How tessellation became the mutt's nuts in the fashion world | Alex Bellos | Science. Mathematics has never been so fashionable! Last year Paul Smith launched a T-shirt whose patterned design, below, was inspired by the Dutch artist and geek hero M C Escher (1898-1972). One of Escher’s favourite techniques was tessellation – which is the mathematical term for covering an area with tiles that don’t overlap and leave no gap.
Often a tessellation uses only one shape of tile. The charm of a good tessellation is to find an interesting single tile, such as the dove in the Paul Smith T-shirt. British artist Sam Kerr designed the Paul Smith T-shirt and he has collaborated with London-based accessories brand Marwood to design tessellations for ties, bow ties and pocket squares that will be on sale later in the year. Sam has got so fascinated by tessellations that he has kept on designing them for fun. "The fact that this tessellation is created by a rubber stamp is crucial to its concept. He has also experimented with tessellations of clothes. What reaction do you get from your work?
Dspace.mit.edu/bitstream/handle/1721.1/65438/747036909.pdf?...1. Chen-Gackstatter. Institute of Geometry. One part of this research is project `Computing Multilayer Freeform Surfaces', funded by the Österreichische Forschungsförderungsgesellschaft (FFG), which is conducted in cooperation with TU Wien and Waagner-Biro. Another part is the the project `Computational Differential Geometry', which is part of the National Research Network Industrial Geometry" (S92), funded by the Austrian Science Fund (FWF).
The implementation of freeform shapes in architecture is an area which encompasses great challenges in engineering as well as novel design ideas, and which consequently has high public exposure. However, the geometric basics of doubly curved surfaces realized as steel/glass constructions with planar faces remained largely unexplored. Planar quadrilateral faces and truly freeform geometries seemed mutually exclusive. Moebius Transformations Revealed. Prof. Dr. Helmut Pottmann / Institute of Discrete Mathematics and Geometry. Address Education Dr. techn. in Mathematics, Vienna University of Technology, 6/83 'Mag. rer. nat.' (comparable to M.S.) in Mathematics, Vienna University of Technology, 4/82 Study of Mathematics and Descriptive Geometry, Vienna University of Technology, 9/77-6/83 Professional Experience Research Interests Industrial Geometry Architectural Geometry Discrete Differential Geometry Relations between Geometry, Numerical Analysis and Approximation Theory Computer Aided Geometric Design, Geometric Modelling and Computer Vision Applications of Geometry in Manufacturing Kinematical Geometry and Robot Kinematics Publications Books H.
Deutsche Ausgabe: Architekturgeometrie, Springer & Bentley Institute Press (2010), 1st Edition., 474 S. 650 Abb. in Farbe., Geb. Geometry lies at the core of the architectural design process. This book has been written as a textbook for students of architecture or industrial design. Selected Publications 2013 Selected Publications 2012 Selected Publications 2011 (c) H.
Sketching Dynamic Geometry on the iPad by @belchd. Institute of Geometry. Institute of Geometry. Institute of Geometry. [MIT Design and Computation Group] Geometries || Algebras. SCI-Arc: Advances in Architectural Geometry 2012. Video Panorama. A video panorama of Universities and Research Laboratories experiments will be held from 27th to 30th in the Forum -1 of the Museum. It will show recent Developments in Architectural Geometry and Computation, curated by AAG 2012 Organization Committee & Aurélien Lemonier, Curator at the Centre Pompidou. ENSA Ecole nationale supérieure d’architecture Paris-Malaquais, France: The preview can be seen at this adress: Teaching by Félix Agid et Minh Man Nguyen under the supervision of Philippe Morel, Maurizio Brocato et Christian Girard Titles : Experiment in computational architecture + digital fabrication Students :Deleforge Adrien, El Arabi Rim, Gaudilliere Nadja, Gobin Tristan, Gomez Herrera yostino Herbera Theo, Aziza Guermazi, Jaidi Lina, Jlil Taoufik, Kutlu Meite, Shen Yuan, Thellier Arthur, Usai Sylvain, Lily Lutz, (Columbia University) Dauphant Thomas (ESA) EPFL : Ecole polytechnique fédérale de Lausanne, Switzerland SASAKI lab.
Keynote Speakers. Symposium Keynote Speakers Jan Knippers, Knippers Helbig Advanced Engineering Jan Knippers, Prof. Dr. Ing., is a partner in Knippers Helbig Advanced Engineering. He completed his studies of engineering studies at the Technische Universität Berlin in 1992, receiving a Ph.D., and founded his own firm together with Thorsten Helbig in 2001 in Stuttgart and in 2009 in New York City. Philip Ball, Physicist and science writer Philip Ball is a freelance writer. Pierre Alliez, INRIA Sophia-Antipolis Pierre Alliez is Senior Researcher at INRIA Sophia-Antipolis – Mediterranee. Chuck Hoberman, Hoberman Associates Chuck Hoberman, is the founder of Hoberman Associates, a multidisciplinary practice that utilizes transformable principles for a wide range of applications including consumer products, deployable shelters and structures for aerospace.
Public lecture Speakers: Toyo Ito, Architect Mutsuro Sasaki, Engineer Toyo Ito was born in 1941. Shape Space Exploration of Constrained Meshes (Siggraph Asia 2011) LGG | Publications. Minimal Surface Archive. Triply Periodic Minimal Surfaces. Classical Surfaces. Instantanés d'architecture : Bernard Cache, Objectile, Paris. Geometric Modeling and Industrial Geometry. Tessellations by Polygons - EscherMath. Seville, Spain. Explorations The explorations for this section include: Explorations using Geogebra For those who have access to The Geometer's Sketchpad the following explorations are available.
The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy. [1]. Some Basic Tessellations Recall that a polygon is a closed plane figure made by joining line segments. The fundamental question we will discuss in this section is: Which polygons tessellate? More precisely, which polygons can be used as the only tile in a monohedral tessellation of the plane? Before moving on, you may want to do the Tessellation Exploration: The Basics The most common and simplest tessellation uses a square. Stacks of these strips cover a rectangular region and the pattern can clearly be extended to cover the entire plane. All parallelograms tessellate. Special parallelograms such as rectangles, and rhombuses also tessellate.
All triangles tessellate. and Then . ETH - Applied Geometry Group - Architectural Geometry. Short Summary The objective of this project is to investigate mathematical concepts, robust algorithms, scalable geometric optimization techniques, and flexible data structures to form a comprehensive toolset for architectural freeform surface design taking into account construction processes and rationalization. Project Description ”With the use of digital technologies, the design information is the construction information. (...) It is the digitally-based convergence of representation and production processes that represents the most important opportunity for a profound transformation of the profession...”Architecture in the digital age: Design and Manufacturing - Branko Kolarevic Recent advances in construction and material technology have enabled the use of freeform surfaces as striking elements in contemporary architecture.
Today’s Computer Aided Design software provides intuitive interfaces for the design of arbitrarily complex freeform surfaces. Symmetry Publications. Geometric Modeling and Industrial Geometry. Scientific Publications. Geometric Multi-Covering.R. Strauss, F. Isvoranu, G. Elber CAD / Graphics, 2013 (Proceedings). Large scale double curved glass facades made feasible - The Arena Corinthians West Facade.A. Schiftner, M. Eigensatz, M. Kilian, G. Ruled Free Forms. Architectural Caustics — Controlling Light with Geometry. Architectural Geometry from Research to Practice: The Eiffel Tower Pavilions. Design of Self-supporting Surfaces. Paneling the Eiffel Tower Pavilions. Case Studies in Optimization of Glass-panelized Architectural Freeform Designs. Circular Arc Structures. Case Studies in Cost-Optimized Paneling of Architectural Freeform Surfaces. Tiling Freeform Shapes With Straight Panels: Algorithmic Methods. Statics-Sensitive Layout of Planar Quadrilateral Meshes.
Ruled Surfaces for Rationalization and Design in Architecture. Designing Quad-dominant Meshes with Planar Faces. Paneling Architectural Freeform Surfaces. Geodesic Patterns. Packing circles and spheres on surfaces. Curved folding. Evolute. Advances in Architectural Geometry 2012. Advances in Architectural Geometry 2010. Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the final construction. Modern geometric computing provides a variety of tools for the efficient design, analysis, and manufacturing of complex shapes. On the one hand this opens up new horizons for architecture. On the other hand, the architectural context also poses new problems to geometry. Around these problems the research area of architectural geometry is emerging. It is situated at the border of applied geometry and architecture. This symposium will bring together researchers from the fields of architecture and geometry to discuss recent advances in research and practice and to identify and address the most challenging problems.
[Link to the 2008 conference] [Link to the 2012 conference] BBC | The Code -- S01E02 - Shapes.