Finds from the Seaside

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

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

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

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

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

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

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.