Twisted Beams on Surface

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

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

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

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

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

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

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