Browsing by Author "Levin, David I. W."

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    EigenFit for Consistent Elastodynamic Simulation Across Mesh Resolution
    (ACM, 2019) Chen, Yu Ju (Edwin); Levin, David I. W.; Kaufmann, Danny; Ascher, Uri; Pai, Dinesh K.; Batty, Christopher and Huang, Jin
    Elastodynamic system simulation is a key procedure in computer graphics and robotics applications. To enable these simulations, the governing differential system is discretized in space (employing FEM) and then in time. For many simulation-based applications keeping the spatial resolution of the computational mesh effectively coarse is crucial for securing acceptable computational efficiency. However, this can introduce numerical stiffening effects that impede visual accuracy. We propose and demonstrate, for both linear and nonlinear force models, a new method called EigenFit that improves the consistency and accuracy of the lower energy, primary deformation modes, as the spatial mesh resolution is coarsened. EigenFit applies a partial spectral decomposition, solving a generalized eigenvalue problem in the leading mode subspace and then replacing the first several eigenvalues of the coarse mesh by those of the fine one at rest. EigenFit's performance relies on a novel subspace model reduction technique which restricts the spectral decomposition to finding just a few of the leading eigenmodes. We demonstrate its efficacy on a number of objects with both homogenous and heterogenous material distributions.
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    Latent-space Dynamics for Reduced Deformable Simulation
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Fulton, Lawson; Modi, Vismay; Duvenaud, David; Levin, David I. W.; Jacobson, Alec; Alliez, Pierre and Pellacini, Fabio
    We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks. We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping function, we solve the true equations of motion in the latent-space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore, our method works well with existing force-approximation cubature methods.
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    Levitating Rigid Objects with Hidden Rods and Wires
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Kushner, Sarah; Ulinski, Risa; Singh, Karan; Levin, David I. W.; Jacobson, Alec; Mitra, Niloy and Viola, Ivan
    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 are as-hiddenas- 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.