ARC 4303B
Aspects of Asian architecture
Spring 2002–03

Defining style formally: shape grammar

Week 3, 2003.01.23

Assignment 2 in

Paper: validity of criteria.

Read TAMA paper (Li 2002).

• Chan Tak Yan

• Li Tsz Kai, Ken: version 1 (PDF, 12 KB), version 2 (PDF 12 KB)

• Mui Cheuk Chi, Joyce (PDF, 8 KB)

• To Sin Yeung (PDF, 20 KB)

TAMA paper

How can we relate Chomsky’s definitions to our computational approach to Chinese architecture?

In what ways does a user interact with a style grammar?

What are the expert and naïve approaches to style? How are they similar, different? (See the CUHK newsletter article.)

Explain the claim that “[s]tyle is not ‘out there’; it is a human construct.”

Informal introduction to shape grammar

To create and use grammars correctly, you must understand some technical details. These can be difficult to understand, but we will look only briefly and informally. For full details, see Stiny (1977).

A shape is a drawing composed of straight lines.

A rule has a left shape, a right shape, and an arrow: A → B.

A grammar consists of an initial shape and some rules.

One shape A is a subshape of another shape B, written as A ≤ B, if and only if every line in A is also in B.

The Euclidean transformations are reflection, rotation, scaling, translation, and finite compositions of these. A transformation t of a shape s is the shape denoted by t(s).

The result of applying an assignment g to a parameterized shape s is the shape denoted by g(s). In practice, we do not state explicitly the conditions on the assignment, as long as there is no chance of ambiguity; contrast the Flash and ice-ray grammars.

Example: ice-ray grammar.

Using a shape grammar

To apply a rule A → B to the current shape C, compare the left shape A and the current shape C. If there is a match, subtract (erase) the left shape A from the current shape C and add (draw) the right shape B. A new current shape C′ results. (This is easily seen in the Flash grammar.) The procedure can be written like this:

if t(A) ≤ C, then C′ := [C – t(A)] + t(B)

To generate a design, apply a rule to the current shape (or, if you are just beginning, the initial shape) and transform it, producing a new current shape. Continue until finished.

The ice-ray grammar (Stiny 1977)

A parametric grammar.

What does this grammar do, informally? Formally?

How does this grammar satisfy the three criteria of understanding?

What are the three roles of the grammar’s user?

One-minute paper

What is the main thing you learned?

What is your main question?

Assignment 3 out

Revised assignment. Refine the constraints in Stiny’s (1977) ice-ray grammar so that it will generate only designs in the language. Demonstrate.

Original assignment. Using Knight’s (1981) grammar, create two Japanese tearooms. They should not appear as examples in the article, should be approximately the same size, and should be as different from each other as you can make them. Draw neatly, show each step of the derivation (including the rule number), and annotate as necessary. If you find anything unexpected, write about it.

PDF format. Wu Qiong, MIT.

Next class (2003.02.06)

A shape grammar of the Yingzao fashi

References