arXiv subjects

Stefan Pillwein

Publications and source records attributed to Stefan Pillwein.

5 recordsLinked to original sources

arXiv2026

Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized, time-coupled deformation trajectories. Starting from inverse tracing -- collapsing the deployed structure with a lightweight rod model while recording node paths under a shared parameter -- we obtain feasible node paths and formulate a polyline approximation problem that selects {globally synchronized} time steps and minimizes a robust tail-aggregated deviation measure under monotonicity constraints. {We solve the resulting non-smooth optimization problem via global optimization to obtain compact, synchronized displacement sequences for all paths simultaneously}. We evaluate the method using geometry-centric metrics (deviation versus step count, scaling with trajectory count) and demonstrate its utility by driving finite element deployment simulations that avoid intermediate buckling and capture deployment-induced prestress.

cs.GR↗

arXiv2021

Generalized Deployable Elastic Geodesic Grids

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.

cs.GR↗

arXiv2021

Design and Fabrication of Multi-Patch Elastic Geodesic Grid Structures

Elastic geodesic grids (EGG) are lightweight structures that can be deployed to approximate designer-provided free-form surfaces. Initially, the grids are perfectly flat, during deployment, a curved shape emerges, as grid elements bend and twist. Their layout is based on networks of geodesic curves and is found geometrically. Encoded in the planar grids is the intrinsic shape of the design surface. Such structures may serve purposes like free-form sub-structures, panels, sun and rain protectors, pavilions, etc. However, so far the EGG have only been investigated using a generic set of design surfaces and small-scale desktop models. Some limitations become apparent when considering more sophisticated design surfaces, like from free-form architecture. Due to characteristics like high local curvature or non-geodesic boundaries, they may be captured only poorly by a single EGG. We show how decomposing such surfaces into smaller patches serves as an effective strategy to tackle these problems. We furthermore show that elastic geodesic grids are in fact well suited for this approach. Finally, we present a showcase model of some meters in size and discuss practical aspects concerning fabrication, size, and easy deployment.

cs.GR↗

arXiv2020

Design and Fabrication of Elastic Geodesic Grid Structures

Elastic geodesic grids (EGG) are lightweight structures that can be easily deployed to approximate designer provided free-form surfaces. In the initial configuration the grids are perfectly flat, during deployment, though, curvature is induced to the structure, as grid elements bend and twist. Their layout is found geometrically, it is based on networks of geodesic curves on free-form design-surfaces. Generating a layout with this approach encodes an elasto-kinematic mechanism to the grid that creates the curved shape during deployment. In the final state the grid can be fixed to supports and serve for all kinds of purposes like free-form sub-structures, paneling, sun and rain protectors, pavilions, etc. However, so far these structures have only been investigated using small-scale desktop models. We investigate the scalability of such structures, presenting a medium sized model. It was designed by an architecture student without expert knowledge on elastic structures or differential geometry, just using the elastic geodesic grids design-pipeline. We further present a fabrication-process for EGG-models. They can be built quickly and with a small budget.

cs.GR↗

arXiv2020

On Elastic Geodesic Grids and Their Planar to Spatial Deployment

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.

cs.GR↗