On Elastic Geodesic Grids and Their Planar to Spatial Deployment

TL;DR

This paper introduces elastic geodesic grids as a new planar-to-spatial deployable structure that approximates freeform surfaces, combining geometric design with physical simulation, and validated through fabrication and laser scanning comparisons.

Contribution

It presents a geometric approach for designing elastic geodesic grids that avoids numerical optimization, enabling easy fabrication and deployment of complex freeform surface approximations.

Findings

Successfully fabricated small-scale elastic geodesic grid models.

Empirical validation through laser scans confirms the accuracy of the geometric approach.

Demonstrated versatility of the method with varying complexity structures.

Abstract

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.