Month: June 2023

He Chen, Elie Diaz, Cem Yuksel

We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.

Shortest Path to Boundary for Self-Intersecting Meshes

Gilles Daviet

We devise a local–global solver dedicated to the simulation of Discrete Elastic Rods (DER) with Coulomb friction that can fully leverage the massively parallel compute capabilities of moderns GPUs. We verify that our simulator can reproduce analytical results on recently published cantilever, bend–twist, and stick–slip experiments, while drastically decreasing iteration times for high-resolution hair simulations. Being able to handle contacting assemblies of several thousand elastic rods in real-time, our fast solver paves the ways for new workflows such as interactive physics-based editing of digital grooms.

Interactive Hair Simulation on the GPU using ADMM

Hang Yin, Mohammad Sina Nabizadeh, Baichun Wu, Stephanie Wang, Albert Chern

The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.

Fluid Cohomology

Tianye Xie, Minchen Li, Yin Yang, Chenfanfu Jiang

We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmented contact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method.

A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling