Twisted Beams on Surface

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


Download the gh-definition 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.

Le Topologicon

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:

Crocheting the Lorenz Manifold

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

Cairo Attractor

A diamond grid locally distorted by a cairo attractor


The moving attractor

Download the definition here

Cairo Tiling

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.

Bricks

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

(c) by Gramanzio & Kohler

More Geodesic Shells

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

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.

Beams on Surface

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

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

MapLines.zip

Strips & Rivets

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

StripsAndRivets.zip

Isocurve Wireframe

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

Isocurve.zip