Pith. sign in

REVIEW 3 major objections 3 minor 39 references

Progressively Projected Newton's Method

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Selective, residual-guided projection secures Newton descent with 90% fewer Hessian projections.

desk verdict Useful empirical method with a real flaw: the descent guarantee is unsupported and the fallback claim doesn't hold. read the letter →

arxiv 2505.21013 v2 pith:GWSG246C submitted 2025-05-27 cs.GR

José Antonio Fernández-Fernández , Fabian Löschner , Jan Bender This is my paper
classification cs.GR
keywords ProgressivelyProjectedNewtonresidual-drivenheuristicselectiveeigenprojectionoptimization-basedtimeintegrationincrementalpotentialdescentdirectiondeformablebodysimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Progressively Projected Newton (PPN) sets out to replace Projected Newton (PN) in dynamic simulation by showing that a descent direction can be secured without projecting every element Hessian. The paper's core claim is that a cheap residual-driven heuristic — project the elements with the largest assembled residual, tighten the tolerance if the linear solve still fails, relax it after success — identifies the few elements that actually make the global Hessian indefinite. Across benchmarks covering deformable solids, cloth, frictional contact, and rigid bodies, PPN performs fewer than 10% of the projections required by PN or Project-on-Demand Newton and, in most cases, converges in fewer Newton iterations, making it the fastest solver in the study. The reported exception is very large time steps and quasistatic problems, where the lack of mass-matrix regularization makes full projection the better choice.

What carries the argument

The central mechanism is a residual-driven partition of element Hessians into an unprojected set $H_u$ and a projected set $H_p$, with an element moved into $H_p$ when $\|S_e g\|_\infty > \delta$, where $S_e$ selects the assembled degrees of freedom of element $e$ and $g$ is the current energy gradient. The adaptive tolerance $\delta$ — tightened by $\alpha = 0.5$ when indefiniteness is detected and relaxed by $\beta = 2$ after a successful Newton step — is what makes the projection progressive rather than fixed. Two engineering pieces carry the method: an SPD linear solver that exits early on indefiniteness (a negative pivot in LLT factorization, or a negative curvature direction in PCG), and incremental in-place assembly of the correction $\Delta H_e = \hat{H}_e - H_e$, which preserves sparsity and reuses existing assembly routines. Since the residual values are already computed by Newton's method, the heuristic adds no extra cost.

What would settle it

Construct a dynamic simulation in which the large-residual elements are all positive definite while the negative curvature resides in small-residual elements; if PPN then requires near-full projection to obtain a descent direction, the residual heuristic is refuted. The paper's own two-matrix example shows the phenomenon is possible in principle, so the test is concrete.

Watch

Extended reading notes

Core claim

The paper argues and demonstrates empirically that per-element Hessian projection is over-broad in two ways: it projects elements even when the assembled matrix is already positive definite, and it projects all elements even when only a sparse subset of them contributes the negative curvature. PPN instead starts each Newton iteration from the unmodified Hessian, has the linear solver signal indefiniteness, and projects only those element Hessians whose assembled residual exceeds an adaptive tolerance, expanding the projected set progressively until the solve succeeds. The tolerance is tightened by $\alpha = 0.5$ on failure and relaxed by $\beta = 2$ after a successful step, which keeps the global Hessian close to the true Hessian. The paper claims this preserves the descent-direction guarantee of PN while cutting element projections by an order of magnitude and, in most dynamic scenarios, also reducing Newton iterations by up to 50%.

Load-bearing premise

The load-bearing premise is that the elements with the largest assembled residual are the ones whose projection restores positive definiteness of the global Hessian; the paper offers empirical support but no proof of that correlation, and if it fails PPN can project the wrong elements without a guarantee of obtaining an SPD matrix.

Editorial extensions

If this is right

  • In typical dynamic scenes with $\Delta t = 1/30$ s, substituting PPN for PN in an existing pipeline should reduce element Hessian projections by over 90% and cut Newton iterations by up to 50%.
  • Because numerical eigendecompositions dominate projection cost, PPN narrows the performance gap between automatic-differentiation codebases and hand-tuned analytic-projection implementations.
  • PPN reduces to plain Newton when the unmodified Hessian stays solvable, so it adds no overhead in contact-free or lightly stressed regimes.
  • For very large time steps and quasistatic problems, the paper reports that PN remains preferable, so users in those regimes should not switch unconditionally.
  • The size of the speedup depends on the linear solver: PCG yields up to $\times 2.5$ over PN, while direct LLT factorization shows only modest gains because factorization dominates runtime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the residual-ranking heuristic could be replaced or augmented by a local curvature estimate, and the ablation suggests such a criterion might reduce failed linear solves at extreme settings even though $\alpha = 0.5, \beta = 2$ is not finely tuned.
  • A further extension the authors do not pursue is a hybrid scheduler that projects unconditionally for the first iterations and switches to PPN once the residual concentrates, which could address the quasistatic weakness.
  • The method's premise also applies outside time integration, to any second-order optimizer with element-wise assembled Hessians, such as shape optimization or material design, whenever global indefiniteness is localized.
  • One could turn the heuristic into a certificate by computing, after the final projected set is chosen, whether any unprojected element still carries a negative eigenvalue; the paper offers no such check.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper proposes Progressively Projected Newton (PPN), a Newton-type solver for optimization-based time integration. Instead of projecting every element Hessian before assembly as in Projected Newton (PN), PPN starts each Newton iteration with the unmodified Hessian and, whenever the linear solver reports indefiniteness, projects only those element Hessians whose assembled residual exceeds an adaptive threshold δ. The threshold is tightened after each failed solve and relaxed after a successful step. The method is evaluated on deformable solids, cloth, frictional contact, and rigid bodies, with PCG and direct Cholesky solvers, and is reported to use only a small fraction of the element projections of PN or Project-on-Demand Newton (PDN), often with fewer Newton iterations and lower runtime.

Significance. If the empirical claims hold, PPN is a practically valuable drop-in replacement for PN in dynamic simulation pipelines that rely on numerical eigendecompositions: it substantially reduces projection cost and keeps the global Hessian closer to the true Hessian, which plausibly explains the observed convergence benefits. The paper's strengths are its broad benchmark across contact-rich and contact-free scenes, resolutions, time steps, tolerances, and solvers; the ablation of the hyperparameters; and the explicit runtime breakdowns that identify eigenprojection as a dominant cost. The main weaknesses are the absence of a termination or descent guarantee for the residual-selection heuristic, the lack of the claimed full-projection fallback in Algorithm 1, and abstract/conclusion statements that overstate the consistency of the projection reductions.

major comments (3)
  1. [Section 4, Algorithm 1] The text states that PPN 'can fall back to full projection if necessary,' but Algorithm 1 contains no such fallback: the inner loop only tightens δ and never projects all elements. Consequently, the algorithm has no termination guarantee when indefiniteness is localized in an element whose assembled residual is zero or very small. Concretely, for Ψ(x,y) = −0.5 a x² + 0.5 k(x−y)² + 0.5 l(y−c)² at (0,0), with a > kl/(k+l), the global gradient is (0, −lc), the first element has residual 0 and Hessian −a, and the second element has a positive definite Hessian. Algorithm 1 never selects the indefinite first element, so every solve remains indefinite and δ decreases forever; full projection is never reached. Section 6 explicitly concedes that the heuristic is 'not tied to actual assembled indefiniteness.' Please either add a genuine full-projection fallback with a proof of finite termination, or substantially weaken the claims of guaranteed descent directions and robustness.
  2. [Abstract and §5.2 / Fig. 5] The abstract claims that PPN 'consistently performs fewer than 10% of the projections required by PN or PDN,' and the conclusion repeats that PPN 'consistently performs 90% fewer projections.' The paper's own results contradict the word 'consistently': §5.2 reports that across resolutions, time steps, and tolerances, PPN projects 'between 30% and 5%' of elements, and Fig. 5 shows cases above 10%, especially at Δt = 100 ms. The abstract should state the observed range and explicitly carry the caveat that PPN struggles for very large time steps and quasistatics, where PN remains preferable.
  3. [Section 4, Projection heuristic; Section 6] The paper presents the residual heuristic as the key mechanism for choosing projection subsets, but the only justification is the motivational observation that residual forces vanish at a stationary point. That observation does not imply that residual magnitude identifies elements whose contribution makes the assembled Hessian indefinite; a zero residual at a saddle point can coexist with an indefinite element Hessian. The paper acknowledges this gap in Section 6, yet the Introduction and Conclusion still claim that PPN 'guarantees descent directions' and that it is a 'direct replacement' for PN. Please present PPN's selection rule as an empirical heuristic with a clearly stated correctness caveat, or supply a proof under explicit assumptions.
minor comments (3)
  1. [Section 1 and Table 1] The time step is reported as 'Δt = 1/30 ms' in the text and as '1/30' under a column labeled 'Δt [ms]' in Table 1; the intended value is presumably 1/30 s (≈33.3 ms). Please correct the units consistently.
  2. [Algorithm 1, line 8] The notation 'partial_project_to_PD(H, g > δ)' is ambiguous; please define it explicitly, e.g. project all elements e for which ‖S_e g‖∞ > δ, using the selection matrix introduced in Section 4.
  3. [Section 5.1] The statement that a final fully projected Hessian solve is performed for verification but its cost is excluded from timing should be stated more prominently, since it affects the fairness of runtime comparisons for PN, which performs that projection at every iteration.

Circularity Check

0 steps flagged · score 1.0 of 10

PPN's residual heuristic is an empirical ansatz; its headline numbers are measured against independent baselines, so no circular reduction is present.

full rationale

The paper's central claim is that residual-driven selective projection is empirically faster and needs fewer projections. This is not derived from the tuned parameters: alpha and beta are chosen on the Press scene by ablation, then the same scene is used as one benchmark, but the headline claims are supported by a multi-scene comparison (Press, U-Turn, quasistatic, cloth, impacts) in which PPN, PN, and PDN are all executed under identical tolerances and time stepping. The residual heuristic itself is presented as a heuristic ('we define our heuristic: prioritize projecting element Hessians from regions ... with larger assembled residual'), and Section 6 explicitly concedes it is 'not tied to local assembled indefiniteness'; an unproven heuristic is a correctness/robustness limitation, not a circular definition. The PDN baseline comes from prior work by overlapping authors (Longva et al. 2023), but it is used as a compared baseline, not as the proof of PPN's guarantees, and its results are external published results rather than a premise smuggled into the derivation. The descent-direction 'guarantee' rests on the fallback-to-full-projection claim; the exact-zero residual counterexample shows that fallback can fail to trigger, which is a termination/robustness gap, not an equivalence between the input and the output. No equation in the paper defines the predicted quantity in terms of the fitted parameters or vice versa.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on an empirical heuristic plus two tuned hyperparameters. No new physical entities are introduced. The method's guarantees depend on standard linear algebra facts and on the residual-correlation heuristic, which is the main unproven ingredient.

free parameters (2)
  • alpha (tightening factor) = 0.5
    Chosen by ablation on the Press scene (Fig. 3) to minimize runtime; used in all other experiments.
  • beta (release factor) = 2.0
    Chosen by ablation on the Press scene (Fig. 3); controls how quickly the projection threshold relaxes after a successful Newton step.
assumptions (4)
  • ad hoc to paper Residual magnitude indicates local indefiniteness: elements with larger assembled residual are the ones whose projection restores positive definiteness of the global Hessian.
    Stated in Section 4, Projection heuristic. Not proven; the paper argues residuals vanish at the stationary point and assumes this correlates with the location of negative curvature.
  • standard math A successful PCG run (no negative curvature encountered) yields a descent direction even if the matrix is not SPD.
    This is the Newton-CG property from Nocedal and Wright, cited in Section 4.1. Standard result.
  • domain assumption The assembled Hessian is the sum of element Hessians, and clamping eigenvalues of a subset can be updated incrementally without changing sparsity.
    Standard finite element assembly; used in Algorithm 1 and Eq. (5).
  • domain assumption Early termination of LLT on a negative pivot and of PCG on a negative curvature direction reliably detects indefiniteness.
    Standard behavior of these solvers, described in Section 4.1.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Progressively Projected Newton's Method." pith.science (2026). https://pith.science/paper/GWSG246C

@misc{pith2026250521013,
  author       = {Pith},
  title        = {Pith review of: Progressively Projected Newton's Method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GWSG246C}},
  note         = {Machine review of arXiv:2505.21013}
}
read the original abstract

Newton's Method is widely used to find the solution of complex non-linear simulation problems in Computer Graphics. 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 residual to cheaply determine the subset of element Hessians to project. The global Hessian thus remains closer to its original form, reducing both the number of Newton iterations and the amount of required eigen-decompositions. We compare PPN with PN and Project-on-Demand Newton (PDN) in a comprehensive set of experiments covering contact-free and contact-rich deformables (including large stiffness and mass ratios), co-dimensional, and rigid-body simulations, and a range of time step sizes, tolerances and resolutions. PPN consistently performs fewer than 10% of the projections required by PN or PDN and, in the vast majority of cases, converges in fewer Newton iterations, which makes PPN the fastest solver in our benchmark. The most notable exceptions are simulations with very large time steps and quasistatics, where PN remains a better choice.

Figures

Figures reproduced from arXiv: 2505.21013 by the authors.

Figure 1
Figure 1. Press. (a) Four elastic orange boxes drop into a rigid cylinder; (b) a press descends; (c) the press then rotates, forcing the boxes to roll under pressure due to friction. (d) Top: cumulative count of projected element Hessians, highlighting that PPN projects only 8 % of all elements; bottom: cumulative runtime highlighting that PPN completes the simulation in 65 % of the time required by PN and PDN. (e) Global eig… view at source ↗
Figure 2
Figure 2. Rolling sphere. A deformable sphere with initial horizontal velocity rolls on a flat surface. Different Newton step velocity tolerance are used: 10−1m s−1 (yellow), 10−2m s−1 (blue), 10−3m s−1 (green), 10−4m s−1 (red). 5.2 Experiments Ablation. We begin showcasing the effect of the projection adap￾tivity parameters 𝛼 (tighten) and 𝛽 (release) in PPN. We run the “Press” scene ( [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figure 3
Figure 3. Ablation test for the projection aggressiveness of PPN with an itera [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Runtime breakdown for the chosen parametrization of PPN in the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 7
Figure 7. Figure 7: U-Turn. Two elastic cylinders are interlaced and twisted. Above, we compare solvers under varying Young’s moduli (top) and densities (bottom). Below, the initial and final states are shown. All simulations except the “Hard-Soft” produce the same deformation. 0 100 200 …
Figure 8
Figure 8. Figure 8: Armadillo slingshot. An elastic armadillo is pulled and then re￾leased. Comparison between solvers on top, largest deformation states below. Large Ratios. We compare all three solvers in simulations fea￾turing large stiffness (𝐸 = 106–1010 Pa) and density (𝜌 = 101– 104…
Figure 6
Figure 6. Figure 6: Quasistatic extrusion. An elastic box is stretched by twice its size in a quasistatic setting using different resolutions (rows) and Poisson’s ratios (colums). Solvers use different colors, and eigenvalue filtering different shading: solid for clamping and hatched for …
Figure 9
Figure 9. Figure 9: Twisting cloth. A cloth cylinder is twisted by rotating its ends in opposite directions using three mesh resolutions. Final configuration of the finest resolution shown inside the plot. 0 5000 10000 15000 20000 25000 30000 35000 Runtime [s] PN PDN PPN #N: 22 | ph: 100.…
Figure 10
Figure 10. Figure 10: Armadillo drop. 160 elastic armadillos are dropped into a rigid box. Comparison between solvers on top. Initial and final state below. 1282 and 2562 in [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

39 extracted references · 17 canonical work pages

  1. [6]

    arXiv:2303.02156 arXiv Preprint

    SymX: Energy-based Simulation from Symbolic Expressions. arXiv:2303.02156 arXiv Preprint. Xiao-Ming Fu and Yang Liu

    work page arXiv

  2. [9]

    ACM Transactions on Graphics 43, 6 (Nov

    A Mesh-based Simulation Framework using Automatic Code Generation. ACM Transactions on Graphics 43, 6 (Nov. 2024), 1–17. https://doi.org/10.1145/3687986 Daniel Holz, Stefan Rhys Jeske, Fabian Löschner, Jan Bender, Yin Yang, and Sheldon Andrews

    doi:10.1145/3687986 2024

  3. [10]

    Computer Graphics Forum (2025)

    Multiphysics Simulation Methods in Computer Graphics. Computer Graphics Forum (2025). https://doi.org/10.1111/cgf.70082 Kemeng Huang, Floyd M. Chitalu, Huancheng Lin, and Taku Komura

    doi:10.1111/cgf.70082 2025

  4. [11]

    ACM Transactions on Graphics 43, 2 (March 2024), 1–18

    GIPC: Fast and Stable Gauss-Newton Optimization of IPC Barrier Energy. ACM Transactions on Graphics 43, 2 (March 2024), 1–18. https://doi.org/10.1145/3643028 L. Kharevych, Weiwei Yang, Y. Tong, E. Kanso, J. E. Marsden, P. Schröder, and M. Desbrun

    doi:10.1145/3643028 2024

  5. [16]

    ACM Transactions on Graphics 41, 4 (July 2022), 67:1–67:14

    Affine body dynamics: fast, stable and intersection-free simulation of stiff materials. ACM Transactions on Graphics 41, 4 (July 2022), 67:1–67:14. https://doi.org/10.1145/ 3528223.3530064 Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman

    arXiv 2022

  6. [17]

    ACM Trans- actions on Graphics 39, 4 (Aug

    Incremental potential contact: intersection-and inversion-free, large-deformation dynamics. ACM Trans- actions on Graphics 39, 4 (Aug. 2020). https://doi.org/10.1145/3386569.3392425 Minchen Li, Danny M. Kaufman, and Chenfanfu Jiang

    arXiv 2020

  7. [18]

    ACM Transactions on Graphics 40, 4 (July 2021), 1–24

    Codimensional incremental potential contact. ACM Transactions on Graphics 40, 4 (July 2021), 1–24. https: //doi.org/10.1145/3450626.3459767 Xuan Li, Minchen Li, Xuchen Han, Huamin Wang, Yin Yang, and Chenfanfu Jiang

    arXiv 2021

  8. [19]

    In ACM SIGGRAPH 2024 Conference Papers (SIGGRAPH ’24)

    A Dynamic Duo of Finite Elements and Material Points. In ACM SIGGRAPH 2024 Conference Papers (SIGGRAPH ’24) . Association for Computing Machinery, Article 97, 11 pages. https://doi.org/10.1145/3641519.3657449 Huancheng Lin, Floyd M. Chitalu, and Taku Komura

    arXiv 2024

Show all 39 references
  1. [20]

    ACM Transactions on Graphics 41, 6 (Nov

    Isotropic ARAP Energy Using Cauchy-Green Invariants. ACM Transactions on Graphics 41, 6 (Nov. 2022), 1–14. https://doi.org/10.1145/3550454.3555507 Tiantian Liu, Adam W. Bargteil, James F. O’Brien, and Ladislav Kavan

    2022

  2. [23]

    arXiv:2311.14526 arXiv Preprint

    Pitfalls of Projection: A study of Newton-type solvers for incremental potentials. arXiv:2311.14526 arXiv Preprint. Fabian Löschner, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Andreas Longva, and Jan Bender

    arXiv

  3. [24]

    Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3, Article 46 (Aug

    Micropolar Elasticity in Physically-Based Animation. Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3, Article 46 (Aug. 2023), 24 pages. https://doi.org/10.1145/3606922 F. Löschner, J. A. Fernández-Fernández, S. R. Jeske, and J. Bender

    2023 doi

  4. [25]

    Computer Graphics Forum 43, 8 (2024)

    Curved Three- Director Cosserat Shells with Strong Coupling. Computer Graphics Forum 43, 8 (2024). https://doi.org/10.1111/cgf.15183 Miles Macklin, Kenny Erleben, Matthias Müller, Nuttapong Chentanez, Stefan Jeschke, and Tae-Yong Kim

    2024 doi

  5. [28]

    Springer Science & Business Media

    Numerical optimization. Springer Science & Business Media. https://doi.org/10.1007/978-0-387-40065-5 Matthew Overby, George E. Brown, Jie Li, and Rahul Narain

    doi

  6. [29]

    IEEE Transactions on Visualization and Computer Graphics 23, 10 (Oct 2017), 2222–2234

    ADMM⊇ Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints. IEEE Transactions on Visualization and Computer Graphics 23, 10 (Oct 2017), 2222–2234. https://doi.org/10.1109/TVCG.2017.2730875 R. Radovitzky and M. Ortiz

    2017

  7. [31]

    Computer Graphics Forum 41, 5 (2022), 113–124

    TinyAD: Automatic Differentiation in Geometry Processing Made Simple. Computer Graphics Forum 41, 5 (2022), 113–124. https://doi.org/10.1111/cgf.14607 Alvin Shi and Theodore Kim

    2022 doi

  8. [32]

    Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3 (Aug

    A Unified Analysis of Penalty-Based Collision Energies. Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3 (Aug. 2023), 1–19. https://doi.org/10.1145/3606934 Anna Shtengel, Roi Poranne, Olga Sorkine-Hornung, Shahar Z. Kovalsky, and Yaron Lip- man

    2023 doi

  9. [33]

    ACM Transactions on Graphics 36, 4 (July 2017), 1–11

    Geometric optimization via composite majorization. ACM Transactions on Graphics 36, 4 (July 2017), 1–11. https://doi.org/10.1145/3072959.3073618 Breannan Smith, Fernando De Goes, and Theodore Kim

    2017

  10. [35]

    ACM Transactions on Graphics 38, 1 (Feb

    Analytic Eigensystems for Isotropic Distortion Energies. ACM Transactions on Graphics 38, 1 (Feb. 2019), 1–15. https://doi.org/10.1145/3241041 Joseph Teran, Eftychios Sifakis, Geoffrey Irving, and Ronald Fedkiw

    2019 doi

  11. [37]

    ACM Transactions on Graphics 35, 6, Article 212 (Dec

    Descent Methods for Elastic Body Simulation on the GPU. ACM Transactions on Graphics 35, 6, Article 212 (Dec. 2016), 10 pages. https://doi.org/10.1145/2980179.2980236 Zhendong Wang, Yin Yang, and Huamin Wang

    2016

  12. [38]

    ACM Transactions on Graphics 42, 6 (Dec

    Stable Discrete Bending by Ana- lytic Eigensystem and Adaptive Orthotropic Geometric Stiffness. ACM Transactions on Graphics 42, 6 (Dec. 2023), 1–16. https://doi.org/10.1145/3618372 Haomiao Wu and Theodore Kim

    2023 doi

  13. [39]

    https://doi.org/10.1111/cgf.14104 Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross

    89–100. https://doi.org/10.1111/cgf.14104 Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross

    doi

  14. [40]

    Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3 (Aug

    An Eigenanalysis of Angle-Based Deformation Energies. Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, 3 (Aug. 2023), 1–19. https://doi.org/10.1145/3606929 Tianyi Xie, Minchen Li, Yin Yang, and Chenfanfu Jiang

    2023 doi

  15. [41]

    ACM Transactions on Graphics 42, 4 (July 2023), 122:1–122:14

    A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling. ACM Transactions on Graphics 42, 4 (July 2023), 122:1–122:14. https://doi.org/10.1145/3592115

    2023 doi

  16. [1999]

    Computer Methods in Applied Mechanics and Engineer- ing 172, 1–4 (April 1999), 203–240

    Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineer- ing 172, 1–4 (April 1999), 203–240. https://doi.org/10.1016/s0045-7825(98)00230-8 P. Schmidt, J. Born, D. Bommes, M. Campen, and L. Kobbelt

    1999 doi

  17. [2005]

    Association for Computing Machinery, 181–190

    Robust Qua- sistatic Finite Elements and Flesh Simulation (SCA ’05). Association for Computing Machinery, 181–190. https://doi.org/10.2312/SCA/SCA05/181-190 Huamin Wang and Yin Yang

    doi

  18. [2006]

    In Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’06)

    Geometric, variational integrators for computer animation. In Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’06). 43–51. https://doi.org/10.2312/SCA/SCA06/043-051 Theodore Kim

    2006 doi

  19. [2011]

    ACM Transactions on Graphics 30, 4 (July 2011), 1–8

    Example-based elastic materials. ACM Transactions on Graphics 30, 4 (July 2011), 1–8. https://doi.org/10.1145/2010324.1964967 Progressively Projected Newton’s Method • 9 Jorge Nocedal and Stephen Wright

    2011

  20. [2013]

    ACM Transactions on Graphics 32, 6 (Nov

    Fast simulation of mass-spring systems. ACM Transactions on Graphics 32, 6 (Nov. 2013), 1–7. https://doi.org/10.1145/2508363.2508406 Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan

    2013

  21. [2014]

    ACM Trans- actions on Graphics 33, 4 (July 2014), 154:1–154:11

    Projective dynamics: fusing constraint projections for fast simulation. ACM Trans- actions on Graphics 33, 4 (July 2014), 154:1–154:11. https://doi.org/10.1145/2601097. 2601116 Anka He Chen, Ziheng Liu, Yin Yang, and Cem Yuksel. 2024c. Vertex Block Descent. ACM Transactions on...

    2014

  22. [2015]

    IEEE Transactions on Visualization and Computer Graphics 21, 10 (Oct

    Optimization Integrator for Large Time Steps. IEEE Transactions on Visualization and Computer Graphics 21, 10 (Oct. 2015), 1103–1115. https: //doi.org/10.1109/tvcg.2015.2459687 Philipp Herholz, Tuur Stuyck, and Ladislav Kavan

    2015

  23. [2017]

    ACM Transactions on Graphics 36, 4 (July 2017), 116a:1

    Quasi-Newton Methods for Real-Time Simulation of Hyperelastic Materials. ACM Transactions on Graphics 36, 4 (July 2017), 116a:1. https://doi.org/10.1145/3072959.2990496 Andreas Longva, Fabian Löschner, José Antonio Fernández-Fernández, Egor Larionov, Uri M Ascher, and Jan Bender

    2017

  24. [2018]

    ACM Transactions on Graphics 37, 2 (March 2018), 1–15

    Stable Neo-Hookean Flesh Simulation. ACM Transactions on Graphics 37, 2 (March 2018), 1–15. https: //doi.org/10.1145/3180491 Breannan Smith, Fernando De Goes, and Theodore Kim

    2018 doi

  25. [2019]

    ACM Transactions on Graphics 38, 4 (July 2019), 1–15

    Anisotropic elasticity for inversion-safety and element rehabilitation. ACM Transactions on Graphics 38, 4 (July 2019), 1–15. https://doi.org/10.1145/3306346.3323014 Theodore Kim and David Eberle

    2019

  26. [2020]

    Computer Graphics Forum 39, 8 (Nov

    A Finite Element Formulation of Baraff-Witkin Cloth. Computer Graphics Forum 39, 8 (Nov. 2020), 171–179. https://doi.org/10.1111/cgf.14111 Theodore Kim, Fernando De Goes, and Hayley Iben

    2020 doi

  27. [2021]

    ACM Transactions on Graphics 40, 4 (July 2021), 183:1–183:16

    Intersection-free rigid body dynamics. ACM Transactions on Graphics 40, 4 (July 2021), 183:1–183:16. https://doi.org/10.1145/3450626.3459802 José Antonio Fernández-Fernández, Ralph Lange, Stefan Laible, Kai O. Arras, and Jan Bender

    2021

  28. [2022]

    InACM SIGGRAPH 2022 Courses (SIGGRAPH ’22)

    Dynamic deformables: implementation and pro- duction practicalities (now with code!). InACM SIGGRAPH 2022 Courses (SIGGRAPH ’22). ACM, 1–259. https://doi.org/10.1145/3532720.3535628 Lei Lan, Danny M. Kaufman, Minchen Li, Chenfanfu Jiang, and Yin Yang

    2022

  29. [2023]

    In ACM SIGGRAPH 2023 Conference Proceedings (SIGGRAPH ’23)

    Multi-Layer Thick Shells. In ACM SIGGRAPH 2023 Conference Proceedings (SIGGRAPH ’23) . Association for Computing Machinery, 1–9. https: //doi.org/10.1145/3588432.3591489 Yuan-Yuan Cheng, Ligang Liu, and Xiao-Ming Fu

    2023

  30. [2024]

    In 2024 IEEE International Conference on Robotics and Automation (ICRA)

    STARK: A Unified Framework for Strongly Coupled Simulation of Rigid and Deformable Bodies with Frictional Contact. In 2024 IEEE International Conference on Robotics and Automation (ICRA) . https://doi.org/10.1109/ICRA57147. 2024.10610574 José Antonio Fernández-Fernández, Fabia...

    2024

  31. [2025]

    Computer Graphics Forum (April 2025)

    Eigenvalue Blending for Projected Newton. Computer Graphics Forum (April 2025). https://doi.org/10.1111/ cgf.70027 Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M. Kaufman, and Daniele Panozzo

    2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.