arXiv subjects

Ty Trusty

Publications and source records attributed to Ty Trusty.

6 recordsLinked to original sources

arXiv2026

FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes

We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

cs.GR↗

arXiv2025

Coordinate Condensation: Subspace-Accelerated Coordinate Descent for Physics-Based Simulation

We introduce Coordinate Condensation, a variant of coordinate descent that accelerates physics-based simulation by augmenting local coordinate updates with a Schur-complement-based subspace correction. Recent work by Lan et al. 2025 (JGS2) uses perturbation subspaces to augment local solves to account for global coupling, but their approach introduces damping that can degrade convergence. We reuse this subspace but solve for local and subspace displacements independently, eliminating this damping. For problems where the subspace adequately captures global coupling, our method achieves near-Newton convergence while retaining the efficiency and parallelism of coordinate descent. Through experiments across varying material stiffnesses and mesh resolutions, we show substantially faster convergence than both standard coordinate descent and JGS2. We also characterize when subspace-based coordinate methods succeed or fail, offering insights for future solver design.

cs.GR↗

arXiv2025

Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation

We present a multi-level elastodynamics timestep solver for accelerating incremental potential contact (IPC) simulations. Our method retains the robustness of gold standard IPC in the face of intricate geometry, complex heterogeneous material distributions and high resolution input data without sacrificing visual fidelity (per-timestep relative displacement error of $\approx1\%$). The success of our method is enabled by a novel, sparse, geometry- and material-aware basis construction method which allows for the use of fast preconditioned conjugate gradient solvers (in place of a sparse direct solver), but without suffering convergence issues due to stiff or heterogeneous materials. The end result is a solver that produces results visually indistinguishable and quantitatively very close to gold-standard IPC methods but up to $13\times$ faster on identical hardware.

cs.GR↗

arXiv2025

FastAtlas: Real-Time Compact Atlases for Texture Space Shading

Texture-space shading (TSS) methods decouple shading and rasterization, allowing shading to be performed at a different framerate and spatial resolution than rasterization. TSS has many potential applications, including streaming shading across networks, and reducing rendering cost via shading reuse across consecutive frames and/or shading at reduced resolutions relative to display resolution. Real-time TSS shading requires texture atlases small enough to be easily stored in GPU memory. Using static atlases leads to significant space wastage, motivating real-time per-frame atlassing strategies that pack only the content visible in each frame. We propose FastAtlas, a novel atlasing method that runs entirely on the GPU and is fast enough to be performed at interactive rates per-frame. Our method combines new per-frame chart computation and parametrization strategies and an efficient general chart packing algorithm. Our chartification strategy removes visible seams in output renders, and our parameterization ensures a constant texel-to-pixel ratio, avoiding undesirable undersampling artifacts. Our packing method is more general, and produces more tightly packed atlases, than previous work. Jointly, these innovations enable us to produce shading outputs of significantly higher visual quality than those produced using alternative atlasing strategies. We validate FastAtlas by shading and rendering challenging scenes using different atlasing settings, reflecting the needs of different TSS applications (temporal reuse, streaming, reduced or elevated shading rates). We extensively compare FastAtlas to prior alternatives and demonstrate that it achieves better shading quality and reduces texture stretch compared to prior approaches using the same settings.

cs.GR↗

arXiv2024

Subspace Mixed-FEM for Real-Time Heterogeneous Elastodynamics

We propose a reduced space mixed finite element method (MFEM) built on a Skinning Eigenmode subspace and material-aware cubature scheme. Our solver is well-suited for simulating scenes with large material and geometric heterogeneities in real-time. This mammoth geometry is composed of 98,175 vertices and 531,565 tetrahedral elements and with a heterogenous composition of widely varying materials of muscles ($E= 5\times10^5$ Pa), joints ($E=1\times10^5$ Pa), and bone ($E=1\times10^{10}$ Pa). The resulting simulation runs at 120 frames per second (FPS).

cs.GR↗

arXiv2022

Mixed Variational Finite Elements for Implicit, General-Purpose Simulation of Deformables

We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating projections solver with a superset of the desirable properties of many previous fast solution strategies. This framework fits a range of elastic constitutive models and remains stable across a wide span of timestep sizes, material parameters (including problems that are quasi-static and approximately rigid). It is efficient to evaluate and easily applicable to volume, surface, and rods models. We demonstrate the efficacy of our approach on a number of simulated examples across all three codomains.

cs.GR↗