SCA 2023: Eurographics/SIGGRAPH Symposium on Computer Animation

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https://diglib.eg.org/handle/10.2312/3543889

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Browsing SCA 2023: Eurographics/SIGGRAPH Symposium on Computer Animation by Subject "Based Simulation"

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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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    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.