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Architectural Explorations: A Formal Representation for Generation and Transformation of Design Geometry
    Design is often described as an exploration: a search for an adequate solution amongst a space of alternatives (Simon 1969). It involves the development and transformation of alternatives. Composition of spatial relations such as symmetry, hierarchy, grid-alignment, and proportion, termed “design structures,” help in the development of these architectural alternatives, and are used as compositional principles during their transformation.

    During the exploratory, early phases of design, configurations continually evolve. Both configuration elements and their relational structure are subject to change. Defining structures, exploring variations within structures, and redefining structures are the common means of transforming alternatives. Such transformations are necessary for developing design configurations and improving their quality.

    Transformations of design structures, which often yield intellectually stimulating results, are labor intensive; they require indiŽvidual modification of related elements. Such repetitive interaction considerŽably slows down the exploration, and often discourages it completely, particularly when configurations are complex and interrelations are numerous.

    My research is motivated by the following factors: (i) the necessity of flexible geometry for early design exploration; (ii) the intellectual stimulation provided by the exploration of structure; (iii) the difficulty involved in transforming design structures; (iv) the lack of computational support for design exploration; and (v) the lack of comprehensive representations for architecturally significant design structures.

    I have developed a framework of strategies that allows designers to explore complex configurations by manipulating their organizational structure. This framework, named Interactive Configuration Exploration (ICE), consist of two parallel endeavors: a notation and a computer implementation. The ICE notation is a formalism for describing shapes and configurations, by means of their generative and relational structures. The ICE implementation is a 3D modeling system that supports the exploration of such shapes and configurations through the transformation of their structures.

    The approach used is to separate the structures from configuration elements. In this manner, we can use structures to summarize configurations in the ICE notation, and use structures as manipulation handles to control the configuration in the ICE system.

    The principal vehicle in ICE is the regulator, which is an abstraction that captures a single unit of structure (i.e., a single relationship within a configuration). For instance, a grid structure is captured by alignment lines; a symmetry structure is captured by a reflection axis or center of rotation. Regulators, which are inspired by regulating lines, encapsulate a mathematical formula that determines the relationship between elements.

    The ICE notation enumerates and classifies the various types of regulators. It defines composition strategies and generation methods in order to represent the widest possible range of configurations. Furthermore, it captures a method for generation as well as a set of applicable transformations for any given configuration, based on its organizational structure. The ICE notation is not merely a geometric descriptor. It allows the derivation of additional geometric information, such as subshapes, boundaries, lengths, areas, volumes, and midpoints by means of simple computations on the notation strings. Additionally, it is possible to derive steps for transforming one configuration into another, by means of a simple algorithm.

    The ICE system, offers a higher-level of interaction with design configurations though regulators. These regulators maintain control over configuration elements, thus imposing relational constraints and propagating changes within the configuration. The parameters of regulators are manipulation handles; therefore, a user can transform the configuration, either completely or partially, by applying simple changes to the regulator. Such explorations yield significant transformations with relatively short paths, since manipulating a spatial relation results in the simultaneous transformation of multiple elements.
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