D-Form Geometry

Using two developable surfaces with the same perimeter length joined on their edges self computes 3D forms without spuriouscreases.

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Comment by Tony Wills on November 6, 2017 at 11:39

I discovered what I have called 'D-Form Geometry'. I took my idea to mathematicians who were very surprised that such a simple concept had not been discovered or worked on before. D-Form geometry enables an infinite set of 3D forms to be created just by joining two developable isotropic surfaces with the same length of perimeter. Where the shapes start being joined and the shapes used define the final D-Form. This concept can be extrended to joining holes in sheet material or surfaces and holes.

Credit is due to the following professors for their wisdom, help and encouragement : Erik Demaine (MIT), Helmut Pottman (TuWein), Alan Ball (Birmingham) and David Singmaster (South Bank).

For practical, manufacturing purposes, D-Forms have been used as moulds for concrete street furniture, carbon fibre propellor blades and sculptural exhibition signage. From an aesthetic point of view, had they been known they might have inspired the work of Brancusi, Calder, Hepworth and Gabo.

I want designers and manufacturers to use D-Form geometry so is in the 'creative commons' with only one caveat; that the source should be given thus: From an original discovery by Tony Wills, product designer at Wills Watson+Associates.

Defining a D-Form from two developable surfaces into the 3D form that it will make is essentially impossible in currend CAD programmes. Professor Helmut Pottman and his team in Vienna are best placed to create the algorithms and I hope that geometry kernel developers will take notice.

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