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Design By Differential Geometry

Design By Differential Geometry

Yesterday I  saw something beautiful.

It is the battle between architecture and structural engineering; fought in real time; on a computer no more powerful than my throw-away laptop.

A flat, abstract, shape, lane in plane; a mesh atop- waiting. A point is picked, dragged into the third dimension; constrained in space, time, and probability. The elements rise to catch this separatist. The new surface rests, self-supporting- a volume of air. Another node is chosen, this time from the edge- thrown; racing towards the centre. Immediately this structural cloth begins to retract; forming a cave- desperate to maintain its structural integrity as the freedoms are limited.

Differential geometry structure pulled up.

Push me; Pull me; Drag me into being.

Just as stability is obtained, the apex is anointed by our unseen deity, who begins to pull the face of the hollow forward; urging it to cantilever precariously- forming a dangerous over-hang. But our three dimensional surface structure begins to fight-back, transforming with every frame; sinking the once cavernous opening into a cantledge. It is adapting, countering, maintaining its self-supporting nature; wrestling against a maker who is now clearly intent on its destruction. Already the prescribed lean is declining. The onslaught is over- the contours settle into a more canny form.

Differential geometry optimises and rationalises.

I know my limits; I can protect myself.

Suddenly, what was once a drab grid of mesh elements is alive with a rainbow of compressions and tensions; pockets of intense stresses and swathes of underutilised material mock austerity. Free of manipulation, the structure begins to optimise; in slow-motion the lofted surface shimmers with millions of subtle changes. In a second the chaotic division of forces has been rationalised; the aesthetic unharmed.

Differential geometry levels the stresses.

Immediate rationalisation

It is the battle between architecture and structural engineering; fought in real time; on a computer no more powerful than my throw-away laptop. As art begins to sink its sky hooks into this vulnerable child of conceptual design, physics takes a stand; grounding the structure in reality. In this realm we can wonder not only the conceivable, but the probable.

A marriage of form and function.

For those of you who are wondering why I seem to be off-loading free-form Year 11 poetry (without the angst); it is because I attended a talk from Dr Helmut Pottmann on Computational Differential Geometry and Fabrication Aware Design as part of a distinguished speaker series at UCL. It ended with a demo of software created through this research; approaching the structural concerns of design through geometrical constraints, rather than stress limits.

What I’ve described happened, in real-time, but so far YouTube has failed me in providing anything to your good selves. In a later post I’ll try and sum up those bits of the lecture I managed to follow (without a background in, or even a prepared definition of, differential geometry). I have, however, found the original paper– if you find yourselves in need of some more academic reading…

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  1. […] few weeks ago I was rhapsodising about a lecture I had been to on differential geometry, which ended in a remarkable video where a […]