Kotsopoulos S, Ph.D. Dissertation, Massachusetts Institute of Technology, 2005
II. Shape Computation Theory
1. Introduction
2. Computational Theory
3. Computational Design Theory
4. Shape Computation
4. 1. SHAPE CALCULUS
4. 2. SHAPE GRAMMAR
5. Constructing Design Concepts
6. Discussion
A computational theory includes some abstract deductive part and some syntactic-interpretive part.
The deductive part is an environment where calculations of some kind may take place.
The syntactic-interpretive part includes statements that associate empirical meaning to the calculations.
Shape computation theory deals mainly with form, the elements of space, and their possible interactions.
The interaction of forms is captured by a calculus for shapes of 0, 1, 2 and 3 dimension and by syntactic-interpretive
rule statements. Shape computation theory offers the means to understand and to treat design formally.
This study examines how designers can construct step-by-step processes to develop their spatial ideas.
It is proposed that the design process begins with a design hypothesis, (or design concept) that is expressed in
response to a problem. A designer derives the spatial and other consequences of a hypothesis, and performs
tests on the basis of programmatic and other criteria.
A design concept provides a general schema for further exploration. It establishes a flexible interrelationship
among the elements that one considers crucial for the design. It is not a repetition or analysis of the building
program, but an act of synthesis that involves previous experience, and inspiration. Design concepts may include
several interrelated components: spatial, semantic, functional, etc. This study focuses on the spatialcomponent of
such concepts.
It is proposed that in the design process one examines the consequences of a hypothesis. These consequences
can be approached as calculations according to rules with varying degrees of explicitness and extensiveness.
The rules are first stated in their more general format, as rule schemata. Rule schemata represent certain
patterns of activity. The character of the entire process is conditional. An effect is accomplished provided that some
conditions are satisfied.
The more effective, for the purpose, sequence of actions becomes clear only after several tests. When a number of
rule schemata and rules is established, then it becomes possible to arrange them in a non-redundant system.
This system is called grammar. Provided that the search has been carefully done, the ordering of rules does not
create new information. Moreover, the rules can be ordered in different ways.
In order to make explicit the use of rule schemata and rules in the studio we must draw our attention on the
process of the development of designs from design concepts. Also, it needs to be shown how designers move on
to produce design descriptions, while taking into account a variety of interconnected problems.
The next two chapters examine the properties of architectural description and its role in the construction of design
concepts. Chapter III presents the properties of spatial elements in architectural descriptions. Chapter IV shows
how architectural description is put into use in the generation of designs from a design concept, which obtains the
role of an initial hypothesis .