In recent decades, the popularity of freeform shapes in contemporary architecture poses new challenges to digital design. One of them is the process of rationalization, i.e. to make freeform skins or structures affordable to manufacture, which draws the most attention from geometry researchers. In this thesis, we aim to realize this process with simple geometric primitives, circular arcs. We investigate architectural surfaces and structures consisting of circular arcs. Our focus is lying on how to employ them nicely and repetitively in architectural design, in order to decrease the cost in manufacturing. Firstly, we study Darboux cyclides, which are algebraic surfaces of order ≤ 4. We provide a computational tool to identify all families of circles on a given cyclide based on the spherical model of M ̈obius geometry. Practical ways to design cyclide patches that pass through certain inputs are presented. In particular, certain triples of circle families on Darboux cyclides may be suitably arranged as 3-webs. We provide a complete classification of all possible 3-webs of circles on Darboux cyclides. We then investigate the circular arc snakes, which are smooth sequences of circu- lar arcs. We evolve the snakes such that their curvature, as a function of arc length, remains unchanged. The evolution of snakes is utilized to approximate given surfaces by circular arcs or to generated freeform shapes, and it is realized by a 2-step pro- cess. More interestingly, certain 6-arc snake with boundary constraints can produce a smooth self motion, which can be employed to build flexible structures. Another challenging topic is approximating smooth freeform skins with simple panels. We contribute to this problem area by approximating a negatively-curved 5 surface with a smooth union of rational bilinear patches. We provide a proof for vertex consistency of hyperbolic nets using the CAGD approach of the rational B ́ezier form. Moreover, we use Darboux transformations for the generation of smooth sur- faces composed of Darboux cyclide patches. In this way we not only eliminate the restriction to surfaces with negative Gaussian curvature, but, also obtain surfaces consisting of circular arcs.

FAD * for Stadsgårdskajen Re-introduction of some of the knowledge from the master builder to the contemporary architect. This project investigates the interaction between designing architecture and building architecture in a computer controlled context. Algorithms have been developed to simulate and control an automated in situ brick stacking process. Brick laying is a well researched topic for robotic processes. It is an ideal material for building with robots (in Stockholm) since it is a generic building block that is cheap and easy to produce locally. Corbeled vaults, instead of keystone vaults, can be built without support and with all identical elements and are therefore also suitable for robotic fabrication.  The algorithms have been incorporated in a parametric model that have been used to develop public building at Stadsgårdskajen, Stockholm. FAD is about creating and explore a different architectural expression as well as reintroducing the brick as a relevant construction material for Stockholm. / FAD* för Stadsgårdskajen Återinförande av några av byggmästarens förmågor till den samtida arkitekten I detta examensarbete undersöks förhållandet mellan att designa arkitektur och att bygga arkitektur i en datorkontrollerad miljö. Algoritmer har utarbetats för att simulera och styra en automatiserad in situ murningsprocess. Inom fabrikation och automatisering med industrirobotar är tegelband ett välundersökt ämne. Tegel är ett idealiskt material vid byggande med robotar. Det är enkelt och billigt att framställa och tegel som byggkloss är en lämplig typologi för addativ fabrikation med robotar. Valv byggda genom utkragning istället för traditionella valvbågar kan byggas utan stöd och med identiska element. Därför är denna byggnadsteknik även lämplig för additiv fabrikation med robotoar. Algoritmerna har intergrerats i en parametrisk modell som har använts för att formge en offentlig byggnad på Stadsgårdskajen i Stockholm. FAD handlar såväl om skapande och utforskande av ett nytt arkitekturspråk som av återinförande av tegel som ett betydelsefullt konstruktionsmaterial i Stockholm.

La conception de réseaux de courbes nécessite la considération de plusieurs facteurs: la stabilité de la structure, l'efficience matérielle, et l'aspect esthétique - des objectifs complexes et interdépendants rendant la conception manuelle difficile. Nous présentons une nouvelle méthode permettant de simplifier des réseaux de courbes destinés à la fabrication. Pour un ensemble de courbes 3D donné, notre algorithme en sélectionne un sous-ensemble stable. Bien que la stabilité soit traditionnellement mesurée par l'ordre de grandeur des déformations entraînées par des charges prédéfinies, une telle approche peut s'avérer limitante. Elle ne tient ni compte des effets de vibration pour les structures de grandes tailles, ni des multiples possibilités de forces appliquées pour les structures et objets de plus petite taille. Ainsi, nous optimisons directement pour une déformation minimale avec la charge dans le pire des cas (de l'anglais "worst-case"). Notre contribution technique est une nouvelle formulation de la simplification de réseaux de courbes pour la stabilité dans le pire des cas. Celle-ci mène à un problème d'optimisation semi-définie positive en nombres entiers (MI-SDP). Malgré que résoudre ce problème MI-SDP directement est irréaliste dans la plupart des cas, une intuition physique nous mène à un algorithme vorace efficace. Enfin, nous démontrons le potentiel de notre approache à l'aide plusieurs réseaux de courbes et validons l'efficacité de notre méthode en la comparant de façon quantitative à des approaches plus simples. / Designing curve networks for fabrication requires simultaneous consideration of structural stability, cost effectiveness, and visual appeal - complex, interrelated objectives that make manual design a difficult and tedious task. We present a novel method for fabrication-aware simplification of curve networks, algorithmically selecting a stable subset of given 3D curves. While traditionally, stability is measured as the magnitude of deformation induced by a set of predefined loads, predicting applied forces for common day objects can be challenging. Instead, we directly optimize for minimal deformation under the worst-case load. Our technical contribution is a novel formulation of 3D curve network simplification for worst-case stability, leading to a mixed-integer semi-definite programming problem (MI-SDP). We show that while solving MI-SDP directly is impractical, a physical insight suggests an efficient greedy heuristic algorithm. We demonstrate the potential of our approach on a variety of curve network designs and validate its effectiveness compared to simpler alternatives using numerical experiments.