Generalized Deployable Elastic Geodesic Grids

TL;DR

This paper introduces a geometric method for designing deployable elastic gridshells that are planar, easy to fabricate, and capable of approximating complex 3D surfaces without physical simulations.

Contribution

It presents a novel differential geometry-based algorithm for creating elastic grids that are planar and can approximate arbitrary free-form surfaces, including non-convex boundaries.

Findings

The method accurately approximates complex 3D surfaces.

The resulting gridshells are inexpensive and easy to deploy.

The approach is fast, enabling quick prototyping.

Abstract

Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid bends and approximates the given 3d surface. Our method is based purely on the notions from differential geometry of curves and surfaces and avoids any physical simulations. In particular, we introduce a well-defined elastic grid energy functional that allows identifying networks of curves that minimize the bending energy and at the same time nestle to the provided input surface well. Further, we generalize the concept of such grids to cases where the surface boundary does not need to be convex, which allows for the creation of sophisticated and visually pleasing shapes. The algorithm finally ensures that the 2d grid is perfectly planar, making the resulting gridshells inexpensive, easy to fabricate, transport, assemble, and finally also to deploy. Additionally, since the whole structure is pre-strained, it also comes with load-bearing capabilities. We evaluate our method using physical simulation and we also provide a full fabrication pipeline for desktop-size models and present multiple examples of surfaces with elliptic and hyperbolic curvature regions. Our method is meant as a tool for quick prototyping for designers, architects, and engineers since it is very fast and results can be obtained in a matter of seconds.