The basic idea is that of top-down design - beginning with a very abstract representation, and elaborating that, in step-by-step fashion, into a complete and detailed representation. The basic operations are real-time parametric variation of designs (using the mouse and slide bar) and substitution of objects. Essentially, then, a knowledge-base in Topdown implements a kind of parametric shape grammar.

The main applications of Topdown are in introductory teaching of CAD, and (since it provides a very quick and easy way for a user to develop detailed geometric models) to provide a uniform front-end for a variety of different applications. The shell, and some example knowledge-bases, are publicly available.

This paper discusses the principles of the Topdown Shell, the implementation of knowledge bases within it, and a variety of practical design applications.

The presentation will present our experience to-date in using conventional computer graphic tools to represent design ideas and contrast it with a video demonstration of our prototypical dynamic urban design modelling software for the Silicon Graphics IRIS computers.

Mathematics and especially geometry have found increasing application in the computer-based design environment of our day. The computer has become the central tool in the modern design environment, replacing the brush, the paints, the pens and pencils of the artist. However, if the artist does not master the internal working of this new tool thoroughly, he can neither develop nor express his creativity. If the designer merely learns how to use a computer-based tool, he risks producing designs that appear to be created by a computer. From this perspective, many design schools have included computer courses, which teach not only the use of application programs but also programming to modify and create computer-based tools.

In the current academic educational structure, different techniques are used to show the interrelationship of design and programming to students. One of the best examples in this area is an application program that attempts to teach the programming logic to design students in a simple way. One of the earliest examples of such programs is the Topdown Programming Shell developed by Mitchell, Liggett and Tan in 1988 . The Topdown system is an educational CAD tool for architectural applications, where students program in Pascal to create architectural objects. Different examples of such educational programs have appeared since then. A recent fine example of these is the book and program called “Design by Number” by John Maeda . In that book, students are led to learn programming by coding in a simple programming language to create various graphical primitives.

However, visual programming is based largely on geometry and one cannot master the use of computer-based tools without a through understanding of the mathematical principles involved. Therefore, in a model for design education, computer-based application and creativity classes should be supported by "mathematics for design" courses. The definition of such a course and its application in the multimedia design program is the subject of this article.

A highly unusual feature of PHIDIAS II is that it implements all of its functions using only hypermedia mechanisms. Complex vector graphic drawings and objects are represented as composite hypermedia nodes. Inference and critiquing are implemented through use of what are known as virtual structures [Halasz 1988], including virtual links and virtual nodes. These nodes and links are dynamic (computed) rather than static (constant). They are defined as expressions in the same language used for queries and are computed at display time. The implementation of different kinds of functions using a common set of mechanisms makes it easy to use them in combination, thus further augmenting the system's functionality.

PHIDIAS supports design by informing architects as they develop a solution's form. The idea is thus not to make the design process faster or cheaper but rather to improve the quality of the things designed. We believe that architects can create better buildings for their users if they have better information. This includes information about buildings of given types, user populations, historical and modern precedents, local site and climate conditions, the urban and natural context and its historical development, as well as local, state and federal regulations.

Our results fall in three major categories: 1) pedagogical discoveries about learning to design with a computer, which is greater than the sum of learning to design and learning about computers; 2) design exercises based on the Macintosh environment, exploiting the unique graphic qualities of the machine while simultaneously developing the ideas and drawing skills needed in the preliminary stages of design; 3) descriptions of the studio environment, including hardware, software, workstation layouts, security solutions, and other practical information that might be useful to others who are contemplating a similar project.

The "Calor" problem requires the move of a famous residence to a hot arid climate. The residence must then be redesigned in the original architect's style so the building becomes as energy efficient as possible in its new arid environment. The students are required to use as design criteria a new building program, the design philosophy of the original architect, and appropriate passive energy techniques that will reduce the thermal stress on the building. The building's energy response is measured by using an envelope energy analysis program called "Calor".

Much of the learning comes from imposing a new set of restraints on a famous piece of architecture and asking the student to redesign it. The students not only need to learn and use a different design philosophy, but also develop new skills to communicate their ideas on the computer. Both Macintosh and IBM computers are used with software ranging from Microsoft Works, Superpaint, AutoCAD, MegaCAD, Dr Halo, to Calor.