 components: action, vector and label.  The action component       determines if the shape is a line or a point.  The vector component describes the x and y displacement of the       shape.  The label component determines the name of the label. For example, a horizontal parti line that is 5 units       long is described as:

(( action "line") (vector  5  0)  (label  "parti"))

A shape is described as a series of vector displacements that are connected from end to end.  For example, the       following describes a “parti” square that is 5 units by 5 units in size.

(((action "line") (vector 5 0)  (label "parti"))    ((action "line") (vector 0 5)  (label "parti"))    ((action "line") (vector -5 0) (label "parti"))    ((action "line") (vector 0 -5) (label "parti")))

To describe a parametric shape, the numbers in the vector displacement description are substituted with       variables.hape is described as a series of vector displacements that are connected from end to end.       The following describes a schema that finds all parti rectangles.

(((action "line")  (vector l 0) (label "parti"))    ((action "line") (vector 0 w) (label "parti"))    ((action "line") (vector (- l) 0) (label "parti"))    ((action "line") (vector 0 (- w)) (label "parti")))

Restrictions can be set on the geometry variables to limit the type of sub-shapes found. Theses restrictions are       added in the binding-constraints component of the schema. The following example restricts the size of the square       to be less than 10 units.

((binding-constraints    (l (< l 10))    (w (< w 10)))