image

Focus

Studying the principle of minimal surface and mesh relaxation skills, subsequently applied to a design project.

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.

image

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).

image image

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.

image

Triple 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 irredundant 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.

Project Lead: Digital Building Technologies, ETH-Zurich

Tutors: Benjamin Dillenburger, Mania Aghaei Meibodi, Andrei Jipa

MAS Students 2016/17: Shaun Dai-Syuan Wu, Ahmed Elshafei