This study sheds light on a holistic understanding of muqarnas with its historical, philosophical and conceptual backgrounds on one hand and formal, structural and algorithmic principles on the other hand. The vault-like Islamic architectural element, muqarnas, is generally considered to be a non-structural decorative element. Various compositional approaches have been proposed to reveal the inner logic of these complex geometric elements. Each of these approaches uses different techniques such as measuring, unit-based decoding or three-dimensional interpretation of two-dimensional patterns. However, the reflections of the inner logic onto different contexts, such as the usage of different initial geometries, materials or performative concerns, were neglected. In this study, we offer a new schema to approach the performative aspects of muqarnas tectonics. This schema contains new sets of elements, properties and relations deriving partly from previous approaches and partly from the technique of folding. Thus, this study first reviews the previous approaches to analyse the geometric and constructional principles of muqarnas. Second, it explains the proposed scheme through a series of algorithmic form-finding experiments. In these experiments, we question whether 'fold', as one of the performative techniques of making three-dimensional forms, contributes to the analysis of muqarnas in both a conceptual and computational sense. We argue that encoding vault-like systems via geometric and algorithmic relations based on the logic of the 'fold' provides informative and intuitive feedback for form-finding, specifically in the earlier phases of design. While focusing on the performative potential of a specific fold operation, we introduced the concept of bifurcation to describe the generative characteristics of folding technique and the way of subdividing the form with respect to redistribution of the forces. Thus, in this decoding process, the bifurcated fold explains not only to demystify the formal logic of muqarnas but also to generate new forms without losing contextual conditions.
RESUMO: Este estudo apresenta resultados e descobertas de uma experimentação de três passos para integrar técnicas de modelagem e design analógico e digital, com especial atenção para o aumento do rendimento do comportamento de curvatura e curvilinearidade dos materiais de superfície planar rígidos. No âmbito do processo de experimentação, o papelão foi utilizado como material, as ações de corte e flexão foram utilizadas como técnicas e o corte a laser e o ambiente de script visual foram envolvidos como ferramentas. São examinados os potenciais de técnicas de materiais subtraíveis, tais como operações de corte, curvatura, incisão. A experimentação abrange a geração de padrão, incorporação de padrões de corte ao material plano 2D e remapeamento de padrões 2D em superfícies 3D, com base nos conhecimentos adquiridos na fase anterior e na exploração de novas superfícies de forma livre em 3D tanto em ambientes físicos como digitais. O modelo de experimentação de três passos apresentado tem potenciais para contribuir com os estudos pedagógicos focados nas abordagens exploratórias e criativas para a formação e fabricação de projetos integrativos. PALAVRAS-CHAVE:Flexão; Criação; Corte a Laser; Fabricação Digital; Técnicas Materiais; Curvatura Dupla.ABSTRACT: This study presents the outcomes and findings of a three-step experimentation to integrate analog and digital design and modeling techniques, with a particular focus on augmenting the affordance of bending behavior and curvilinearity of rigid planar surface materials. In the scope of the experimentation process, cardboard was used as a material, cutting and bending actions were utilized as techniques and laser cut and visual scripting environment were involved as tools. The potentials of subtractive material techniques such as cut, bend, kerf operations are examined. The experimentation covers hands-on pattern generation, embedment of cut patterns to 2D planar material, re-mapping 2D patterns onto 3D surfaces based on the insights gained in the previous phase and exploration of new 3D freeform surfaces both in physical and digital environments. The three-step experimentation model presented has potentials to contribute to the pedagogical studies focusing on explorative and creative approaches for integrative design formation and fabrication processes.
This paper presents the process and products from research on 'a movement behavior ' , transforming
The act of changing the direction of a sheet surface along a non-straight curve is a specific case of curved folding. From an architectural point of view, curved folding is an exciting operation. One or a couple of operation can generate highly complex shell-like spatial enclosure. From a digital design perspective, the implementation of curved folding with the built-in toolsets of available computer-aided design softwares is a challenging problem. The equilibrium state of curved folded geometry is needed to be found with a computational form-finding strategy. To use curved folding as a digital design operation, we introduce a new tool through developing a digital procedure for form-finding. The tool we develop can enable the experimentation with curved folding in the early stage of design process and facilitate the subsequent design development. In this article, we briefly present the literature focusing on curved folding in computational geometry, as well as the scope and description of a subclass of curved folding operation. Then, we introduce a digital tool, CURVED.IT through a design manual for its implementation and an algorithmic framework for its extension. Lastly, we discuss the design examples generated by CURVED.IT, and the potentials of the tool.
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