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Item Eigenvalue Blending for Projected Newton(The Eurographics Association and John Wiley & Sons Ltd., 2025) Cheng, Yuan-Yuan; Liu, Ligang; Fu, Xiao-Ming; Bousseau, Adrien; Day, AngelaWe propose a novel method to filter eigenvalues for projected Newton. Central to our method is blending the clamped and absolute eigenvalues to adaptively compute the modified Hessian matrix. To determine the blending coefficients, we rely on (1) a key observation and (2) an objective function descent constraint. The observation is that if the quadratic form defined by the Hessian matrix maps the descent direction to a negative real number, the decrease in the objective function is limited. The constraint is that our eigenvalue filtering leads to more reduction in objective function than the absolute eigenvalue filtering [CLL∗24] in the case of second-order Taylor approximation. Our eigenvalue blending is easy to implement and leads to fewer optimization iterations than the state-of-the-art eigenvalue filtering methods.Item A Semi-Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence(The Eurographics Association and John Wiley & Sons Ltd., 2025) He, Xiaowei; Liu, Shusen; Guo, Yuzhong; Shi, Jian; Qiao, Ying; Bousseau, Adrien; Day, AngelaIn simulating fluids using position-based dynamics, the accuracy and robustness depend on numerous numerical parameters, including the time step size, iteration count, and particle size, among others. This complexity can lead to unpredictable control of simulation behaviors. In this paper, we first reformulate the problem of enforcing fluid compressibility/incompressibility into an nonlinear optimization problem, and then introduce a semi-implicit successive substitution method (SISSM) to solve the nonlinear optimization problem by adjusting particle positions in parallel. In contrast to calculating an intermediate variable, such as pressure, to enforce fluid incompressibility within the position-based dynamics (PBD) framework, the proposed semiimplicit approach eliminates the necessity of such calculations. Instead, it directly employs successive substitution of particle positions to correct density errors. This method exhibits reduced dependency to numerical parameters, such as particle size and time step variations, and improves consistency and stability in simulating fluids that range from highly compressible to nearly incompressible. We validates the effectiveness of applying a variety of different techniques in accelerating the convergence rate.Item BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics(The Eurographics Association and John Wiley & Sons Ltd., 2025) Wu, Yuhan; Umetani, Nobuyuki; Bousseau, Adrien; Day, AngelaWe propose BlendSim, a novel framework for editable simulation using spacetime optimization on the lightweight animation representation. Traditional spacetime control methods suffer from a high computational complexity, which limits their use in interactive animation. The proposed approach effectively reduces the dimensionality of the problem by representing the motion trajectories of each vertex using continuous parametric Bézier splines with variable keyframe times. Because this mesh animation representation is continuous and fully differentiable, it can be optimized such that it follows the laws of physics under various constraints. The proposed method also integrates constraints, such as collisions and cyclic motion, making it suitable for real-world applications where seamless looping and physical interactions are required. Leveraging projective dynamics, we further enhance the computational efficiency by decoupling the optimization into local parallelizable and global quadratic steps, enabling a fast and stable simulation. In addition, BlendSim is compatible with modern animation workflows and file formats, such as the glTF, making it practical way for authoring and transferring mesh animation.Item Rest Shape Optimization for Sag-Free Discrete Elastic Rods(The Eurographics Association and John Wiley & Sons Ltd., 2025) Takahashi, Tetsuya; Batty, Christopher; Bousseau, Adrien; Day, AngelaWe propose a new rest shape optimization framework to achieve sag-free simulations of discrete elastic rods. To optimize rest shape parameters, we formulate a minimization problem based on the kinetic energy with a regularizer while imposing box constraints on these parameters to ensure the system's stability. Our method solves the resulting constrained minimization problem via the Gauss-Newton algorithm augmented with penalty methods. We demonstrate that the optimized rest shape parameters enable discrete elastic rods to achieve static equilibrium for a wide range of strand geometries and material parameters.Item A Unified Multi-scale Method for Simulating Immersed Bubbles(The Eurographics Association and John Wiley & Sons Ltd., 2025) Wretborn, Joel; Stomakhin, Alexey; Batty, Christopher; Bousseau, Adrien; Day, AngelaWe introduce a novel unified mixture-based method for simulating underwater bubbles across a range of bubble scales. Our approach represents bubbles as a set of Lagrangian particles that are coupled with the surrounding Eulerian water volume. When bubble particles are sparsely distributed, each particle, typically smaller than the liquid grid voxel size, corresponds to an individual spherical bubble. As the sub-grid particles increase in local density our model smoothly aggregates them, ultimately forming connected, fully aerated volumetric regions that are properly resolved by the Eulerian grid. We complement our scheme with a continuous surface tension model, defined via the gradient of the bubbles' local volume fractions, which works seamlessly across this scale transition. Our unified representation allows us to capture a wide range of effects across different scales-from tiny dispersed sub-grid air pockets to fully Eulerian two-phase interfacial flows.