SIGGRAPH 2008 > For Attendees > New Tech Demos > Artifacts of Research

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Artifacts of Research: On Singularities

Theme: SIGGRAPH Core
South Lobby

This research rediscovers a classical mathematical model collection - originally made by hand in plaster in the 1800's - and transforms it using contemporary CAD, mathematical-modeling, and rapid-prototyping techniques.

The models shown at SIGGRAPH 2008 represent 23 types of singularities possible on a cubic surface. These models were originally made by Carl Rodenberg, under the direction of the founder of modern topology Felix Klein (1849-1925), and represent an attempt to catalog a portion of the mathematical universe. The display also includes new transparent models of the Clebsch Diagonal Cubic and its famous configuration.

Though I consider the work to be architectural research, the effort could result in an educational exhibition similar to Mathematica: A World of Numbers and Beyond, created with funding from IBM, by the architects Charles and Ray Eames in the 1960s.

Currently, I am producing a limited-edition series of these models in chrome-plated bronze. I hope to continue the work with larger-scale fabrications.

This work is the result of a uniquely hybrid modeling. And beyond their sublime beauty, the new models address a surprisingly large number of current digital technology issues involving computational geometry, discrete differential geometry, and algebraic geometry as well as their relation to nurbs, mesh, and reverse engineering. In particular, parametric and zero-sum implicit equations - as both mesh and nurbs - were combined to create these models. The methodology is described in more detail on the Universal Joint Design web site.

This work is computationally based contemporary architectural research, and I am conducting parallel research on both large-scale fabrication of so-called "free-form" structure and the emerging field of architectural geometry. Inevitably, the research informs the work of my design-build firm, Universal Joint, based in Austin, Texas.

Jonathan Chertok
Universal Joint Design