Welcome

ACM Transactions on Graphics (SIGGRAPH) - Honorable Mention

We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle–grid liquid solvers: temporal undersampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of perstep time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plugin by collapsing to slab-integrated 3D grid fields for projection. Building on recent particle-based phase-field work, we reuse the particle-to-grid weight accumulators as a conceptual space–time phase field, providing variable-coefficient projection weights and eliminating the need for per-step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.

Eurographics Tutorial

Physics simulation is a cornerstone of many computer graphics applications, ranging from video games and virtual reality to visual effects and computational design. The number of techniques for physically-based modeling and animation has thus skyrocketed over the past few decades, facilitating the simulation of a wide variety of materials and physical phenomena. These course notes provide an in-depth introduction to multiphysics simulation methods for computer graphics, covering the mathematical foundations, key algorithms, and practical considerations behind the most widely used approaches. We focus on methods developed by the computer graphics community for simulating various physical phenomena and materials -- including rigid and deformable bodies, fluids, and granular materials -- as well as the interactions between them. For each method, we present the underlying mathematical framework with detailed derivations and discuss how different materials and coupling strategies fit into the formulation. A selection of software frameworks that offer out-of-the-box multiphysics modeling capabilities is also presented. Finally, we touch on emerging trends in physics-based animation, including machine learning-based methods which have become increasingly popular in recent years.

Computer Graphics Forum (Eurographics)

Newton's Method is widely used to find the solution of complex non-linear simulation problems. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to assembly — a strategy known as Projected Newton (PN) — but this perturbation often hinders convergence. In this work, we observe that projecting only a small subset of element Hessians is sufficient to secure a descent direction. Building on this insight, we introduce Progressively Projected Newton (PPN), a novel variant of Newton's Method that uses the current iterate's residual to cheaply determine the subset of element Hessians to project. The benefit is twofold: most eigendecompositions are avoided and the global Hessian remains closer to its original form, reducing the number of Newton iterations. We compare PPN with PN and Project-on-Demand Newton (PDN) in a comprehensive set of experiments covering contact-free and contact-rich deformables, co-dimensional and rigid-body simulations, and a range of time step sizes, tolerances and resolutions. PPN reduces the amount of element projections in dynamic simulations by one order of magnitude while simultaneously improving convergence, consistently being the fastest solver in our benchmark.