Creating smooth surface models with ElasticSurfaceEmbedding.jl

In this talk, I introduce ElasticSurfaceEmbedding.jl, a package for creating holdable surfaces by weaving paper strips. I'll discuss the process of embedding pieces of a target surface into a plane and minimizing their elastic strain energy. The presentation aims to engage a diverse audience such as mathematicians, physicists, and handicraftsmen, and explore interdisciplinary implications. Physical examples will be showcased onsite.

In general, creating a surface from a planar material requires splitting the surface into small pieces to avoid large strain in the medium. The most non-trivial part of this project is how to find the planar shapes which become deformed into each piece of the surface. We characterized this shape by minimizing the strain energy in the medium. The minimization problem is formulated by weak-form PDE, and it can be solved numerically with ElasticSurfaceEmbedding.jl. This package uses B-spline-based Galerkin method and Newton-Raphson method internally. See my recent paper for more information.

I will bring some curved woven surfaces I made onsite. The top image is a catenoid and a helicoid which can be deformed into each other (watch video on YouTube).

The presentation slides are available at the following URL: https://www.docswell.com/s/hyrodium/5JL8EQ-JuliaCon2023.