arXiv subjects

Danny M. Kaufman

Publications and source records attributed to Danny M. Kaufman.

17 recordsLinked to original sources

arXiv2026

Variational r-Adaptive Cloth Simulation

We present the first r-adaptive method for simulating cloth dynamics and statics with frictional contact in modern cloth pipelines. Thin cloth requires high effective spatial resolution to reproduce wrinkles, folds, buckling, and sharp contact features. However, applying existing variational r-adaptivity to piecewise-linear shells reveals two coupled failure modes. Discretized incremental-potential (IP) optimization can become trapped in poor local minima, yielding suboptimal physical configurations. It can also lower IP artificially by collapsing elements, invalidating the finite-element approximation on which the objective relies. We address both problems with degeneracy-activated quality regularization. The regularizer remains inactive for well-shaped elements, preserving anisotropic adaptation and local densification, but becomes strong near degeneracy. It suppresses spurious low-energy basins, improves escape from suboptimal physical minima, and prevents element bunching, a cloth-specific failure in which elements progressively collapse as cloth slides across sharp contact features. For practical performance, we introduce a dynamic nonlinear solver that exploits within-timestep coherence through accelerated derivative evaluation and dynamic IPC tolerance updates for r-adaptive iterative trust-region (ITR) solves. This yields a 3-6x speedup over prior optimal ITR. Experiments on challenging frictional-contact scenarios show that, under equal vertex-count and time-budget constraints, our method achieves higher visual fidelity than fixed meshes.

cs.GR↗

arXiv2026

Differentiable Variable Fonts

Editing and animating text appearance for graphic designs, commercials, etc. remain highly skilled tasks requiring detailed, hands on efforts from artists. Automating these manual workflows requires balancing the competing goals of maintaining legibility and aesthetics of text, while enabling creative expression. Variable fonts, recent parametric extensions to traditional fonts, offer the promise of new ways to ease and automate typographic design and animation. Variable fonts provide custom constructed parameters along which fonts can be smoothly varied. These parameterizations could then potentially serve as high value continuous design spaces, opening the door to automated design optimization tools. However, currently variable fonts are underutilized in creative applications, because artists so far still need to manually tune font parameters. Our work opens the door to intuitive and automated font design and animation workflows with differentiable variable fonts. To do so we distill the current variable font specification to a compact mathematical formulation that differentiably connects the highly non linear, non invertible mapping of variable font parameters to the underlying vector graphics representing the text. This enables us to construct a differentiable framework, with respect to variable font parameters, allowing us to perform gradient based optimization of energies defined on vector graphics control points, and on target rasterized images. We demonstrate the utility of this framework with four applications: direct shape manipulation, overlap aware modeling, physics based text animation, and automated font design optimization. Our work now enables leveraging the carefully designed affordances of variable fonts with differentiability to use modern design optimization technologies, opening new possibilities for easy and intuitive typographic design workflows.

cs.GR↗

arXiv2025

Unlocking Thickness Modeling for Codimensional Contact Simulation

In this work we analyze and address a fundamental restriction that blocks the reliable application of codimensional yarn-level and shell models with thickness, to simulate real-world woven and knit fabrics. As discretizations refine toward practical and accurate physical modeling, such models can generate non-physical contact forces with stencil-neighboring elements in the simulation mesh, leading to severe locking artifacts. While not well-documented in the literature, this restriction has so far been addressed with two alternatives with undesirable tradeoffs. One option is to restrict the mesh to coarse resolutions, however, this eliminates the possibility of accurate (and consistent) resolution simulations across real-world material variations. A second alternative instead seeks to cull contact pairs that can create such locking forces in the first place. This relaxes resolution restrictions but compromise robustness. Culling can and will generate unacceptable and unpredictable geometric intersections and tunneling that destroys weaving and knitting structures and cause unrecoverable pull-throughs. We address these challenges to simulating real-world materials with a new and practical contact-processing model for thickened codimensional simulation, that removes resolution restrictions, while guaranteeing contact-locking-free, non-intersecting simulations. We demonstrate the application of our model across a wide range of previously unavailable simulation scenarios, with real-world material yarn and fabric parameters and patterns, challenging simulation conditions and mesh resolutions, and both rod and shell models, integrated with the IPC barrier.

cs.GR↗

arXiv2025

Progressing Level-of-Detail Animation of Volumetric Elastodynamics

We extend the progressive dynamics model (Zhang et al., 2024) from cloth and shell simulation to volumetric finite elements, enabling an efficient level-of-detail (LOD) animation-design pipeline with predictive coarse-resolution previews facilitating rapid iterative design for a final, to-be-generated, high-resolution animation of volumetric elastodynamics. This extension to volumetric domains poses significant new challenges, including the construction of suitable mesh hierarchies and the definition of effective prolongation operators for codimension-0 progressive dynamics. To address these challenges, we propose a practical method for defining multiresolution hierarchies and, more importantly, introduce a simple yet effective topology-aware algorithm for constructing prolongation operators between overlapping (but not necessarily conforming) volumetric meshes. Our key insight is a boundary binding strategy that enables the computation of barycentric coordinates, allowing several off-the-shelf interpolants -- such as standard barycentric coordinates, Biharmonic Coordinates (Wang et al., 2015), and Phong Deformation (James, 2020) -- to serve as "plug-and-play" components for prolongation with minimal modification. We show that our progressive volumetric simulation framework achieves high-fidelity matching LOD animation across resolutions including challenging dynamics with high speeds, large deformations, and frictional contact.

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

Adaptive Algebraic Reuse of Reordering in Cholesky Factorization with Dynamic Sparsity Pattern

Cholesky linear solvers are a critical bottleneck in challenging applications within computer graphics and scientific computing. These applications include but are not limited to elastodynamic barrier methods such as Incremental Potential Contact (IPC), and geometric operations such as remeshing and morphology. In these contexts, the sparsity patterns of the linear systems frequently change across successive calls to the Cholesky solver, necessitating repeated symbolic analyses that dominate the overall solver runtime. To address this bottleneck, we evaluate our method on over 150,000 linear systems generated from diverse nonlinear problems with dynamic sparsity changes in Incremental Potential Contact (IPC) and patch remeshing on a wide range of triangular meshes of various sizes. Our analysis using three leading sparse Cholesky libraries, Intel MKL Pardiso, SuiteSparse CHOLMOD, and Apple Accelerate, reveals that the primary performance constraint lies in the symbolic re-ordering phase of the solver. Recognizing this, we introduce Parth, an innovative re-ordering method designed to update ordering vectors only where local connectivity changes occur adaptively. Parth employs a novel hierarchical graph decomposition algorithm to break down the dual graph of the input matrix into fine-grained subgraphs, facilitating the selective reuse of fill-reducing orderings when sparsity patterns exhibit temporal coherence. Our extensive evaluation demonstrates that Parth achieves up to a 255x and 13x speedup in fill-reducing ordering for our IPC and remeshing benchmark and a 6.85x and 10.7x acceleration in symbolic analysis. These enhancements translate to up to 2.95x and 5.89x reduction in overall solver runtime. Additionally, Parth's integration requires only three lines of code, resulting in significant computational savings without the requirement of changes to the computational stack.

math.NA↗

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↗

arXiv2023

Convergent Incremental Potential Contact

Recent advances in the simulation of frictionally contacting elastodynamics with the Incremental Potential Contact (IPC) model have enabled inversion and intersection-free simulation via the application of mollified barriers, filtered line-search, and optimization-based solvers for time integration. In its current formulation the IPC model is constructed via a discrete constraint model, replacing non-interpenetration constraints with barrier potentials on an already spatially discretized domain. However, while effective, this purely discrete formulation prohibits convergence under refinement. To enable a convergent IPC model we reformulate IPC potentials in the continuous setting and provide a first, convergent discretization thereof. We demonstrate and analyze the convergence behavior of this new model and discretization on a range of elastostatic and dynamic contact problems, and evaluate its accuracy on both analytical benchmarks and application-driven examples.

math.NA↗

arXiv2022

Topology Optimization with Frictional Self-Contact

Contact-aware topology optimization faces challenges in robustness, accuracy, and applicability to internal structural surfaces under self-contact. This work builds on the recently proposed barrier-based Incremental Potential Contact (IPC) model and presents a new self-contact-aware topology optimization framework. A combination of SIMP, adjoint sensitivity analysis, and the IPC frictional-contact model is investigated. Numerical examples for optimizing varying objective functions under contact are presented. The resulting algorithm proposed solves topology optimization for large deformation and complex frictionally contacting scenarios with accuracy and robustness.

math.OC↗

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↗

arXiv2022

Affine Body Dynamics: Fast, Stable & Intersection-free Simulation of Stiff Materials

Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, numerical models of a rigid body continue to pose a number of known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit this problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art stiff simulations. We trace the challenges in the rigid-body IPC (incremental potential contact) method to the necessity of linearizing piecewise-rigid (SE(3)) trajectories and subsequent constraints. ABD instead relaxes the unnecessary (and unrealistic) constraint that each body's motion be exactly rigid with a stiff orthogonality potential, while preserving the rigid body model's key feature of a small coordinate representation. In doing so ABD replaces piecewise linearization with piecewise linear trajectories. This, in turn, combines the best from both parties: compact coordinates ensure small, sparse system solves, while piecewise-linear trajectories enable efficient and accurate constraint (contact and joint) evaluations. Beginning with this simple foundation, ABD preserves all guarantees of the underlying IPC model e.g., solution convergence, guaranteed non-intersection, and accurate frictional contact. Over a wide range and scale of simulation problems we demonstrate that ABD brings orders of magnitude performance gains (two- to three-order on the CPU and an order more utilizing the GPU, which is 10,000x speedups) over prior IPC-based methods with a similar or higher simulation quality.

cs.GR↗

arXiv2021

Codimensional Incremental Potential Contact

We extend the incremental potential contact (IPC) model for contacting elastodynamics to resolve systems composed of codimensional DOFs in arbitrary combination. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending IPC to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically-consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend the IPC model to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (resp. mid-lines) of shells (resp. rods) will not move closer than applied thickness values. This enables us to account for thickness in the contact behavior of codimensional structures and so robustly capture challenging contacting geometries; a number of which, to our knowledge, have not been simulated before. Third, codimensional models, especially with modeled thickness, mandate strict accuracy requirements that pose a severe challenge to all existing continuous collision detection (CCD) methods. To address these limitations we develop a new, efficient, simple-to-implement additive CCD (ACCD) method that applies conservative advancement to iteratively refine a lower bound for deforming primitives, converging to time of impact.

cs.GR↗

arXiv2020

Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time-stepping of the Material Point Method (MPM) irrespective of simulated materials and conditions. HOT is an MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit. HOT provides convergent simulations "out-of-the-box" across widely varying materials and computational resolutions without parameter tuning. As an implicit MPM time stepper accelerated by a custom-designed Galerkin multigrid wrapped in a quasi-Newton solver, HOT is both highly parallelizable and robustly convergent. As we show in our analysis, HOT maintains consistent and efficient performance even as we grow stiffness, increase deformation, and vary materials over a wide range of finite strain, elastodynamic and plastic examples. Through careful benchmark ablation studies, we compare the effectiveness of HOT against seemingly plausible alternative combinations of MPM with standard multigrid and other Newton-Krylov models. We show how these alternative designs result in severe issues and poor performance. In contrast, HOT outperforms the existing state-of-the-art, heavily optimized implicit MPM codes with an up to 10x performance speedup across a wide range of challenging benchmark test simulations.

cs.GR↗

arXiv2019

Neural Re-Simulation for Generating Bounces in Single Images

We introduce a method to generate videos of dynamic virtual objects plausibly interacting via collisions with a still image's environment. Given a starting trajectory, physically simulated with the estimated geometry of a single, static input image, we learn to 'correct' this trajectory to a visually plausible one via a neural network. The neural network can then be seen as learning to 'correct' traditional simulation output, generated with incomplete and imprecise world information, to obtain context-specific, visually plausible re-simulated output, a process we call neural re-simulation. We train our system on a set of 50k synthetic scenes where a virtual moving object (ball) has been physically simulated. We demonstrate our approach on both our synthetic dataset and a collection of real-life images depicting everyday scenes, obtaining consistent improvement over baseline alternatives throughout.

cs.CV↗

arXiv2019

Bounce and Learn: Modeling Scene Dynamics with Real-World Bounces

We introduce an approach to model surface properties governing bounces in everyday scenes. Our model learns end-to-end, starting from sensor inputs, to predict post-bounce trajectories and infer two underlying physical properties that govern bouncing - restitution and effective collision normals. Our model, Bounce and Learn, comprises two modules -- a Physics Inference Module (PIM) and a Visual Inference Module (VIM). VIM learns to infer physical parameters for locations in a scene given a single still image, while PIM learns to model physical interactions for the prediction task given physical parameters and observed pre-collision 3D trajectories. To achieve our results, we introduce the Bounce Dataset comprising 5K RGB-D videos of bouncing trajectories of a foam ball to probe surfaces of varying shapes and materials in everyday scenes including homes and offices. Our proposed model learns from our collected dataset of real-world bounces and is bootstrapped with additional information from simple physics simulations. We show on our newly collected dataset that our model out-performs baselines, including trajectory fitting with Newtonian physics, in predicting post-bounce trajectories and inferring physical properties of a scene.

cs.CV↗

arXiv2018

Blended Cured Quasi-Newton for Geometric Optimization

Optimizing deformation energies over a mesh, in two or three dimensions, is a common and critical problem in physical simulation and geometry processing. We present three new improvements to the state of the art: a barrier-aware line-search filter that cures blocked descent steps due to element barrier terms and so enables rapid progress; an energy proxy model that adaptively blends the Sobolev (inverse-Laplacian-processed) gradient and L-BFGS descent to gain the advantages of both, while avoiding L-BFGS's current limitations in geometry optimization tasks; and a characteristic gradient norm providing a robust and largely mesh- and energy-independent convergence criterion that avoids wrongful termination when algorithms temporarily slow their progress. Together these improvements form the basis for Blended Cured Quasi-Newton (BCQN), a new geometry optimization algorithm. Over a wide range of problems over all scales we show that BCQN is generally the fastest and most robust method available, making some previously intractable problems practical while offering up to an order of magnitude improvement in others.

math.OC↗

arXiv2011

Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We additionally, however, also consider invariant preservation over persistent, simultaneous and/or frequent boundary interactions. Appropriately formulating geometric methods to include such conditions has long-remained challenging due to the inherent nonsmoothness they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Leveraging discrete variational techniques, we construct a family of geometric numerical integration methods that not only obtain the usual desirable properties of momentum preservation, approximate energy conservation and equality constraint preservation, but also enforce multiple simultaneous inequality constraints, obtain smooth unilateral motion along constraint boundaries and allow for both nonsmooth and smooth boundary approach and exit trajectories. Numerical experiments are presented to illustrate the behavior of these methods on difficult test examples where both smooth and nonsmooth active constraint modes persist with high frequency.

math.NA↗