Browsing by Author "Kim, Theodore"

Now showing 1 - 7 of 7
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    Deep Fluids: A Generative Network for Parameterized Fluid Simulations
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Kim, Byungsoo; Azevedo, Vinicius C.; Thuerey, Nils; Kim, Theodore; Gross, Markus; Solenthaler, Barbara; Alliez, Pierre and Pellacini, Fabio
    This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of the data, our generative model is able to accurately approximate the training data set, while providing plausible interpolated in-betweens. The proposed generative model is optimized for fluids by a novel loss function that guarantees divergence-free velocity fields at all times. In addition, we demonstrate that we can handle complex parameterizations in reduced spaces, and advance simulations in time by integrating in the latent space with a second network. Our method models a wide variety of fluid behaviors, thus enabling applications such as fast construction of simulations, interpolation of fluids with different parameters, time re-sampling, latent space simulations, and compression of fluid simulation data. Reconstructed velocity fields are generated up to 700x faster than re-simulating the data with the underlying CPU solver, while achieving compression rates of up to 1300x.
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    An Eigenanalysis of Angle-Based Deformation Energies
    (ACM Association for Computing Machinery, 2023) Wu, Haomiao; Kim, Theodore; Wang, Huamin; Ye, Yuting; Victor Zordan
    Angle-based energies appear in numerous physics-based simulation models, including thin-shell bending and isotropic elastic strands. We present a generic analysis of these energies that allows us to analytically filter the negative eigenvalues of the second derivative (Hessian), which is critical for stable, implicit time integration. While these energies are usually formulated in terms of angles and positions, we propose an abstract edge stencil that succinctly parameterizes the edge deformation, and allows us to derive generic, closed-form analytical expressions for the energy eigensystems. The resultant eigenvectors have straightforward geometric interpretations. We demonstrate that our method is readily applicable to a variety of 2D and 3D angle-based elastic energies, including both cloth and strands, and is up to 7× faster than numerical eigendecomposition.
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    Fast and Robust Stochastic Structural Optimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Cui, Qiaodong; Langlois, Timothy; Sen, Pradeep; Kim, Theodore; Panozzo, Daniele and Assarsson, Ulf
    Stochastic structural analysis can assess whether a fabricated object will break under real-world conditions. While this approach is powerful, it is also quite slow, which has previously limited its use to coarse resolutions (e.g., 26x34x28). We show that this approach can be made asymptotically faster, which in practice reduces computation time by two orders of magnitude, and allows the use of previously-infeasible resolutions. We achieve this by showing that the probability gradient can be computed in linear time instead of quadratic, and by using a robust new scheme that stabilizes the inertia gradients used by the optimization. Additionally, we propose a constrained restart method that deals with local minima, and a sheathing approach that further reduces the weight of the shape. Together, these components enable the discovery of previously-inaccessible designs.
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    A Finite Element Formulation of Baraff-Witkin Cloth
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Kim, Theodore; Bender, Jan and Popa, Tiberiu
    The Baraff-Witkin [BW98] model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff-Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As-Rigid-As-Possible (ARAP) energy, and its shearing term is a crossfiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi-positive-definite projection methods. Finally, our analysis suggests a generalized Baraff-Witkin energy with non-orthogonal warp and weft directions.
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    Lifted Curls: A Model for Tightly Coiled Hair Simulation
    (ACM Association for Computing Machinery, 2023) Shi, Alvin; Wu, Haomiao; Parr, Jarred; Darke, A.M.; Kim, Theodore; Wang, Huamin; Ye, Yuting; Victor Zordan
    We present an isotropic, hyperelastic model specifically designed for the efficient simulation of tightly coiled hairs whose curl radii approach 5 mm. Our model is robust to large bends and torsions, even when they appear at the scale of the strand discretization. The terms of our model are consistently quadratic with respect to their primary variables, do not require per-edge frames or any parallel transport operators, and can efficiently take large timesteps on the order of ~1/30 of a second. Additionally, we show that it is possible to obtain fast, closed-form eigensystems for all the terms in the energy. Our eigenanalysis is sufficiently generic that it generalizes to other models. Our entirely vertex-based formulation integrates naturally with existing finite element codes, and we demonstrate its efficiency and robustness in a variety of scenarios.
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    A Shape Modulus for Fractal Geometry Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Schor, Alexa L.; Kim, Theodore; Memari, Pooran; Solomon, Justin
    We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be ''painted'' onto meshes.
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    A Unified Analysis of Penalty-Based Collision Energies
    (ACM Association for Computing Machinery, 2023) Shi, Alvin; Kim, Theodore; Wang, Huamin; Ye, Yuting; Victor Zordan
    We analyze a wide class of penalty energies used for contact response through the lens of a reduced frame. Applying our analysis to both spring-based and barrier-based energies, we show that we can obtain closedform, analytic eigensystems that can be used to guarantee positive semidefiniteness in implicit solvers. Our approach is both faster than direct numerical methods, and more robust than approximate methods such as Gauss-Newton. Over the course of our analysis, we investigate physical interpretations for two separate notions of length. Finally, we showcase the stability of our analysis on challenging strand, cloth, and volume scenarios with large timesteps on the order of 1/40 s.