Levitating Rigid Objects with Hidden Rods and Wires Eurographics 2021

Sarah Kushner, Risa Ulinski, Karan Singh, David I.W. Levin, Alec Jacobson

University of Toronto

Our optimization finds hidden supports to hold rigid objects (green) in their locations despite gravity. Rods (orange) resist tension, compression and bending, while wires (black) resist tension. Supports connect between objects or to the input support surface (blue). Rods are hidden behind occlusions in the scene for a possibly disconnected distribution of viewpoints (red) provided by the user. Here, a collection of space-themed objects seemingly hover in the corner of a room. The supporting truss is hidden from the front and through the window.
Our optimization finds hidden supports to hold rigid objects (green) in their locations despite gravity. Rods (orange) resist tension, compression and bending, while wires (black) resist tension. Supports connect between objects or to the input support surface (blue). Rods are hidden behind occlusions in the scene for a possibly disconnected distribution of viewpoints (red) provided by the user. Here, a collection of space-themed objects seemingly hover in the corner of a room. The supporting truss is hidden from the front and through the window.

Abstract

We propose a novel algorithm to efficiently generate hidden structures to support arrangements of floating rigid objects. Our optimization finds a small set of rods and wires between objects and each other or a supporting surface (e.g., wall or ceiling) that hold all objects in force and torque equilibrium. Our objective function includes a sparsity inducing total volume term and a linear visibility term based on efficiently pre-computed Monte-Carlo integration, to encourage solutions that areas-hidden-as-possible. The resulting optimization is convex and the global optimum can be efficiently recovered via a linear program. Our representation allows for a user-controllable mixture of tension-, compression-, and shear-resistant rods or tension-only wires. We explore applications to theatre set design, museum exhibit curation, and other artistic endeavours.

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BibTeX

@article{Kushner:Levitating:2021,
  title = {Levitating Rigid Objects with Hidden Rods and Wires},
  author = {Sarah Kushner and Risa Ulinski and Karan Singh and David I.W. Levin and Alec Jacobson},
  year = {2021},
  journal = {Computer Graphics Forum}, 
}

Acknowledgements

This research is funded by New Frontiers of Research Fund (NFRFE–201), NSERC Discovery (RGPIN2017–05235, RGPAS–2017–507938), the Ontario Early Research Award program, the Canada Research Chairs Program, the Fields Centre for Quantitative Analysis and Modelling and gifts by Adobe Systems, Autodesk and MESH Inc. We would like to thank Michael Tao, Silvia Sellán and Rinat Abdrashitov for proofreading; John Hancock for IT and fabrication hardware support; the anonymous reviewers for their helpful comments.