eat-a-bug

RhinoVAULT Workshop in Innsbruck

2012-01-16T17:36:00.003+01:00

Invited by Günther H. Filz and Rupert W. Maleczek, the Block Research Group will give a workshop at koge, University of Innsbruck, Austria, as part of the Ringvorlesung 2012. Prof. Philippe Block, Matthias Rippmann and myself will lead a design workshop using RhinoVAULT, a plug-in for Rhino, that allows for the intuitive design of compression-only shapes, offering a maximum control of the geometry.

Building the Bubble - Architecture and Financial Crisis

2012-01-13T10:09:00.013+01:00

Since a few days a report by Barclays Capital that points out correlation between skyscraper boom and economic crisis is topic of international news, e.g. BBC and BI. Economist Andrew Lawrence suggested in 1999 the Skyscraper Index, as predictor of economic crisis.

The relation between skyscraper building and finance has earlier been discussed earlier in the great book Form Follows Finance by Caroll Willis.

Furthermore, I found an interesting figure related to this topic on page 94 in Alex Lehnerer’s Book Grand Urban Rules, showing the relation between industrial production and building height limitations in Chicago.

Cooperation: The Engineer and the Architect

2011-12-18T14:30:00.017+01:00

This book, edited by Aita Flury, describes recent developments in the relation between architect and engineer in the design process, with focus on Switzerland and Germany. With contributions by Markus Peter, Adolf Krischanitz, Jürg Conzett, Mike Schlaich, Jospeh Schwartz and many others.

"This book provides a thorough description of just how varied and complex, how stressful and yet inspiring the cooperation between architect and engineer can be, and which projects become possible only through a cooperation of these two professions. [..] As such, it provides architects and students with the tools for future cooperation" (Birkhäuser.ch)

A snapshot of the realted panel discussion at the DAZ, on page 212/213.

Watch lectures by Fritz Neumeyer, Stefan Polónyi, Yves Weinand, Joseph Schwartz, and others, from the related symposium at the ETH Zurich online here.

Watch Prof. Block’s Lecture Online

2011-11-17T19:00:00.012+01:00

Prof. Block, founder of the BLOCK Research Group, has been invited on October 31, 2011 for his first departmental lecture at the College of Design, University of Minnesota, USA. Invited for the lecture series “Global Practices in Architecture”, he talked about “New Masonry Vaults: Learning from the old master builders to design a better future”.

Modelling Funicular Structures

2011-10-23T17:19:00.044+02:00

Funicular structures are structures whose geometry is based on the funicular polygon, a term from graphic statics. Such structures work mainly with axial forces, almost without bending. Typical examples are arches and cables.

At the IABSE-IASS Symposium 2011 in London, I presented novel parametric tools for structural design in early stages. These have been developed at the Chair for Structural Design, ETH Zurich. Download the paper here.

Based on concepts of graphic statics, custom Grasshopper components have been implemented that allow for the interactive modelling of a planar funicular polygon in Rhino. Straight lines are interpreted as external forces, axial forces in the funicular are represented by tubes, red tubes are in tension, blue tubes are in compression. The tube section is proportional to the magnitude of the axial force.

These tools facilitate intuitive modelling of funicular, hence efficient, structural systems.

3D Printed Stone Vault

2011-10-15T23:54:00.037+02:00

At the Design Modelling Symposium in Berlin, a 3d printed vault prototype, designed by Norbert Palz and Ricardo Gomes, has been exibited.

The vaulted structure has been additively fabricated using the d-shape techology, it is 3d printed from an artificial sandstone.

The prototype has been designed using RhinoVAULT.

Padua Pavilion at ETH

2011-10-06T23:36:00.015+02:00

Yesterday evening, on the ETH Zurich campus, the Padua Pavilion has been opened. It is a structure made of recycled timber, developed and built in two weeks by students of the studio Tom Emerson.

Structural consultancy and live music by Marcel Aubert.

Patents by Rem Koolhaas

2011-09-27T11:23:00.031+02:00

Some of the famous architects and builders from the 20th century, as e.g. Le Corbusier, Buckminster Fuller, and Luigi Nervi, considered themselves as inventors and held several patents. Rem Koolhaas contributed in 2004 to this specific topic in an ironic way:

These and several other fake patents have been published in the book Content and the Bejing Manifesto.

In the same year, Rem Koolhaas also applied for a real patent, for a Panel for architectural design:

Open Source Architecture?

2011-08-30T11:47:00.074+02:00

Time seems to be ripe for the development of an open design license for architecture. The manifesto of Open Source Architecture (OSArc) has been published few months ago in domus.

Yesterday, Daniel Davis raised the exciting question, whether Evolute is right to patent a certain geometry of a freeform roof construction.

This question is related to the discussion, whether it is right and possible to patent architecture in general. In 2007, there has been a heated discussion in Switzerland and internationally, about a patent by the Swiss architect Hans Zwimpfer, concerning a special housing type. After a fight with the Swiss architectural societies BSA and SIA, he managed to claim patent rights for his invention in Europe the USA. While this US lawyer defends the idea of applying patent law to architecture in specific cases, this Swiss lawyer states that it is more appropriate to protect a work of architecture, as cultural artifact, by the more flexible copyright law, rather than the rigorous patent law.

Considering that patent law seems to be applicable to the rather fuzzy case of Zimpfer’s architectural innovation, there seems to be a good chance for Pottmann and RFR to defend their protected rights concerning geometric innovation of support structures.

The introduction of an Open Source Architecture license may be a way to actively defend intellectual property in architecture against protection by others.

Herzog & de Meuron online

2011-08-26T15:16:00.012+02:00

Since Wednesday, HdM’s website is finally online. Interesting design though...

Experimental Wood Structures at ETH

2011-08-25T17:08:00.029+02:00

Lately, a variety of experimental wooden pavilions have been erected at the ETH Hönggerberg campus, Zurich.

A pavilion made from bent plywood, designed and built by students of the AA Emtech, with support form the Structural Design chair.

Two pavillons built as reciprocal frame structures, as part of a research project at the chair of Architecture and Technology.

Jaú, designed and built by students from the studio Tom Emerson. Watch the time-lapse here.

The Sequential Structure 2, Build by students of the chair of Architecture and Digital Fabrication, in cooperation with the BLOCK Research Group.

OpenStreetMap for Rhino

2011-06-24T00:43:00.028+02:00

Using rhino.python, a script has been written, that imports a static map from OpenStreetMap as background bitmap to Rhino, based on an address and zoom level entered by the user. In a first step, the geographical location of the address is identified using the Nominatim API. The location coordinates are used as input parameter for the MapOf service. Finally, the map image obtained from the web service is placed as background bitmap, in the right scale according to the zoom level.

Additionally, an appropriate EarthAnchorPoint is set based on the geographical location and scale. This allows for the export of geometry in relation to the imported static map to Google Earth using the KML format. The units of the Rhino file are automatically changed to meters, in order to obtain the right scale of the map.

Download the script here.

Computation for Sustainable Architecture and Urbanism

2011-06-09T13:10:00.009+02:00

An upcoming symposium at ETH, Zurich: "The aim of this first symposium on computation for sustainable architecture and urbanism is to discuss information-based approaches that augment design processes and descisions towards sustainable buildings and cities." (SUAT)

Attila Csörgő

2011-05-22T13:18:00.023+02:00

Last weekend, I saw the great exhibition "Archimedean Point" by the Hungarian artist Attila Csörgö in the Kunsthalle Hamburg: "Csörgõ’s work explores the margin between art and science. The artist conducts thorough experiments with precise machines of his own design and optical apparatuses that reinforce his likewise epistemological and playful, humorous approach. His interests lie in optical illusions, metamorphoses of space into surface as well as hypnotic plays of light that touch upon mechanical movements and other inventions, where he combines imagination and a curiosity for various physical and mathematical phenomena." For a describtion of the work by the artist himself, view the interview (Part 1 and Part 2).

Dodecaherdon=Icosaherdon (1999) is a kinetic construction, based on geometric correspondances between platonic solids. The dodecaherdon is transformed into the icosaherdon and reverse.

Möbius Space (2006-2010) an endless panorama photograph on a möbius strip, taken by a special camera.

Spherical Vortex (1999) is the path of a flashlight bulb made by connecting three seperate whirling movements of different velocity.

RhinoVAULT - Shell Design for Rhino

2011-05-11T21:00:00.001+02:00

RhinoVAULT is a plug-in for Rhino, being developed at the BLOCK Research Group by Matthias Rippmann, myself and Philippe Block, that allows for the intuitive design of compression-only shapes, offering a maximum control of the geometry. This software is written particularly for shaping unreinforced masonry vaults, but can also be used for designing efficient freeform shells. Based on the Thrust Network Approach (TNA), which uses a force network as discretization of the shape, it is possible to internally redistribute forces within the network using force diagrams.

A first application of the tool is a prototype of a freeform Catalan thin-tile vault erected at the ETH Campus, Zurich, Switzerland. It was planned and build by Lara Davis, and designed by Matthias Rippmann.

Pictures (c) by BLOCK Research Group

Möbius Loop-Pasta

2011-05-09T22:48:00.006+02:00

Thanks to Steve Kass, Möbius strips are not only feeding the mind. (via Nerdcore)

Lecture at ESA

2011-04-26T13:59:00.005+02:00

Philipp Eversmann and Paul Ehret kindly invited me to give a lecture at the Ecole Spéciale d'Architecture, Paris, on April 30, as part of the seminar In Silico Design. Recent research from the BLOCK Research Group and the Chair of Structural Design, both ETH Zurich, will be presented.

"What do you want, brick?"

2011-04-16T15:02:00.003+02:00

To express is to drive.

And when you want to give something presence,

you have to consult nature.

And there is where Design comes in.

And if you think of Brick, for instance,

and you say to Brick,

"What do you want Brick?"

And Brick says to you

"I like an Arch."

And if you say to Brick

"Look, arches are expensive,

and I can use a concrete lentil over you.

What do you think of that?"

"Brick?"

Brick says:

"... I like an Arch"

Louis Kahn

from John Lobell: Between Silence and Light, p. 59.

Geometry and Proportion in Structural Design

2011-03-30T13:19:00.031+02:00

A great book about construction history:

"This collection of essays covers the wide range of topics about structural design, structural design approaches and structural pioneers in honor of the Spanish architect Ricardo Aroca. [...] He radically changed the structural education of architectural students. Aroca pushed it away from a primary analytical analysis towards the discovery of the flow of forces [...] This book includes most important and interesting thoughts on the relation between architectural and structural forms and the fact that both disciplines – architecture and engineering – have differing approaches to the function of a structure." Cited from the book review by
Annette Bögle. The only handicap for me is, that some of the essays written in spanish are not translated into english.

In his essay, Santiago Huerta, one of the book's editors, discusses the fascinating theorem of transformation of structures by William Rankine, first described in the Manual of Applied Mechanics (1858). Huerta's full article can be downloaded here.

Bugs for Breakfast

2011-03-18T16:59:00.006+01:00

Very promising new blog by David Rutten, the creator of Grasshopper. With a nice name ...

Geometry of the Venetian Gondola

2011-03-10T17:27:00.021+01:00

On my last trip to Venice I realized, that the shape of the venetian gondola is not only elegant, but also functional and higly optimized. Developed in the mid-19th-century, the sections of the boat are asymmetric, in order to balance the weigth of the gondoliere, who stands one side of the boat. Referred to the traditional Tramontin shipyard, the geometry of the boat is curved in plan, according to the weight of the oar.

Plans (c) by Gilberto Penzo.

Photo (c) by Alberto de Marco.

Carlo Borer's Sculpture '422' Completed

2011-03-01T09:47:00.009+01:00

Pictures (c) by Carlo Borer.

In previous posts I reported about the design and fabrication process of this piece of art.

Rhumblr - Blogging from Rhino to Tumblr

2011-02-13T19:48:00.044+01:00

Document your design process online with on click!

I used Rhino.Python to write a script, that posts the current view to your Tumblr account. A service in Tumblr automatically sends your posts to Twitter, if enabled. The script uses the Tumblr API.

Download rhumblr.py and installation instructions here.

Fabrication of Carlo Borer's Sculpture

2011-01-29T14:45:00.016+01:00

The artist Carlo Borer and a 1:4 scale model of the sculpture.

Carlo rolling a chrome steel sheet at Senn AG

... verifying a curvature radius.

Grasshopper tools have been used in the design and fabrication process of the sculpture. Pictures (c) by Paul F. Talman.

Free-Form Masonry Featured on Wired.com!

2011-01-04T13:36:00.004+01:00

Thanks to Andrea Graziano, who tweeted eat-a-bug's last post on twitter, Bruce Sterling saw it and posted it on Wired.com!

Advances in Free-Form Masonry

2010-12-22T12:23:00.022+01:00

This model of a free-form compression-only vault has been build using rapid prototyping. It stands just by gravity and friction. It is part of a research project of the BLOCK Research Group at the ETH Zurich. Two publications describe details about the structural models and the design process.

Form and force diagrams in plane, the force distribution in the network, and the form of the network in 3d.
The form-finding process is based on TNA, a method developed by Philippe Block.

Pictures and movie (c) by BLOCK Research Group

New Evolutions in ZipShape

2010-12-02T09:46:00.024+01:00

Christoph Schindler, co-founder of schindlersalmerón, develops the principle of ZipShape since 2007, in order to build curved elements from cnc-manufactured plain material without molds.

An element consists of two differently slotted panels that only interlock if bent to the desired curvature.

A grasshopper definition worked out during a workshop at the CITA Copenhagen shows the dependency between slot geometry and global curvature.

The newest development allows the fabrication of developable twisted surfaces.

This principle has been applied to a sculpture produced and tested at the Bern University of Applied Sciences in Biel.

Twisted Beams on Surface

2010-11-28T11:40:00.011+01:00

Twisted beams with custom cross-section curve aligned normal to a given surface.

Download the gh-definition here.

PQ Mesh Design: Morpharchitecture Workshop - Lyon 2010

2010-11-07T18:10:00.009+01:00

The gh definition presented here has been used for the design of a shell structure build from sheet material at Les Grandes Ateliers, Lyon, by architecture students of Ecole nationale supérieure d'architecture de montpellier and the TU Delft.

The pq design tool ensured the planarity of the quadrilateral faces, that allowed the fabrication of the shell from flat sheet material.

Photo by Robert Vierlinger.

Developable Surface Optimization

2010-10-26T22:32:00.030+02:00

The artist Carlo Borer asked me to implement tailored developable surface modelling tools for rhino.

Using Grasshopper together with the evolutionary algorithm solver Galapagos, an optimization routine for lofted surface strips towards developable surfaces has been implemented.

Gaussian curvature of original and optimized surface. For developable surfaces, the gaussian curvature is zero.

Carlo Borer: 401, 2009.

Benoît Mandelbrot has died

2010-10-17T20:50:00.022+02:00

Benoît Mandelbrot, father of fractal geometry and chaos theory, has died last thursday. The idea of self-similarity in nature and mathematics is described in his great book The Fractal Geometry of Nature.

The picture above shows the Mandelbrot set, a set of points in the complex plane, the border of the set is a fractal.

Not only coastlines, fern, and the vegatable romanesco exhibit self-similarity, but also stock price charts. Mandelbrot describes a fascinating, unorthodox view on finacial theory in his book The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward.

Mandelbrot's TEDTalk from 2010.

Architecture and Governmental Violence

2010-10-04T20:01:00.051+02:00

Stuttgart 21, the project for a new train station in Stuttgart, Germany, started with a winning competition entry by Christoph Ingenhoven and Partner, Frei Otto, Büro Happold, Leonhardt and Andrae, in the year 2000. The picture shows Frei Otto's model used for form-finding of the roof. The main functional idea behind the project is the transformation of the existing dead-end station into an underground through station.

A strong opposition against the expensive billion-euro project has been formed by the citzens of Stuttgart.

Frei Otto is now a strong opponent to the project, his position can be found in Stuttgarter Zeitung (in German). A strong supporter of the project is Werner Sobek, Professor at TU Stuttgart and successor to Frei Otto. His statment to the project can be found in Stuttgarter Nachrichten (in German).

On last Thursday, September 30, the police used water canons and tear gas against peaceful protesters, who tried to protect the trees in the park against cut down. BBC and The Guardian reported about this incident. Since chancellor Angela Merkel strongly supports the Stuttgart 21 project, it seems to become a hot election issue, even in national scale.

Interactive PQ Mesh by Daniel Piker

2010-10-04T17:08:00.006+02:00

This great piece of work is based on Kangaroo, a physics engine for grasshopper.The original video and a lot of more great stuff can be found on Danie Pikerl's vimeo account. The concept of circular and conical meshes is described in a paper written by H. Pottmann and J. Wallner.

Planar Quad Mesh Design Pt. 2

2010-09-30T16:35:00.008+02:00

Some examples:

The principles of the tool are:
- all nodes are located on a ray through the point in the direction of the normal
- the distance from input surface to pq mesh is adjustable
- two of the edges are controlled by the graph-mapper

Planar Quad Mesh Design Pt. 1

2010-09-18T22:24:00.019+02:00

A parametric tool for the design of planar quadliteral meshes based on uv-grid and normal directions of a design-driving NURBS surface.

The glazed freeform grid shell of the hippo house in the berlin zoo, has been designed by Schlaich, Bergerman + Partner. It consists of planar quadliterals, the geometry is based on a translational surface.

In this paper, a comprehensive discussion about geometric aspects of surface tesselation, by H.Pottmann et. al., can be found. A direct parametric approach, developed by Gehry Partners and Schlaich, Bergemann & Partners is described in this paper.

Download the definition for the planar quad mesh tool here.

Advances in Architectural Geometry 2010

2010-09-13T08:02:00.003+02:00

Since Friday, the proceedings volume of the Advances in Architectural Geometry Conference 2010 is available. The book is published by Springer Verlag.

The Bubble Room

2010-08-29T16:01:00.011+02:00

An underwater dome, shaped by the buoyancy force of an oxygen bubble. This beautiful piece of subaqueous architecture has been build by Jordan Needham and his familiy at the bottom of a Nevada mountain lake. Found on the boingboing blog.

The pictures are screenshots from the movie below.

Creative Data Symposium

2010-08-23T18:51:00.009+02:00

On 24.8.2010, I will give a lecture titled The Geometry of Forces at the creative data symposium at CITA, Royal Danish Academy of Fine Arts.

Parametric Paperstrip

2010-08-16T11:24:00.015+02:00

This parametric model represents the geometry of a twisted straight paperstrip. Length, width, and twist are adjustable.

Some example strips. By definition these surfaces are developable.

The paperstrip as generative element. (c) by Michael Hensel and Achim Menges, Arch+ 188 p.20.

Download the definition here. Another interesting approach has been done by Daniel Piker.

Finds from the Seaside

2010-07-28T22:50:00.014+02:00

On a trip to the seaside near Istanbul, Turkey I found some beautiful biological examples.

A nice example of an algae, ulva lactuca.

An eroded rabbit's skull from behind.

A wing of an insect, probably a cricket.

Geometry of Structural Form

2010-07-16T12:04:00.034+02:00

I am glad to announce that the paper "Geometry of Structural Form" for the conference Advances in Architectural Geometry 2010 has been accepted. My recent research, done at the the ETH Chair of Structural Design, will be presented. Techniques for parametric structural design, based on graphic statics, are described in this paper.

This grasshopper definition has been inspired by Nicholas Grimshaw's Waterloo Station, London.

(c) Grimshaw Architects

Parametric Vault

2010-06-14T18:52:00.032+02:00

Based on TNA, I implemented together with Philippe Block a grasshopper definition for the generation of structural freeform vaults. The image shows a structural surface with an non-uniform force distribution. This work is part of a resarch project done at the ETH Zurich.

This model of a compression-only vault has been build using rapid prototyping. It stands just by gravity and friction.

Implementation-wise the matrix computation routines from rhino SDK have been used inside grasshopper vb.net nodes. Download the grasshopper definition here. A tutorial video shows the use of the definition.

Thrust Network Analysis

2010-06-08T18:47:00.016+02:00

Thrust Network Analysis, a new method for generating compression-only vaulted surfaces and networks was developed by Philippe Block as part of his PhD. Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but offering a viable extension to fully three-dimensional problems.

Form and force diagram, and the resulting compression only network.

Parametric explorations of the indeterminacy of compression-only networks by the modification of the force diagram.

TNA has been used for the structural design of the Mapungubwe National Park Interpretive Centre by Architect Peter Rich.

Interactive Graphic Statics

2010-05-11T15:24:00.030+02:00

Some nice examples of processing-based interactive graphic static applets have been developed at the MIT. Interactive Thrust is a project started by Philippe Block under supervision of John Ochsendorf.

A truss geometry and its force diagram by Luigi Cremona.

Another great interactiv webpage is Active Statics, developed by Simon Greenwold, Ed Allen and Waclaw Zalewski.

Graphic Statics

2010-05-09T18:38:00.026+02:00

The french mathematician Pierre Varignon (1654-1722) introduced the funicular polygon and the polygon of forces in his work Nouvelle Mecanique ou Statique. He describes a way to construct the form of a hanging rope with attached weights graphicaly. Based on this principle, a technique called graphic statics has been developed in the 19th century. The basic principle of graphic statics is the reciprocal relation between force polygon and funicular polygon. Recomended books: Luigi Cremona: Graphical Calculus (1890) and Edward Allen,Waclaw Zalewski: Form and Forces (2009)

This grasshopper definition generates a funicular polygon for uniform loading. Download here.

The Honeycomb Vase

2010-04-27T10:28:00.012+02:00

Honeycomb Vase, "Made by Bees", by Studio Libertiny.
Seen in the MoMA.

Rapid manufacturing is a process by which computer-controlled lasers solidify liquid or powdered resin to create a three-dimensional rendering of a digital design. By contrast, the Honeycomb Vase was produced through what the artist has called "slow manufacturing": Libertíny constructed a vase-shaped beehive scaffold (to be removed at the end of the process) and then let nature take its course. Forty thousand bees build the vase in one week.

Honeycomb like structure build by humans and machines has been studied by Andrew Kudless and by ILEK students.

Parametric Structural Design Lecture at MIT

2010-04-06T16:53:00.014+02:00

In the 19th century, graphic statics, a geometric method for the analysis of the force distribution in structures, has been developed. This scientific, precise method has an intuitive and descriptive character based on reciprocal force diagrams. The recent emergence of parametric design techniques in architecture enables the construction of associative geometry in CAD systems. In this lecture, a novel approach will be presented, combining parametric tools with historic techniques of graphic statics. This highly interactive three-dimensional procedure provides direct control of form and forces at the same time. The aim of this approach is the integration of the flow of forces into the computer aided design process.

John Ochsendorf kindly invited Lorenz Lachauer to present at the MIT Masonry Research Group on Monday April 12. Recent research from the BLOCK Research Group and the Chair of Structural Design will be presented.

Developable Surface Modelling

2010-03-30T21:40:00.007+02:00

A grasshopper definition for developable surface strips. Download here. Mårten Nettelbladt gives a nice description of developable surface types.

Developable Surfaces in Gehry's Architecture

2010-03-23T13:18:00.008+01:00

Gehry's east river guggenheim project in NYC. The use of flexible sheet material like paper in physical models generates developable geometries.

Dennis Shelden, CTO at gt, describes in his phd thesis several ways to compute developable surfaces. Fig. (c) by Dennis Shelden.

Museum MARTa in Herford, Germany. Most of the roof surfaces are developable. Geometric modelling of the roof construction has been done by Jess Maertterer. Further discription on his page.

Exploring the PQ Strip

2010-03-14T18:23:00.011+01:00

Helmut Pottmann and his colleagues form the Geometric Modeling and Industrial Geometry resarch unit at TU Vienna describe the concept of the PQ strip in this paper. The strip consists of planar quad faces. Fig. (c) by H. Pottmann et al.

By lofting the edges, a developable surface is generated. Developable surfaces can be flattened or unrolled without distortion.

Download a grasshopper definition of the PQ strip here.

John Pickering's Sculptures

2010-02-28T13:24:00.010+01:00

John Pickering is a british sculptor who used the geometric principle of inversion since the 1970s. A book about his great work is published by the AA: Mathematical form: John Pickering and the architecture of the inversion

Kusner Minimal Surface

2010-02-15T07:59:00.005+01:00

Discovered by Rob Kusner, Director of the Center for Geometry, Analysis, Numerics and Graphics (GANG). The Kusner surface is an inversion of the Boy surface. The three discs are planes "reaching infinity".

Le Topologicon

2010-02-06T20:00:00.013+01:00

Le Topologicon is a great comic book about topology. The author is Jean-Pierre Petit who discovered the first parameterization of the boy surface in 1981. He is also the co-founder of the non-profit organization Savoir-sans-frontiers. The book deals with moebius strips, klein bottles, boy surfaces, magnetic fields, surface stiching and a lot more interesting topics. In my opinion, the Topologicon is a must-read for everyone dealing with surface modelling, mesh modelling, subdivision surfaces, surface tesselation, vector fields, deformations, or topological space. Some example pages:

Downloads available again.

2010-02-02T17:29:00.000+01:00

Zamet Center

2010-01-21T08:59:00.008+01:00

The Zamet Center in Rijeka, Croatia by 3LHD architects. A beautiful application of the cairo tiling. Thanks to Calgar for advising me of this project.

Homotopy of Boy and Roman Surface

2010-01-17T17:51:00.027+01:00

In topology, a smooth deformation from one surface in an other is called homotopy. The parameterization of this homotopy can be found on wolfram's page.

The grasshopper definition, download here.

This figures from Werner Boy's paper (1903) show the topological construction of the boy surface.

A proposal for a pavillion by Christophe Delsart and Yvan Ngnodjom based on the boy surface for the ARPAM project.

Boy Surface

2010-01-07T10:58:00.020+01:00

The Boy Surface has been found 1901 by Werner Boy. One obtains a topologicaly equivalent surface by attaching a Möbius strip to a disk along its boundary. Like the Möbius strip this surface is nonorientable.

This beautiful parameterization, based on complex numbers, was discovered in the late 1980s by Rob Kusner and Robert Bryant. In this post the boy surface has already been mentioned on eat-a-bug.

Download the definition here

Crocheting the Lorenz Manifold

2009-12-27T19:13:00.019+01:00

In 2003, Hinke Osinga and Bernd Krauskopf from the Bristol Centre for Applied Nonlinear Mathematics produced the first real model of the Lorenz Attractor surface by knitting.

Download the paper by Osinga & Krauskopf here.

For more information on this topic please visit The Home of Mathematical Knitting

Lorenz Attractor

2009-12-16T08:04:00.013+01:00

The Lorenz attractor has chaotic behaviour, named for Edward N. Lorenz. The movie shows the changing of the attractor with increasing Prandtl number.

Downlad definition here

Istanbul Street Parametrics

2009-11-26T07:46:00.015+01:00

Spirograph toys for sale at the Sultan Ahmet station in Istanbul,Turkey.

Spirograph patterns generated with grasshopper.

Download the definition here

Cairo Attractor

2009-11-18T09:15:00.022+01:00

A diamond grid locally distorted by a cairo attractor

The moving attractor

Download the definition here

Cairo Tiling

2009-11-11T09:30:00.031+01:00

This pentagonal tesselationis called cairo tiling.

3D2REAL: A wall based on the cairo tesselation, designed and build by ILEK students.

Extension of the congress center Davos, currently under construction. The roof structure is based on the cairo tesselation. By Degelo Architekten, Engineer: Dr. Schwartz Consulting

The cairo pattern seems to be a blend of a diamond pattern and a chinese pattern.

Download the definition here.

Sun-Shade Machine

2009-10-31T13:23:00.017+01:00

Inspired by Frei Otto's sun-shade machine, this grasshopper definiton generates the shadow of mesh objects for a given geographical location, date, and time. North is in positive y-direction.

Download the file here

"The sun-shade machine, [...] is an extremly flexible tool for determining in the first phase of planning the areas of insolation and shade. [...] the sun-shade machine offers an infinitely variable adjustment for three parameters: geographical location, month, nd time of the day." IL 30 Vela, Toldos, sun and shade (1986)

Armillary Sphere

2009-10-16T18:40:00.025+02:00

An armillary sphere is a model of the celestrial sphere. The drawing is from Christoph Clavius commentary on the book De Sphaera from 1581.

This grasshopper definition generates the position of ecliptic and sun for a given time, timezone and date at a given position on earth. The real position of the sun deviates from this position by approx. +/- 15 min. The reason is the eccentricity of the earths's orbit around the sun. (see equation of time).

Download the grasshopper definition here

Dreidle Urbanism

2009-09-30T18:35:00.024+02:00

Tracking the tip of a dreidle with processing, and then sending the coordinate data via udp to grasshopper.

Dreidle City in time lapse. Inspired by parmetric urbanism.

Download the definition files here. Udp sending and receiving based on Luis Fraguada's definition.

Tracking with Processing and Grasshopper

2009-09-14T17:10:00.019+02:00

I threw a marble in an iron wok and tracked the motion, using brightness tracking in processing. Then I sended the coordinates of the marble via udp as a list to grasshopper.

The path remindes me of harmonograph curves.

Download the files here. The grasshopper definition is based on Luis Fraguada's work, I used his grasshopper udp receiver and adapted it.

Mesh Deformer

2009-09-01T14:19:00.015+02:00

Inspiered by the IXth chapter of D'Arcy Thompson's On growth and form I build a definition for the deformation of mesh models. The reference surface should be in the XZ plane.

The fish model is from planit3d

Download the grasshopper definition here

Fibonacci Tiling

2009-08-26T20:47:00.028+02:00

Aloe plant, the leaves are arranged in the form of a golden spiral, based on Fibonacci numbers
Picture from CSSNZ

A Fibonacci tiling of the plane

Grasshopper definiton of the tiling for download

I found this picture of Nicholas Grimshaw's Eden project on Katie Bednarz's blog

Parametric Sculpture

2009-08-23T23:02:00.005+02:00

Design by Kyle Scherzing and Lee Farmenter at the AA dLab 2009.

initial experimental setup

volumetric model of the motion path

Reverse Dynamism

2009-08-20T10:32:00.015+02:00

Project for a bridge by Elora Brachmachari, Pierluigi D’Acunto, and Ed Pearce at the AA dLab 2009.

conceptual studies

structure

final rendering

Parametric War

2009-08-19T22:28:00.019+02:00

Design for a suit of armour by Kobpong Khomson, Soo Hyun Jin, and Tji Young Lee at the AA dLab 2009.

folded collar

grasshopper definition of the collar

Physico-Logical Design Workshop

2009-07-31T11:49:00.012+02:00

Toni Kotnik and Lorenz Lachauer will lead a design studio at the AA Summer dLab 2009, 3 - 14 August. In the workshop the process of abstraction of physical phenomena will be exemplified by an investigation into patterns of movement of bodies in space and the architectural utilization of these patterns by means of parametric and geometric variation.

A motion sequence by Eadweard Muybridge

The movement of a drummers hand performing a single stroke

Read Colors From File

2009-07-19T21:24:00.010+02:00

The RGB chanels ploted as surface

The input image

This VB script component reads the RGB values from a jpeg file
Download the grasshopper definition ColorSurface.zip here

Chemnitz Stadion

2009-07-13T11:37:00.027+02:00

Winning competition entry for the Chemnitz Stadion, Germany, 1995, Peter Kulka with Cecil Balmond

The roof structure is based on a spirograph curve, sketches by Cecil Balmond, from his book "Informal", p. 159

Spirograph.zip generates spirograph curves with grasshopper

Busan Towers

2009-07-06T12:53:00.026+02:00

This project is the competion entry of UNStudio for the World Business Centre in Busan, South Korea, 2006. The geometry of the floor plates is based on rolling curves.
Pictures (c) by UNStudio

Rolling curves are also known as spirograph curves.

Formula Tower

2009-06-29T11:23:00.023+02:00

At digital matters, Tobias Wallisser from LAVA presented his Superformula Tower concept. Inspired by this beautiful idea, I created a grasshopper definition for towers based on a simpler formula.

The floor plate shapes are based on this formula:

(in polar coordinates)

r(φ) = 1 - a(1 + Sin(φ b))

FormulaTower.zip

Bricks

2009-06-11T18:53:00.012+02:00

Inspiered by the work of Gramazio & Kohler, I plugged together a grasshopper definition, that generates a perforated brick wall from planar curves. Similiar studies in wood have been made recently at the Graduate School of Design, Harvard

Bricks.zip

Balmond's Sigma Code

2009-06-02T21:37:00.037+02:00

The Search for the Sigma Code has a dense plot and relies on another imaginary narrator (not a monk this time, but) a boy called Enjil. If you have ever wondered why any prime number is greater than three will, when raised to the sixth power, leave a remainder of one when divided by nine, you will be at home with this book. -- Vanessa Thorpe, The Independent On Sunday - 13 September 1998

You get the sigma code of a given number n like this:
1. Calculate the sum s of all digits of n.
2. If s is smaller then 10, s is the sigma value.
3. Else set n=s and return to 1.
With this definition it is possible to calculate the sigma values of number sequences. The result of some simple sequences are beautiful patterns:

This diagrams you obtain from the Fibonacci and the Pell sequence by using (and modifing) the following script: SigmaCode.zip

More Geodesic Shells

2009-05-29T23:27:00.015+02:00

Mårten Nettelbladt kindly adviced me of the Korkeasaari Lookout Tower, an example of a geodesic structure build of wood.

The Japan Pavillion at the expo 2000 by Shigeru Ban and Frei Otto is an example of an geodesic shell build of paper tubes.

Geodesic Shell

2009-05-15T22:10:00.014+02:00

The structure of this shell is woven from isocurves and geodesic curves on a surface. Geodesic curves are also called plank lines, they can be build from straigth, but twisted planks. Mårten Nettelbladt studied them on his blog. Geodesic shells build in wood have been studied at the laboratory for timber construction of the EPFL.

Planks generated from lines on a surface with this script: TwistedBeams.zip

The (straight) bamboo strips of this chinese hat are following geodesic lines. Photo by drs2biz.

Surface Turtle

2009-05-11T21:30:00.022+02:00

This is an implementation of a turtle walking around on a NURBS surface. If the turtle is going straight in small steps, the resulting path is close to a geodesic.

SurfaceTurtle.zip

In general relativity, the straight path in curved spacetime is a geodesic

Local Curvature

2009-04-30T20:39:00.016+02:00

In this example, the turtle is connected with a graph, defining the local curvature of the resulting curve

CurvatureTurtle.zip

The relation between local curvature and the curve shape,

taken from S. Wolframs book, p. 418

Turtle Graphics

2009-04-22T22:32:00.018+02:00

This VB.Net module calculates a turtle path

Read an introduction to Turtle Geometry here

Turtle.zip

An analog turtle build by Grey Walter in the fifties

Beams on Surface

2009-04-02T22:24:00.030+02:00

Beams around lines, aligned normal to surface
Height and width are adjustable

Compare Shigeru Ban's pavillon for the Rice Gallery

BeamsOnSurface.zip

Reciprocal grid, example from Cecil Balmond's book, p. 143

Map Lines

2009-03-26T23:21:00.018+01:00

Maps straight curves from the xy plane on a surface
The mapped lines change length, but remain straight

MapLines.zip

Moebius Strip

2009-03-10T23:14:00.002+01:00

Moebius strip around curve
Number of twists is changeable

MoebiusStrip.zip

Harmonograph

2009-03-03T16:21:00.002+01:00

A nice example from the
Science Museum

Harmonogram generated with grasshopper
More about the harmonograph on Paul Bourke's page

Harmonograph.zip

Mesh Inversion

2009-03-01T19:02:00.004+01:00

"Inverse Dude" modeled by Delaque

MeshInversion.zip

Strips & Rivets

2009-02-22T15:54:00.003+01:00

A sculpture of the Boy Surface at Oberwolfach
Rivets generated from points on surface (grasshopper)
Strips generated from curves on surface (rhinoscript)

StripsAndRivets.zip

Surface Inversion

2009-02-09T19:43:00.003+01:00

For a given sphere with center O and radius k,
inversion maps every point P of a surface on a point P'
More about inversion with rhino on Daniel Piker's blog

SurfaceInversion.zip

Blend Surfaces

2009-02-04T12:28:00.003+01:00

Blend surfaces generated from two input surfaces
The mix is adjustable via slider

BlendSurfaces.zip

Enneper Surface

2009-01-28T23:25:00.003+01:00

Mathematical defined surface generated with grasshopper

Number of waves and range in u-direction is parametric

More mathematical surfaces on Xah Lee's page

Enneper.zip

Isocurve Wireframe

2009-01-22T08:27:00.005+01:00

NURBS curves on surface generated with grasshopper
Number of curves in u- and v-direction is separately adjustable

Isocurve.zip

Klein Bottle

2009-01-11T01:39:00.004+01:00

NURBS surface generated with grasshopper
Shape and diameter of the bottle are changeable

KleinBottle.zip