1,332 research outputs found
Architectural Geometry as Design Knowledge
No full textThe onset of digital design has enabled a new level of experimentation with free-form shapes in contemporary architecture, which has made geometry a fertile area of research over the last decade or so. Helmut Pottmann describes how geometry not only has the potential to inform a more exciting generative approach for architects, but can also make design much more construction aware for the whole design team, enabling a wholly digital workflow from design to fabrication. Copyright © 2010 John Wiley & Sons, Ltd
Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles
No full textWe investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on arbitrary parameter rectangles. For discrete planar quadrilateral nets, circular nets, Q∗-nets and conical nets we obtain a characterization of the corresponding discrete multi-nets. In the limit these discrete nets lead to some classical classes of smooth surfaces. Furthermore, we propose to use the characterized discrete nets as discrete extensions for the nets to obtain structure preserving subdivision schemes.We would like to thank Wolfgang Schief and Jan Techter for many fruitful discussions. This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics.” – www.discretization.de. Helmut Pottmann was supported through Grant I 2978-N35 of the Austrian Science Fund (FWF)
Parametric Design of Tensegrity-Origami Structures
No full textLightweight, deployable, and reusable structures attracted increasing at-tention over the years in terms of construction sustainability. In this research area,tensegrity and origami-inspired structures were extensively investigated for differentapplications. This contribution focuses on the design of two-dimensional geometricpatterns of vertices, edges, and faces that can be used for both tensegrity and origamistructures, which are here analyzed in connection to each other. The design methodol-ogy is based on a semi-analytical form-finding procedure in which two set of equationsare simultaneously solved: the rank-deficiency conditions on the equilibrium operatorfor the tensegrity structure and the developability conditions for the correspondingorigami. In addition, the relation between geometry and selfstress of the obtainedstructures is analyzed by parametric simulations. A 3D modeling workspace – com-bining GrasshopperTMand MatlabTMcodes – supports the design phases from thestudy of the geometric pattern, satisfying the rank-deficiency and the developabilityconditions, to the evaluation of the selfstressed tensegrity configuration. The caseof a Snelson tensegrity tower functioning as a lightweight, deployable, and reusablepavilion is considered to demonstrate the proposed methodology for the design oftensegrity-origami structures
Quad mesh mechanisms
No full textThis paper provides computational tools for the modeling and design of quad mesh mechanisms, which are meshes allowing continuous flexions under the assumption of rigid faces and hinges in the edges. We combine methods and results from different areas, namely differential geometry of surfaces, rigidity and flexibility of bar and joint frameworks, algebraic geometry, and optimization. The basic idea to achieve a time-continuous flexion is time-discretization justified by an algebraic degree argument. We are able to prove computationally feasible bounds on the number of required time instances we need to incorporate in our optimization. For optimization to succeed, an informed initialization is crucial. We present two computational pipelines to achieve that: one based on remeshing isometric surface pairs, another one based on iterative refinement. A third manner of initialization proved very effective: We interactively design meshes which are close to a narrow known class of flexible meshes, but not contained in it. Having enjoyed sufficiently many degrees of freedom during design, we afterwards optimize towards flexibility.This research was partially funded by the National Natural Science Foundation of China under grant number 62088102. Helmut
Pottmann was supported by KAUST baseline funding
Ruled Laguerre minimal surfaces
No full textA Laguerre minimal surface is an immersed surface in ℝ 3 being an extremal of the functional ∫ (H 2/K-1)dA. In the present paper, we prove that the only ruled Laguerre minimal surfaces are up to isometry the surfaces ℝ (φλ) = (Aφ, Bφ, Cφ + D cos 2φ) + λ(sin φ, cos φ, 0), where A,B,C,D ε ℝ are fixed. To achieve invariance under Laguerre transformations, we also derive all Laguerre minimal surfaces that are enveloped by a family of cones. The methodology is based on the isotropic model of Laguerre geometry. In this model a Laguerre minimal surface enveloped by a family of cones corresponds to a graph of a biharmonic function carrying a family of isotropic circles. We classify such functions by showing that the top view of the family of circles is a pencil. © 2011 Springer-Verlag.The authors are grateful to S. Ivanov for useful discussions. M. Skopenkov was supported in part by Mobius Contest Foundation for Young Scientists and the Euler Foundation. H. Pottmann and P. Grohs are partly supported by the Austrian Science Fund (FWF) under grant S92
Freeform Honeycomb Structures
No full textMotivated by requirements of freeform architecture, and inspired by the geometry of hexagonal combs in beehives,
this paper addresses torsion-free structures aligned with hexagonal meshes. Since repetitive geometry is a very
important contribution to the reduction of production costs, we study in detail “honeycomb structures”, which are
defined as torsion-free structures where the walls of cells meet at 120 degrees. Interestingly, the Gauss-Bonnet
theorem is useful in deriving information on the global distribution of node axes in such honeycombs. This paper
discusses the computation and modeling of honeycomb structures as well as applications, e.g. for shading systems,
or for quad meshing. We consider this paper as a contribution to the wider topic of freeform patterns, polyhedral
or otherwise. Such patterns require new approaches on the technical level, e.g. in the treatment of smoothness, but
they also extend our view of what constitutes aesthetic freeform geometry
From Helmut Jürgensen’s former students: The game of informatics
No full textPersonal reflections are given on being students of Helmut Jürgensen. Then, we attempt
to address his hypothesis that informatics follows trend-like behaviours through the
use of a content analysis of university job advertisements, and then via simulation
techniques from the area of quantitative economics
Quadrilateral meshes generated by fairing structure lines
Get PDFDas Generieren ästhetisch ansprechender Flächen ist in der architektonischen Geometrie von besonderem Interesse. Dieser Prozess bedingt mitunter das Anwenden geeigneter Glättungsverfahren. In der vorliegenden Diplomarbeit wird der spezielle Fall von diskreten 3-dimensionalen planaren Vierecksflächen betrachtet. Die Glätte eines Netzes wird - nicht wie im kontinuierlichen Fall durch die Differenzierbarkeit, sondern - anhand des Verlaufs einer Strukturlinie bestimmt; je geradliniger ein Polygon wird, umso glatter ist es.Einleitend werden dazu in dieser Arbeit bekannte Glättungsverfahren vorgestellt; wie zum Beispiel das Minimieren von Energiefunktionalen, das Verfahren von Laplace oder Taubin. Anschließend wird ein Fairing-Konzept präsentiert, welches mit Hilfe von Optimierungsmethoden die unerwünschten Zickzacklinien aus dem Netz "glättet". Das Verfahren untersucht vorab jeden Punkt auf dessen Glattheit und fixiert ihn gegebenenfalls. Mit Hilfe einer Gewichtsfunktion kann der Abstand der geglätteten Punkte zu den Ausgangspunkten gesteuert werden. Anhand von Beispielen werden die Ergebnisse der Glättung dieser Fairing-Methode mit denen der bekannten Verfahren von Laplace und Taubin verglichen.One of the main problems in architectural geometry is the generation of aesthetically appealing surfaces. This process occasionally conditions the application of appropriate smoothing methods. In this thesis a particular case of 3-dimensional planar quadrilateral meshes is observed. The smoothness of a quadrilateral mesh is defined, not through differentiability like in the continuous case, but based on the trend of a structure line; the more rectilineal a polygon becomes, the smoother it gets. This thesis also sets out to preliminary introduce well-known smoothing methods; such as the minimization of energy functionals, the Laplacian smoothing method or Taubin's smoothing method. Subsequently an alternative fairing concept is introduced, which 'smoothes' the undesirable zigzag lines with methods of optimization. This approach examines the smoothness of each point in advance and flattens it if necessary. The distance between the smoothed points can be directed towards the initial point via a penalty function. With reference to examples, the results of the smoothing through the alternative fairing method and that of the well-known methods of Laplace and Taubin can be compared
Smalltalk Interpreter in Java
No full textAuthor Helmut Rohregger, BSc.Kurzfassungen in deutscher und englischer SpracheMasterarbeit Universität Linz 201
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