Modeling irregular and complex forms

Computational technologies provide arguably the first real opportunity architectural design has had for a comprehensive description of built form. With the advent of affordable computer-aided design systems (including drafting, modelling, visualization and simulation tools), architects believe they can be in full control of geometric aspects and, through these, of a wide spectrum of other aspects that are implicit or explicit in the geometric representation. This belief is based primarily on the efficiency and effectiveness of computer systems, ranging from the richness and adaptability of geometric primitives to the utility of geometric representations in simulations of climatic aspects. Such capabilities support attempts to design and construct more irregular or otherwise complex forms. These fall under two main categories: (1) parsing of irregularity into elementary components, and (2) correlation of the form of a building with complex geometric structures.The first category takes advantage of the compactness and flexibility of computational representations in order to analyse the form of a design into basic elements, usually elementary geometric primitives. These are either arranged into simple, unconstrained configurations or related to each other by relationships that define e.g. parametric relative positioning or Boolean combinations. In both cases the result is a reduction of local complexity and an increase of implicit or explicit relationships, including the possibility of hierarchical structures.The second category attempts to correlate built form with constraints that derive usually from construction but can also be morphological. The correlation determines the applicability of complex geometric structures (minimally ruled surfaces) to the description of a design. The product of this application is generally variable in quality, depending upon the designer's grounding in geometry and his ability to integrate constraints from different aspects in the definition of the design's geometry.Both categories represent a potential leap forward but are also equally hampered by the rigidity of the implementation mechanisms upon which they rely heavily. The paper proposes an approach to making these mechanisms subordinate to the cognitive and technical aspects of architectural thinking through fuzzy modelling. This way of modelling involves a combination of (a) canonical forms, (b) tolerances around canonical forms and positions, (c) minimal and maximal values, (d) fuzzy boundaries, and (e) plastic interaction between elements based on the dual principles of local intelligence and autonomy. Fuzzy models come therefore closer to the intuitive manners of sketching, while facilitating transition to precise and complex forms. The paper presents two applications of fuzzy modelling. The first concerns the generation of schematic building layouts, including adaptive control of programmatic requirements. The second is a system for designing stairs that can adapt themselves to changes in their immediate environment through a fuzzy definition of geometric and topological parametrization