An iterative surface model for timber construction

In the field of timber construction, we work on surface design that is based on an iterative model called "IFS" (Iterated Function System). The modeled figures must meet certain properties in order to ensure their physical feasibility. For the construction of structures based on timber panels, we research in planarity constraints of quadrilateral meshes. First, we will introduce a particular model for a certain type of planar quadrilateral meshes. This surface model is defined as a certain combination of two polylines. Further, we present some basic properties of the iterative model employed, which is inspired by the IFS model. Finally, we define a surface model generated by an operator that combines two IFS, each describing a one curve.

Un modèle itératif de surfaces pour la construction en bois

Gilles Gouaty, Ivo Stotz, Eric Tosan, Yves Weinand

Dans le cadre de la construction en bois, nous nous intéressons à la modélisation de maillages surfaciques 3D basés sur un modèle itératif inspiré du modèle IFS (Iterated Function System). Les formes modélisées doivent satisfaire certaines propriétés afin d’assurer leur constructibilité physique. Nous nous intéressons ici aux contraintes géométriques de planéité des faces d’un maillage quadrangulaire, permettant la construction d’assemblages de panneaux de bois découpés. Nous décrivons dans un premier temps un modèle permettant de représenter certains types de maillages à faces planes. Ce modèle est défini comme une certaine somme de deux courbes. Nous présentons ensuite quelques propriétés élémentaires du modèle itératif que nous utilisons, inspiré du modèle IFS. Nous définissons enfin un modèle de surfaces générées par un opérateur de combinaison entre deux IFS décrivant chacun une certaine courbe. Nous montrons qu’il peut également être considéré comme un carreau à pôles généré par un produit d’IFS. In the field of timber construction, we work on surface design that is based on an iterative model, which is inspired by the IFS model (Iterated Function System). The modelled figures must meet certain properties in order to ensure their physical feasibility. For the construction of structures based on timber panels, we research in coplanarity constraints of quadrilateral meshes. First, we will introduce a particular model for a certain type of planar quadrilateral meshes. This model is defined as a sum of two curves. Further, we present some basic properties of the iterative model employed, that is inspired by the IFS model. Finally, we define a surface model generated by an operator that combines two IFS, each describing a one curve. We show that the model studied can also be expressed as a pole surface obtained by an IFS product.

2009

Iterative geometric design for architecture

Ivo Stotz

This work investigates on computer aided integrated architectural design and production. The aim is to provide integral solutions for the design and the production of geometrically complex free-form architecture. Investigations on computer aided geometric design and integrated manufacturing are carried out with equal importance. This research is considering an integral and interdisciplinary approach, including computer science, mathematics and architecture. Inspired by fractal geometry, the IFS formalism is studied with regards to discrete architectural geometric design. The geometric design method studied provides new shape control possibilities unifying two separate design paradigms of rough and smooth objects. Capable to design fractal geometric figures, the method also covers the generation of classical objects such as conics and NURBS-curves. Close attention has been paid to the design of iterative free-form surfaces, which are composed entirely out of planar elements. A surface method based on projected vector sums is proposed. The resulting geometric figures are expressed in a discrete form and can be easily translated into a coherent set of constructional elements. The studies for translation of the geometrical elements into constructional elements consider integrated manufacturing. Addressing and numbering of the elements by iterative geometric design are investigated and compared to lexicographically ordered addressing systems, in order to provide an adequate data structure for the design, production and assembly of the constructional elements. For the generation of the data describing constructional elements, problems related to thickening and offset meshes are discussed. Once the global geometry of the constructional part has been computed, parameters are defined for generic automated detailing. Hereby the entire description of the constructional elements is completed. These elements are mapped and packed with regards to the coordinate system of a CNC-machine and the properties and the dimensions of the raw material, providing the complete set of workshop plans needed for integrated manufacturing. For automated generation of machine instructions (G-code), machining strategies – depending on the type of machine used, tool and material properties – are elaborated. Finally, the integrated digital design methods studied within the scope of this thesis are tested and verified by the realization of different reduced scale prototypes. The studied applications range from bearing vault structures to fractal and smooth timber panel shell structures. The developed methods have shown to be efficient for the design and the realization of geometrically complex architectural objects. The required planning effort to handle and manipulate the design and the production data has been greatly reduced. Some of the proposed methods have proved to be robust and general enough to be applied on real world applications. Iterative geometric design provides high degree of design possibilities offering an efficient tool for the creation of smooth and rough free form objects. The possibility to incorporate successive folds in free-form objects allows structural applications.

EPFL2009

Un modèle itératif de surfaces pour la construction en bois

Gilles Gouaty, Ivo Stotz, Eric Tosan, Yves Weinand

2009

Iterative geometric design for architecture

Ivo Stotz

EPFL2009