Minimal Surface [XYZ]

[XYZ] Minimal Surface MAS DFAB ETH Zurich

Task

• Direct modeling and manipulation of minimal surface. Determine the exact construction of your surface from its fundamental region and study its geometric construction.
• Generate the surface through algorithm (parametric definition). Regenerate the surface parametrically(Grasshopper of Processing), apply mesh relaxation, apply thickness and aggregate surface to create a larger assembly.

Minimal Surface Manipulation

Minimal surfaces are the minimum amount of surface area that spans between a “closed” set of edges curves located within a 3-dimensional Cartesian grid. Constructing minimal surfaces can be thought of as a negotiation between a regulating “bounding box” and the “topological surfaces” that span between them. They appear “all over nature in phase transition models as the inter phrase between two states, as the shapes of soap bubbles in fluid mechanic, and have been of great importance in the study of Riemannian geometry” (Guilen.N, Ache.A). Minimal surfaces have long served as a reference within the architectural discourse. The work of Antoni Gaudi, Feri Otto, Erwin Hauer reflect the potential of these surfaces in architecture.

Triply periodic minimal surfaces are constructed within a cubic bounding box. They can be constructed by symmetric manipulation of fundamental region. The fundamental region is a part of minimal surface, as small of redundant as possible, which determines the whole surface based on its symmetry. A minimal surface can be created by accurate mirroring of the fundamental region along specific edges, which creates a seamless tiling system among surfaces.

Grasshopper Definition :