Subdivided Column

A Procedural Approach to Ornament

The Subdivided Column project explores how a purely operations-based geometric process can generate complex form. It involves the design of an ornamented column using subdivision processes. The allure of these processes is that despite using a very simple input, they can produce something that is extraordinarily complex. One column variant is fabricated as a layered model using 1mm cardboard slices.

Design Concept

In this project, an abstracted doric column is used as an input to a subdivision processes. This input form conveys basic topographical and topological information about the form to be generated. It contains data about the proportions of the the column's shaft, capital, base, as well information about its fluting and entasis.

The process functions by taking each face (or facet) of this doric column and dividing it into four faces. The new faces in turn are further divided again and again, until after many steps one arrives at the final form: an intricate column made of 16 million faces. Each subdivision step adds further levels of detail (or "information") to the form. The first steps of the process influence the overall shape and its curvature, the next steps determine the surface development, while the final steps generate a minuscule texture on top of the broader surfaces.

The resulting columns have a distinct language of form unlike anything created by traditional processes. They exhibit both highly specific local conditions as well as an overall coherency and continuity. Their ornament is in continuous flow, yet it consist of very distinct local formations. The complexity of the columns contrasts with the simplicity of the their generative process and the their initial input.

Column exhibited in ETH Zurich HIL lobby (D-level)

Fabrication

A full-scale prototype of a column was built as a layered model using 1mm cardboard sheets. A program was written to divide the sixteen million faces of the subdivided column into a sequence of of 2700 slices. This program produces files that can be printed directly on the RapLab's laser-cutters. The slices are hollowed out to reduce their weight, and they have common perforations to allow for an easy alignment. The fabricated prototype has a height of 2.7 meters and a mean circumference of 50cm. Despite the 50cm circumference, the laser's cutting path for each slice exceeds 8 meters due to the surface detail. Despite the hollowed out sheets, the column weighs approximately 650kg. The final paint was applied in several coats by Modellbau Zaborowsky.

Stack of cardboard sheet, the negative that the column was cut from

Interior views of the column negative

Background: Subdivision Processes

Subdivision processes have traditionally been used to create smooth rounded forms. For this project, these processes were modified to enable the generation of a much more heterogenous output. Specifically, a series of weights was introduced to allow for specification of new vertex positions as interpolations of previous-generation vertices. In addition, weights were added to control extrusion and rotation of new vertices relative to their parents. The output from each iteration of the process can determine the weight values that are used in the next steps.

Column prototype studies (second image with 9x magnification)

Elective Courses

The subdivision concepts involved in this project were explored in the CAAD elective theory courses Numerical Sculpture 1 (Spring 2010) and Numerical Sculpture 2 (Autumn 2011), taught by Michael Hansmeyer. Both the subdivision program to generate the form and the program to slice the form and produce print files were written in Processing, a programming language that the CAAD department teaches in the bachelor level courses. Please check back for a link to student projects from these courses.

People Involved

Conception, design, and programming: Michael Hansmeyer
Fabrication assistance and expertise: Manuela Koller, Thomas Raoseta, Benjamin Dillenburger, Edyta Augustynowicz
Special thanks to Yves Ebnöther, Reto Klingenfuss, and Alessandro Tellini of the Raplab
Paint applied by Modellbau Zaborowsk team.

Initial column prototype constructed and designed by Florian Hartmann and Jan Wasser.
Course: Numerical Sculpture 1 (Michael Hansmeyer)