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Mr.hilbert in Architectural Curves

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  POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCESacceptée sur proposition du jury:Prof. B. Marchand, président du juryProf. Y. Weinand, directeur de thèseProf. D. Dietz, rapporteur Prof. R. Motro, rapporteur Dr E. Tosan, rapporteur Iterative Geometric Design for Architecture THÈSE N O  4572 (2009)ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE PRÉSENTÉE LE 13 JANVIER 2010À LA FACULTÉ ENVIRONNEMENT NATUREL, ARCHITECTURAL ET CONSTRUITLABORATOIRE DE CONSTRUCTION EN BOISPROGRAMME DOCTORAL EN STRUCTURESSuisse2009 PAR Ivo STOTZ  ABSTRACT 3 Abstract This work investigates on computer aided integrated architectural de-sign and production. The aim is to provide integral solutions for the de-sign and the production of geometrically complex free-form architecture.Investigations on computer aided geometric design and integrated man-ufacturing are carried out with equal importance. This research is con-sidering an integral and interdisciplinary approach, including computerscience, mathematics and architecture.Inspired by fractal geometry, the IFS formalism is studied with re-gards to discrete architectural geometric design. The geometric designmethod studied provides new shape control possibilities unifying twoseparate design paradigms of rough and smooth objects. Capable to de-sign fractal geometric figures, the method also covers the generation of classical objects such as conics and NURBS-curves. Close attention haspayed to the design of iterative free-form surfaces, which are composedentirely out of planar elements. A surface method based on projectedvector sums is proposed. The resulting geometric figures are expressedin a discrete form and can be easily translated into a coherent set of con-structional elements.The studies for translation of the geometrical elements into construc-tional elements consider integrated manufacturing. Addressing and num-bering of the elements by iterative geometric design are investigated andcompared to lexicographically ordered addressing systems, in order toprovide an adequate data structure for the design, production and assem-bly of the constructional elements. For the generation of the data describ-ing constructional elements, problems related to thickening and offsetmeshes are discussed. Once the global geometry of the constructionalpart has been computed, parameters are defined for generic automateddetailing. Hereby the entire description of the constructional elementsis completed. These elements are mapped and packed with regards tothe coordinate system of a CNC-machine and the properties and the di-mensions of the raw material, providing the complete set of workshopplans needed for integrated manufacturing. For automated generation of machine instructions (G-code), machining strategies - depending on thetype of machine used, tool and material properties - are elaborated.Finally, theintegrateddigitaldesignmethodsstudiedwithinthescopeof this thesis are tested and verified by the realization of different reducedscale prototypes. The studied applications range from bearing vault struc-tures to fractal and smooth timber panel shell structures. The developedmethods have shown to be efficient for the design and the realization  4 of geometrically complex architectural objects. The required planningeffort to handle and manipulate the design and the production data hasbeen greatly reduced. Some of the proposed methods have proved to berobust and general enough to be applied on real world applications. Itera-tivegeometricdesignprovideshighdegreeofdesignpossibilitiesofferingan efficient tool for the creation of smooth and rough free form objects.The possibility to incorporate successive folds in free-form objects allowsstructural applications. Keywords:  Free-form architecture, discrete computer aided geomet-ric design, IFS, integrated manufacturing Résumé Cetravails’interesseàlaquestiondelaconceptionetdelaproductionde projets architecturaux assistés par ordinateur. Le but est de dévelop-per des solutions techniques pour le dessin et la production de projet ar-chitecturaux complexes se basant sur des géométries non-standards. Larecherche se concentre à la foi sur des problèmes liés à la modélisationgéométrique assisté par ordinateur et la production automatisée des élé-ments de constructions. Cette recherche considère une approche inté-grale – du dessin à l’objet – et interdisciplinaire intégrant les domainesd’informatique, mathématique et architecture.Inspiré par la géométrie fractale, des systèmes de fonctions itérés(IFS) sont étudiés comme formalisme de modélisation géométrique dis-crète. La méthode de modélisation géométrique étudiée offre de nou-velles possibilités de contrôle de la forme en unifiant le domaine desformes lisses avec le domaine de formes rugueuses. Capable de con-cevoir des objets fractals, la méthode permet également la générationd’objets lisses comme par exemple des NURBS ou des coniques. Desétudes particulières portent sur la modélisation itérative de surfaces librescomposées uniquement d’éléments plans. Ainsi, une méthode de modéli-sation de surface est développée, basée sur la somme vectorielle projetéede deux courbes. Les objets géométriques qui en résultent sont expriméssous une forme discrète et peuvent ainsi facilement être traduits dans unensemble cohérent d’éléments de construction.Les études permettant la traduction des éléments géométriques enéléments de construction considèrent des procédés de fabrication automa-tiqueassistéeparordinateur. L’adressagedesélémentsobtenusparl’algorithmede construction géométrique itérative est étudié et comparé à des sys-tèmes d’adressage ordonnés de manière lexicographique, afin d’obtenir
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