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Design technology for Minimal Surfaces

Collaborators: Research Assistant Alireza Bayramvand (DART, UMICH), Researcher Mehrad Mahnia (FabTory)

A minimal surface is a surface that locally minimizes its total surface area for a given constraint boundary. These surfaces are suitable for application in lightweight structures in architecture as the weight and amount of material are reduced to a minimum. Also, the aggregation of triply periodic minimal surfaces is cellular structures. They create continuous non-self-intersecting surfaces similar to bone microstructure with controllable mechanical properties and can be used as an infill in a sandwich composite building elements. Large-scale 3D printing enables employment of these surfaces across scales (from building's overall form, parts, and infill in a sandwich composite component). There has been very little and almost no design tool to allow intuitive exploration of these forms. 

This research develops computational design software that would allow anyone to generate, explore and visualize minimal  surfaces intuitively instead of using mathematical expressions. We developed algorithms that will enable the generation, visualization, and exploration of minimal surfaces and their associated medial graph in three-dimensional Euclidean space for two set of curves. For any given two sets of curves there is a  minimal surface that mediates between the two sets.

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