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.

Parametric Structural Design Lecture at MIT

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

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

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

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.