Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915952373792768 |
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| author | Pillwein, Stefan Hentschel, Alexander Lukacevic, Markus Musialski, Przemyslaw |
| author_facet | Pillwein, Stefan Hentschel, Alexander Lukacevic, Markus Musialski, Przemyslaw |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17181 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids Pillwein, Stefan Hentschel, Alexander Lukacevic, Markus Musialski, Przemyslaw Graphics Computational Geometry I.3.5; J.6 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. |
| title | Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids |
| topic | Graphics Computational Geometry I.3.5; J.6 |
| url | https://arxiv.org/abs/2312.17181 |