During my 4 month internship at Prat sa. in Toulouse, France, the issue of form-finding came up many times. Tensile architecture has to deal with several very complex algorithms in order to create the best possible shape for a membrane itself and the parts that are required to build it.
First of all the membrane has to be relaxed (minimize surface energy) while respecting several constraints such as fixed points and tension factors. This process is called "Form-finding". In order to tackle this issue we decided to write an implementation of the Force Density Method, which is based on Finite Element Analysis. You can read an in-depth description of this algorithm and its imperfections on the next page.
Then, once the surface has been relaxed, it has to be divided into strips that can be cut from fabric rolls. Finding the ideal borders between strips is very difficult since the surface they are reverse-engineered from already has tension-deformation applied to it. Basically it turns out that the geodesic curve is very close to the ideal cut. A geodesic curve is the shortest curve on a surface that connects two points on the surface.
Once the strips are created on the anti-clastic curved surface, they have to be "unrolled" or "unstretched" so they can be fabricated.
Since a medium size tensile project will quickly result into several dozens of strips, the manual labour is a very big factor in the design process. During my internship we've attempted to automate as many steps as possible.
All theories, experiments and code that originated during this period is not copyrighted by me. I cannot make the source available without express permission of Prat SA (which I don't have). However the underlying pseudocode algorithms are public domain and they can be found on this site along with some implementations.
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