triply periodic minimal surfaces 001

this tests are part of my thesis project 
"Processi di progettazione biodigitali in Architettura: nuova biblioteca universitaria della facoltà di Architettura di Firenze
supervisors: prof. Ulisse Tramonti , prof. Alessio Erioli

Minimal surfaces are defined as surfaces with zero mean curvature. Finding a minimal surface of a boundary with specified constraints is a problem in the calculus of variations and sometimes known as Plateau's problem. Minimal surfaces may also be characterized as surfaces of minimal surface area for given boundary conditions.

Some particular minimal surfaces form three dimensional repetitive structure based on very simple fundamental regions, they are called triply periodic minimal surfaces.

Above is the construction process of Schoen's Manta surface from his fundamental region to the cubical unit cell.

I found many definitions in gh that use repetition of a single nurbs surface (fundamental region) to achieve the complete structure of triply periodic minimal surfaces, but this kind of construction have some problems of continuity on the edge of the surfaces especially when the model is associated to parametric variations, moreover this models create very big files.

So I've written a new definition that use quad mesh component to built the model and later  weld  and smooth the geometry using Meshedit by [uto] and waverbird by Giulio Piacentino.

This method give a smooth and quite correct approximation of the minimal suface that perserve correct continuity even in case of parametric variations and let bigger model thanks to the use of meshes.

The whole definition is still in devlopement but you can download a wip grasshopper file here: link

I will post some application studies soon. 

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