Andrew I-kang Li


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About me

About shape grammars


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The interpreter project

Set up

Create a grammar

Run a grammar

Get out of trouble

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The Yingzao fashi project

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Contact me

i (at) andrew (dot) li

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Nakata lattice


Stouffs, Rudi, and Andrew I-kang Li. 2021. Learning from users and their interaction with a dual-interface shape-grammar implementation. In Cultural DNA 2019, ed. Ji-Hyun Lee, 55–64. Singapore: Springer.

Abstract. We present a shape grammar implementation with two new characteristics. One is that it visual and directly manipulable: users draw the shapes and rules in a modeling application. The other characteristic is advanced technical capabilities, such as non-visual attributes and higher-order elements like surfaces. It consists of three components running in Rhinoceros3d. We also report on workshops that introduced the implementation.

Final manuscript version (PDF, 199 KB)

Li, Andrew I-kang, and Rudi Stouffs. 2020. Towards a useful grammar implementation: beginning to learn what designers want. In Proceedings of the 25th international conference on computer-aided architectural design research in Asia CAADRIA 2020, 153–162. Hong Kong: CAADRIA.

Abstract. We present a general shape grammar implementation that supports subshape detection and handles lines and labeled points in three-dimensional space. Its front and back ends are both set in the CAD application Rhinoceros3d. Information observations of designers using the implementation suggest that they are more interested in producing designs to work with than in using the more specialized features of shape grammars. This in turn suggests that researchers who create such implementations have more to learn about the designers who use them.

Final manuscript version (PDF, 137 KB)

Li, Andrew I-kang. 2018. A whole-grammar implementation of shape grammars for designers. AIEDAM, Artificial intelligence for engineering design, analysis and manufacturing 32(2): 200–207.

Abstract. I present an implementation of shape grammars that is aimed at supporting designers. It has two parts: a grammar editor and a stand-alone interpreter. The editor is the modeling application Rhinoceros3d using Python scripts. The interpreter is general, is three-dimensional, and supports subshape detection. A grammar is a Rhinoceros3d model; thus users can manipulate all its parts directly and immediately. That is, they can modify any shape without selecting or invoking an editor, and they can lay out the parts of the grammar in any way they find meaningful. Using this approach, which I call a whole-grammar approach, users are shielded from most subdomain tasks, like typing text files or specifying transformations. Informal observations suggest that users of this implementation can work effectively.

Paper (corrected proof; 693 KB)

Li, Andrew I-kang. 2017. Implementing shape grammars for designers. In Morphological analysis of cultural DNA: tools for decoding culture-embedded forms, ed. Ji-Hyun Lee, 165–176. Singapore: Springer.

Abstract. For the computational understanding of visual artifacts, shape grammar provides an important theoretical framework. In addition to the theory, there have been numerous computer implementations; these have tended to be proofs of concept. As such, they are essential steps in development, but do not directly help researchers do the kind of analyses seen in the literature, which were done by hand. That is to say, we have a theory but not yet a sturdy tool.

We present a prototype implementation to help designers and design researchers work with shape grammars. This implementation allows users to focus on domain tasks – editing and testing grammars – by shielding them from sub-domain tasks – mechanical tasks like matching shapes and applying rules. A grammar is displayed as a collection of shapes in 3D space that users can manipulate directly; a commercial 3D modeling application is used for this purpose. The components of the implementation are designed to make it easy for users to switch between editing and testing their grammars. The implementation handles emergence and is general. We report on users’ experiences with the implementation in workshops on grammatical design and analysis.

Paper (uncorrected proof; PDF, 420 KB)

Li, Andrew I-kang. 2011. Computing style. Nexus network journal 13: 183–193.

Abstract. Shape grammars are frequently used in analyzing style in architecture and other areas of design. But this is a more subtle task than is usually realized, and some grammatical approaches to design analysis are logically suspect. We examine the framework articulated by Stiny and Mitchell in 1978, fill in the operational gaps, and propose a more comprehensively considered approach to using grammars to compute style.

Paper (PDF, 480 KB)

Li, Andrew I-kang, Liang Chen, Yang Wang, and Hau Hing Chau. 2009. Editing shapes in a prototype two- and three-dimensional shape grammar environment. In Computation: the new realm of architectural design: proceedings of the 27th conference on education and research in computer aided architectural design in Europe, eds. Gülen Çağdaş and Birgül Çolakoğlu, 243–249. Istanbul: eCAADe.

Abstract. Recently we developed a prototype general shape grammar system, called Grammar Environment (Li et al. 2009). It differs from other systems in that it aims to support designers who design with shape grammars. One task of such a system is to support users in editing shapes. The guidelines that we followed in developing Grammar Environment suggested that the shape editing system should both be integrated into the system and be powerful as a drawing tool. This seemed to be contradictory. We decided to make two shape editors: one stronger on integration, the other on drawing power.

Paper (PDF, 2 MB)

Li, Andrew I-kang, Hau Hing Chau, Liang Chen, and Yang Wang. 2009. A prototype system for developing two- and three-dimensional shape grammars. In CAADRIA 2009: proceedings of the 14th international conference on computer-aided architecture design research in Asia, eds. Teng-wen Chang, Erik Champion, Sheng-Fen Chien, and Shang-Chia Chiou, 717–726. Touliu, Taiwan: Department of Digital Media Design, National Yunlin University of Science and Technology.

Abstract. A number of researchers have developed shape grammar systems, with a variety of aims. These systems all help users (to varying degrees) to run grammars, but not to develop grammars. However, we believe that developing grammars is also work and needs to be supported. A system to do this would make it easier and more convenient for people using grammars to do design work. Following the generate-test model, we design and implement a prototype system that supports the user in editing grammars, testing grammars, and switching easily between the two types of activity. We emphasize the graphic nature of the task: the user is all the time working with graphic objects, namely shapes.

Paper (PDF, 227 KB)

Li, Andrew I-kang. 2009. Computing the Yingzao fashi 營造法式的運算解析. In Shuzi yingzao: jianzhu sheji, yunsuan luoji, renshi lilun 數字營造:建築設計,運算邏輯,認識理論, Computational constructs: architectural design, logic and theory, eds. Chen Shouheng 陳壽恆, Li Shuyi 李書誼, and Josh Lobel, 113–125. Beijing: Zhongguo jianzhu gongye chubanshe.

Paper (PDF, 864 KB)

Li, Andrew I-kang. 2005. Thoughts on a designer-friendly shape grammar interpreter. In eCAADe 23: digital design: the quest for new paradigms, eds. José Pinto Duarte, Gonçalo Ducla-Soares, and A. Zita Sampaio, 523–528. Lisbon: Education in Computer Aided Architectural Design in Europe.

Abstract. Discussions of shape grammar interpreters overlook a fundamental issue: the model of the designer’s work. Such a model would provide guidance for developing an interpreter with an appropriate interface. In this paper, I first propose a model in which the designer’s work is to create and test generative specifications of languages of designs. I call this model designer-centered generative design. Then, I examine the characteristics of shape grammar and how they support or impede this model of work. Finally, I discuss the implications for the design of an appropriate shape grammar interpreter. These provide guidelines for implementing such an interpreter for testing.

Paper (PDF, 96 KB)

Li, Andrew I-kang. 2004. Styles, grammars, authors, and users. In Design computing and cognition ’04, edited by John S. Gero, 197–215. Dordrecht, Netherlands: Kluwer Academic Publications.

Abstract. Using a grammar to understand style can be seen, for students, as involving two main tasks: cultivating a standard of stylistic correctness and converging the language defined by the grammar and the language of stylistically correct designs. I discuss a framework for organizing such an experience, consider how it informs the way we write grammars, present an example (including a grammar), and report on a classroom experience.

Paper (PDF, 828 KB)

Li, Andrew I-kang, and Lau Man Kuen. 2004. A set-based shape grammar interpreter, with thoughts on emergence. Paper read at Workshop 3, Implementation issues in generative design systems, “First international conference on design computing and cognition,” Massachusetts Institute of Technology, 17–19 July 2004.

Abstract. We present a set-based interpreter, implemented in Multimedia Flash, of a shape grammar for teaching the language of twelfth-century Chinese wood-frame building sections. We discuss the implementation of various aspects of the shape grammar formalism – shape representation, the part relation, and so on – the usefulness of the interpreter, and thoughts on the role of emergence in grammar interpreters.

Paper (PDF, 256 KB)

Li, Andrew I-kang. 2003. The Yingzao fashi in the information age. Paper presented at “The Beaux-Arts, Paul-Philippe Cret, and twentieth-century architecture in China,” The University of Pennsylvania, 3–5 October 2003.

Li, Andrew I-kang. 2002. A prototype simulated interactive shape grammar. In Design e-ducation: connecting the real and the virtual, Proceedings of the 20th conference on education in computer aided architectural design in Europe, edited by Krzysztof Koszewski and Stefan Wrona, 314–317. Warsaw: eCAADe.

Abstract. Existing shape grammar interpreters have implemented some of the distinguishing features of the formalism, notably emergence or rule application under multiple transformations. By contrast, I implement a grammar in which these capabilities either are not required or can be simulated. This frees a user from mechanical issues, allowing him to pay more attention to the process embodied in the grammar.

Paper (PDF, 75 KB)

Li, Andrew I-kang. 2002. Algorithmic architecture in twelfth-century China: the Yingzao fashi. In Nexus IV: architecture and mathematics, edited by José Francisco Rodrigues and Kim Williams, 141–150. Fuccechio, Italy: Kim Williams Books.

Paper (PDF, 739 KB)

Li, Andrew I-kang. 2001. Teaching style grammatically, with an example from traditional Chinese architecture. In The proceedings of Mathematics & design 2001: the third international conference (3–5 July 2001, Geelong, Australia), 270–277.

Abstract. Most analytical shape grammars have aimed at an authoritative definition of style. This approach deprives the student of an important way of understanding the style, by formulating its definition. But this experience can be understood formally and incorporated into the grammar. An example is given from the 12th-century Chinese building manual Yingzao fashi.

Paper (PDF, 1.2 MB)

Li, Andrew I-kang. 2001. A shape grammar for teaching the architectural style of the Yingzao fashi. PhD dissertation, Department of Architecture, Massachusetts Institute of Technology, Cambridge, Mass.

Abstract. The Yingzao fashi [Building standards] is a Chinese building manual written by Li Jie (d. 1110) and published in 1103. I present a shape grammar for teaching the architectural style – the language of designs – described in this manual. This grammar is distinguished by two objectives, and the technical means used to accomplish them.

First, the grammar is for teaching. Usually, the author of a grammar of a style aims to generate all and only the designs in the language. To do this, he not only writes the grammar, but also judges whether the designs it generates are members of the language. In the Yingzao fashi grammar, on the other hand, I want to generate all and more than the designs in the language. It is then the student who evaluates the designs – does this design belong to the language? – and adjusts the grammar accordingly. Thus the student participates actively in defining the language of designs, and learns that style is a human construct.

Second, the grammar is designerly. As already observed, most authors of style grammars focus on the language of designs; they do not consider how to structure the user’s interaction with the grammar. By contrast, I consider explicitly what the user decides and when he decides it, and organize the grammar accordingly. In other words, I consider process as well as products.

The grammar exploits several technical devices for the first time: the design as an n-tuple of drawings, descriptions, and other elements; the generation of descriptions in the n-tuple; and techniques that are made possible by these devices.

Volume 1, text (PDF, 199 KB)
Volume 2, images (PDF, 1.38 MB)

Li, Andrew I-kang. 2000. Integrating symbolic and spatial information in shape grammars, with an example from traditional Chinese architecture. In CAADRIA 2000: proceedings of the fifth conference of the Association of computer aided architectural design research in Asia (CAADRIA) (18–19 May 2000, Singapore), 245–253.

Abstract. Stiny’s (1981) formulation of descriptions is applied to building sections and their descriptions found in the twelfth-century Chinese building manual Yingzao fashi.

Li, Andrew I-kang. 2000. Users, grammars, and designerliness. In Proceedings of Greenwich 2000: digital creativity symposium (13–15 January 2000, London), 81–85.

Abstract. From the user’s point of view, what characterizes an appropriate interaction with a grammar? What criteria can be used to determine this appropriateness? Are these criteria fixed or changeable? These questions will be considered and, to the extent possible, formalized.

Li, Andrew I-kang. 1999. Expressing parametric dependence in shape grammars, with an example from traditional Chinese architecture. In Proceedings of the fourth conference of the Association of computer aided architectural design research in Asia (CAADRIA) (5–7 May 1999, Shanghai), 265–274.

Abstract. Shape grammars traditionally generate one product at a time. This leads to difficulties when dependent parameters are involved. Parallel grammars are proposed as a solution. As an example, a grammar is shown which generates plans according to the 12th-century Chinese building manual Yingzao fashi.

Li, Andrew I-kang. 1997. Liang Sicheng’s A pictorial history of Chinese architecture. In On what ground(s)? Refereed proceedings of the 1997 annual conference of the Society of architectural historians, Australia and New Zealand (SAHANZ), ed. S. Pickersgill and P. Scriver, 110–119. Adelaide: SAHANZ.

Li, Andrew I-kang, and Jin-Yeu Tsou. 1996. Structural carpentry in the Yingzao fashi. Architronic 5 (2). Dead link. Sorry.

Li, Andrew I-kang, and Jin-Yeu Tsou. 1996. Using virtual models to teach traditional Chinese wood construction. In The introduction of technology: CAAD teaching and research directions in Asia: proceedings of the first conference of the Association of computer aided architectural design research in Asia (CAADRIA) (25–27 April 1996, Hong Kong), ed. Thomas Kvan, 119–130.

Abstract. In this paper we discuss our experience in using virtual models to teach traditional Chinese wood construction. Although our approach is technically simple – we use a kit of modedl parts made with the Solid Modeler of AutoCAD, Release 12 (now Release 13), and customized commands in AutoLISP – we have had excellent results. This is because of the remarkable match between the modelling medium and the highly systematized nature of traditional Chinese wood construction. It is this crucial – and interesting – characteristic that we want students to understand and appreciate.

In our first teaching experience, in the fall term, 1994–95, despite unexpected drawbacks, our approach succeeded. In fact, our students, all Hong Kong Chinese, were surprisingly enthusiastic and even took pride in the sophistication of this uniquely Chinese construction system. In 1995–96, we have used the same kit of parts in two courses: an introduction to Chinese architecture (spring term) and an advanced course in Song dynasty wood construction (fall term).

We first discuss briefly the theoretical basis for our approach. We then describe the assignments, the kit of parts, and supporting materials used in our teaching experiences. Finally, we discuss our findings and consider directions for the future development and improvement of our research.

Li, Andrew I-kang, and Jin-Yeu Tsou. 1995. The rule-based nature of wood frame construction of the Yingzao fashi and the role of virtual modelling in understanding it. In Computing in architectural research: proceedings of the International conference on Chinese architectural history (7–10 August 1995, Hong Kong), 25–40.

Abstract. The wood frame construction system of the Yingzao fashi is rule-based. In this sytstem, the text can be understood as rules, construction as the execution of those rules, and the building as the output of the rules. To illustrate, we discuss a three-bay ting tang and some of the rules which govern its overall form and size. This three-bay ting tang is the smallest hall defined in the Yingzao fashi.

Virtual models offer a critical advantage over real models and drawings. This type of representation allows us to ask questions which are particularly relevant to the rule-based system. We can execute the rules quickly and thus concentrate on the rules, their output, and the relation between them. We propose some areas of research made possible with virtual modelling. One is a study of roof curvature as a product of several rules, including shengqi, cejiao, and juzhe.

Li, Andrew I-kang, and Jin-Yeu Tsou. 1995. Chinese wood frame construction of the twelfth century: The construction system of the Yingzao fashi. CD-ROM.

Li, Andrew I-kang, and Jin-Yeu Tsou. 1994. A computer-based teaching tool for traditional Chinese wood construction. Preconference proceedings: advances in computer-based building design systems: 7th international conference on systems research, informatics and cybernetics (15–21 August 1994, Baden-Baden, Germany), 149–59.

Abstract. In this paper we discuss a method of using virtual modelling to teach and study aspects of traditional Chinese wood construction as prescribed in the building manual Yingzao fashi, published in 1103. There are two types of argument for using virtual modelling. First, there are important conceptual commonalities, the most compelling of which is the distinction between primitive and instance. The Chinese construction system, in its treatment of building components and their relations, makes precisely the same distinction.

Second, the precision of the virtual model and its ease of duplication and modification – its very virtuality – seem to open up new areas of investigation through comparative models. The amount of labor required to make a real model is a serious impediment to comparison studies, which involve multiple models. The meaning of the Chinese construction system lies not in the manufacture of repeated components, but in their combination.

The first phase of this project culminates in the demonstration of a prototype system. We found that users had many operational difficulties, which tended to distract them for more important issues. Based on this demonstration, we propose directions for expansion and refinement in the second phase, which will include use of the system in an advanced undergraduate elective course in architectural history in the fall of 1994–95.

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Yet another design with the variant Nakata curve.

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