Kotsopoulos S, Ph.D. Dissertation, Massachusetts Institute of Technology, 2005
II. Shape Computation Theory
4. Shape Computation
Shape computation theory examines the applications of shape calculation. The prospect of calculating with
shapes, instead of numbers, was set out by Wittgenstein (1956). But the examination of the consequences of
shape calculation was left as an open question. Shape computation was examined in depth for the first time in
Stiny and Gips 1972.
The original contribution of Stiny and Gips was the questioning of the nature of calculating. A new type of
calculation not only with 0-dimensional elements but also with 1 and 2-dimensional elements was proposed, and
put into use. Further empirical basis for the attempt was the observation that a designer producing design-
descriptions performs calculations with points, lines, planes, and solids. A “design” is a finite description
consisting of finite parts, and produced in finite time.
Shape computation was motivated by the desire to provide an intuitive framework for the development of generative
design systems. The systems were named shape grammars. This view implied that each finite description
occurring in space takes the place of an “expression” within a spatial language. Spatial languages include
compositions with certain spatial properties. A shape grammar is a system of syntactical-interpretative rules that
governs the construction of the language.
Therefore, shape computation theory can be roughly summarized by two interrelated parts.
First is the shape calculus, or the algebraic part. The algebraic part deals with the spatial attributes of shapes and
the things that happen when we use them to calculate: each time we add, or subtract shapes, or when we break a
shape into parts, or when we manipulate a shape by using transformations, like rotations, reflections etc. The
standard mathematical tools used in this part are, Boolean algebra, topology, set theory and lattice theory.
Second is the syntactic-interpretive part. The syntactic part deals with the analysis and synthesis of design
languages. It provides the formal means for the construction and interpretation of a number of compositions with
certain attributes that are named design languages. Design languages can find use in industrial or architectural
design, civic engineering, painting and sculpture, etc. Sequences of production rules are employed for the
description of these languages.
4.1. SHAPE CALCULUS
4.2. SHAPE GRAMMAR