Design and fabrication of multi-patch elastic geodesic grid structures

Pillwein, Stefan; Kübert, Johanna; Rist, Florian; Weiss, Tomer

doi:10.1016/j.cag.2021.06.002

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Additionally, a connection between the dual spaces needs to be established for geodesics that start at one boundary and end at the other. However, we can realize such surfaces using our present approach by splitting them into two or more non-convex surfaces [Pillwein et al 2021].…”

Section: Discussion and Conclusion 91 Discussion And Limitationsmentioning

confidence: 99%

“…of the scissor linkage, and additional translational DoF, introduced by the notches. Kinematically, the grids are related to other elastic scissor-like grid structures which use notches [Pillwein et al 2020a[Pillwein et al , 2021[Pillwein et al , 2020b, in contrast to structures with a rotational DoF only Soriano et al 2019].…”

Section: Discussion and Conclusion 91 Discussion And Limitationsmentioning

confidence: 99%

“…In contrast, the method of Pillwein et al [2020b] generates perfectly planar 2d layouts, on the downside, their method is limited to scissor-like convex quadrilateral patches only and does not allow free-form boundaries. While more complex shapes are possible by stitching multiple quadrilateral patches together [Pillwein et al 2020a[Pillwein et al , 2021, an arbitrary boundary is still not possible.…”

Section: Introductionmentioning

confidence: 99%

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Generalized deployable elastic geodesic grids

Pillwein

Weiss²

2021

ACM Trans. Graph.

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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.

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Section: Discussion and Conclusion 91 Discussion And Limitationsmentioning

confidence: 99%

Section: Discussion and Conclusion 91 Discussion And Limitationsmentioning

confidence: 99%