Pith. sign in

REVIEW 3 major objections 6 minor 61 references

SGLDBench: A Benchmark Suite for Stress-Guided Lightweight 3D Designs

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read SGLDBench provides the first integrated benchmark for computing and comparing 3D lightweight design strategies under identical simulation conditions.

desk verdict A genuinely useful integrated benchmark for stress-guided 3D infill design, but the comparative claims need a voxelization convergence check and the code has to actually ship. read the letter →

arxiv 2501.03068 v2 pith:FDAYZTYS submitted 2025-01-06 cs.CE

Junpeng Wang , Dennis R. Bukenberger , Simon Niedermayr , Christoph Neuhauser , Jun Wu , Rüdiger Westermann This is my paper · ORCID
classification cs.CE
keywords topologyoptimizationlatticeinfilllightweightdesignstress-guidedbenchmarksuitecomplianceanalysismultigridelasticitysolvervoxelization
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

This paper introduces SGLDBench, a benchmark suite for generating, analyzing, and comparing 3D lightweight designs produced by different material-layout strategies under identical simulation conditions. The authors claim that no such integrated benchmark existed before: previous work covered individual strategies or 2D test cases, but not a common framework for six distinct strategies. SGLDBench couples an efficient multigrid elasticity solver with a standardized step that voxelizes edge-graph infills into the same Cartesian grid used for simulation, so compliance numbers are comparable across methods. In experiments, the suite reveals properties such as near-equal compliance for geometrically very different infills at a fixed material budget, and different robustness when load directions change.

What carries the argument

The mechanism that carries the comparison is the pipeline that turns every strategy's output into the same representation: field-based strategies already produce voxel material fields, while edge-graph strategies are voxelized into a Cartesian grid via a DDA line-drawing algorithm with 26-neighbor thickening, at a resolution chosen automatically to represent edges with a minimum number of voxels. This material field is then fed to a geometric multigrid finite-element elasticity solver, a preconditioned conjugate-gradient method solving $KU=F$, which computes the compliance $c = U^T K U$, where lower compliance means higher stiffness. Because all six strategies are simulated on the same grid with the same solver, reported differences in stiffness are attributed to the design strategy rather than to the analysis setup. A visual-analysis module additionally compares principal stress directions in the solid and in the infill to explain why some designs deviate from optimal load paths.

What would settle it

A convergence study that recomputes compliance for the same infill at progressively finer voxel resolutions, and shows that the relative ranking of the six strategies changes, would falsify the claim that the benchmark's comparisons are independent of simulation resolution.

Watch

Extended reading notes

Core claim

The central claim is that SGLDBench is the first benchmark that lets researchers and users efficiently compute 3D lightweight designs with different strategies and effectively compare them by mechanical and structural properties. The paper demonstrates this by implementing six reference strategies—density-based topology optimization, porous infill optimization, Voronoi infill, principal-stress-line-guided material layout, conforming lattice structures, and volumetric Michell trusses—and evaluating them on three models with identical boundary conditions and material budgets. On top of the comparisons, the paper reports two findings: at a fixed material budget the stiffness of the tested designs appears nearly independent of geometric infill details, and designs with a more space-filling material distribution resist changed load directions better than designs produced by density-based topology optimization.

Load-bearing premise

The comparison is fair only if the automatically chosen voxel resolution represents every strategy's edges accurately; too coarse a grid would over-thicken thin members, hide real stiffness differences, and could explain the observed compliance insensitivity to geometry.

Editorial extensions

If this is right

  • Any newly added design strategy can be plugged into SGLDBench and compared against the six reference strategies on the same voxel grid, so future lightweight-design papers can report stiffness numbers that are directly comparable.
  • The observed near-equal compliance of geometrically different infills at the same material budget implies that, for the tested models, material volume dominates stiffness more than the specific infill pattern, which shifts design attention to load robustness and manufacturability.
  • The variable-load experiments provide a concrete ranking criterion: when loads may change direction, space-filling designs such as Voronoi, conforming lattice, and Michell trusses outperform density-based topology optimization, while the topology-optimized design is stiffest under its original load.
  • Stress-alignment visualizations identify where conforming lattice structures and volumetric Michell trusses lose the principal stress directions, giving specific targets for improving those methods.

Reading between the lines

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

  • An implication the authors leave implicit is that the near-equal-compliance result may be shaped by the voxelization resolution; a finer grid could change the ranking, so the claim should be read as conditional on the chosen resolution until a convergence study is run.
  • The benchmark's focus on compliance omits failure modes such as buckling, fatigue, and printability; adding those metrics could produce different strategy rankings, and the framework's common grid would make such extensions straightforward.
  • The automatic resolution selection could be extended into a principled rule, such as requiring a minimum number of voxels across a member's cross-section, so that comparisons are fair across methods with different edge thicknesses; this would be a testable improvement to the current setup.
  • The framework suggests a practical workflow for practitioners: optimize under one load case, then re-evaluate under plausible alternative loads, since the suite's variable-load analysis can flag designs that are over-specialized.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper introduces SGLDBench, a MATLAB-based benchmark suite for stress-guided lightweight 3D design. It integrates domain voxelization, boundary-condition specification, a multigrid finite-element elasticity solver, six material-layout strategies (density-based topology optimization, porous infill optimization, Voronoi infill, principal-stress-line-guided layout, conforming lattice structures, and volumetric Michell trusses), a voxelization pipeline that rasterizes edge-based infills into a common Cartesian grid, and WebGL-based visualization for stress analysis. The experimental section demonstrates the suite on three models at resolutions up to roughly 160 million elements, reports solver and optimization timings, compares designs under different material budgets and changed load directions, and analyzes stress-direction alignment. The authors claim that SGLDBench is the first integrated benchmark enabling researchers to compute and compare 3D lightweight designs from different strategies under identical simulation conditions.

Significance. If substantiated, SGLDBench fills a genuine gap: comparisons of lightweight-design strategies are usually performed ad hoc with method-specific implementations and solvers, making cross-method conclusions difficult to reproduce. The suite's tight integration of a common solver, common voxelization, and common evaluation metrics is a valuable engineering contribution. The paper also makes a falsifiable observation—near-equal compliance for geometrically different infills at a fixed material budget (Sec. 4.3)—and provides reproducible infrastructure (code promised to be public upon acceptance) for follow-up work. The main risk is that the fairness and accuracy of the comparison hinge on the voxelization and solver settings, which are not yet demonstrated to be converged; this is fixable with additional experiments.

major comments (3)
  1. [Section 3.4] The automatic selection of the voxel grid resolution is not specified beyond 'a minimum required voxels', and no convergence study is reported. Because all graph-based infills are converted to voxel fields by DDA rasterization plus 26-neighborhood dilation, the reported compliance values and rankings—including the paper's headline observation that stiffness is independent of infill geometry (Sec. 4.3)—are only trustworthy if the chosen resolution preserves the intended edge thickness and connectivity. I request a resolution-convergence experiment: for at least one load case, recompute the compliance of each edge-based infill at two or three finer grid resolutions while holding edge thickness and material budget fixed, and report the changes in compliance, volume fraction, and connected components. The paper should also state the selection criterion for the 'minimum required voxels' used in Fig. 11.
  2. [Section 4.1 / Figs. 1, 10, 13] All compliance comparisons are presented as single numbers without error bars or repeated runs. Several of the strategies involve stochastic components (e.g., Poisson-disk sampling for Voronoi infills) and iterative optimization with stopping tolerances, so at least a small number of repeated runs (or an explicit statement that the methods are deterministic for fixed seeds) is needed to establish that the reported rankings are not within run-to-run variation. In addition, no validation of the multigrid solver's compliance values against a direct solver or a commercial FEA package is provided for a representative case.
  3. [Section 4.3] The claim that 'stiffness appears to be independent of the geometric details of the infills when using the same material budget' is presented as an interesting finding, but the same figure (Fig. 11) uses a single automatically chosen grid resolution and a single run per infill. The over-thickening or bridging of thin members at coarse resolution could plausibly erase geometric differences. Please also report the actual edge thickness in voxels and the ratio of edge diameter to voxel size for the designs in Figs. 1 and 11, and discuss whether the observed compliance insensitivity persists when the resolution is refined.
minor comments (6)
  1. [Section 3.3.5] In the description of the conforming lattice structure, 'feds' should be 'feeds'.
  2. [Section 3.3] 'publically available repository' should read 'publicly available repository'.
  3. [Section 4.1] The sentence 'convergence within 41 solver iterations at a threshold of 1.0 ×10−3' is missing a period; please also state which norm of the residual is used for the termination criterion.
  4. [Section 3.4] The phrase 'minimum required voxels' is grammatically awkward; consider 'the minimum number of voxels required'.
  5. [Section 1] The statement that the codebase 'will be made publicly available upon acceptance' prevents independent verification of the current results; if the repository is already available, please include a link and a version identifier.
  6. [Figure 1 caption] The thickness of the solid coating is not specified; since the material budget is the main comparison variable, state how the coating thickness is chosen and whether it is included in the reported volume fractions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the compliance comparisons are measured by FEA from prescribed geometries, not fitted or defined in terms of the reported results.

full rationale

SGLDBench does not derive a physical quantity from itself. Its pipeline is: prescribed boundary conditions and material budget generate designs via six published/external strategies, Section 3.4 voxelizes edge-based structures, and Section 3.2/Equation (1) computes compliance as c = U^T K U with the multigrid FEA solver. Nothing in this chain defines compliance or the comparative rankings in terms of the output being predicted. The six strategies are taken from prior published works (TO [30], porous infill [31], Voronoi [32], PSL-guided layout [33], conforming lattice via [34], Michell trusses [35]) and are evaluated as black boxes. The authors' own solver [27] and PSL backend [36] are self-citations, but they are used as off-the-shelf implementations; the benchmark conclusions do not rest on accepting those papers' claims on faith because the stiffness values are independently computed by the integrated FEA solver. The observation in Section 4.3 that 'stiffness appears to be independent of the geometric details of the infills when using the same material budget' is an empirical result of the described simulation, not an input: compliance is measured after voxelizing each geometry, and the material budget is enforced by a separate matching procedure. Even if the automatic voxel resolution in Section 3.4 were unvalidated and could bias the numerical comparisons, that is a correctness or robustness concern, not circularity: there is no equation or fitted parameter that is renamed as a prediction, and no load-bearing argument reduces to a self-cited uniqueness theorem. No circular step can be exhibited, so the appropriate finding is no significant circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The benchmark rests on standard assumptions of linear FEA and on the choice of common voxelized representation. No new entities are postulated. The free parameters are user-selected experimental settings rather than fitted parameters; they influence the reported numbers but are not tuned to produce a predetermined conclusion.

free parameters (5)
  • volume_fraction = 0.4 and 0.2
    Material budget used in experiments (Section 4.2); changes affect compliance rankings.
  • edge_thickness = user-defined
    Controls voxelized infill thickness; Section 3.4.
  • voxel_grid_resolution = e.g., 384x256x512 for Bone, 860x430x430 for Cantilever
    Simulation resolution; affects compliance and runtime.
  • Voronoi radius mapping parameters (r_hat and rho) = r_hat as fraction of bounding box, rho in (0,1]
    Defines Poisson disk radii in Equation 5.
  • Michell truss resolution parameter rho = user-defined
    Controls truss density (Section 3.3.6).
assumptions (5)
  • domain assumption Linear elastic material law
    FEA formulation throughout, Section 3.2.
  • domain assumption SIMP model with minimum density for void
    Section 3.3.1.
  • domain assumption Voxel centroid classification for solid/void
    Section 3.1.
  • domain assumption Stress field in the initial solid domain guides infill generation
    Sections 3.3.4-3.3.6.
  • domain assumption A single FEA solver computes all compliance values comparably
    Section 3.2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of SGLDBench: A Benchmark Suite for Stress-Guided Lightweight 3D Designs." pith.science (2026). https://pith.science/paper/FDAYZTYS

@misc{pith2026250103068,
  author       = {Pith},
  title        = {Pith review of: SGLDBench: A Benchmark Suite for Stress-Guided Lightweight 3D Designs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FDAYZTYS}},
  note         = {Machine review of arXiv:2501.03068}
}
read the original abstract

We introduce the Stress-Guided Lightweight Design Benchmark (SGLDBench), a comprehensive benchmark suite for applying and evaluating material layout strategies to generate stiff, lightweight designs in 3D domains. SGLDBench provides a seamlessly integrated simulation and analysis framework, including six reference strategies and a scalable multigrid elasticity solver to efficiently execute these strategies and validate the stiffness of their results. This facilitates the systematic analysis and comparison of design strategies based on the mechanical properties they achieve. SGLDBench enables the evaluation of diverse load conditions and, through the tight integration of the solver, supports high-resolution designs and stiffness analysis. Additionally, SGLDBench emphasizes visual analysis to explore the relationship between the geometric structure of a design and the distribution of stresses, offering insights into the specific properties and behaviors of different design strategies. SGLDBench's specific features are highlighted through several experiments, comparing the results of reference strategies with respect to geometric and mechanical properties.

Figures

Figures reproduced from arXiv: 2501.03068 by the authors.

Figure 1
Figure 1. Infill designs computed using the strategies provided by SGLDBench. All designs consume roughly the same amount of material [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. SGLDBench’s visual analysis options. (a) Major (brown) and minor (green) PSLs according to boundary conditions from Fig. 1. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Element-based computation layout. M is the number of hexahedral simulation elements, Ke0 is the generic element stiffness matrix and Ue is the element-wise displacement matrix. Different colors represent the 8 node-based displacement vectors per element. With each column li in Ue, MATLAB computes the product Ke0 ·li . vectors at the vertices are organized into columns of an element￾wise displacement matrix, as illus… view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Material layout optimization with density-based TO (a) and porous infill optimization (b). Compliance history is depicted by the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Stress-aware Voronoi infill. (a) Scalar von Mises stress field. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Major (brown) and minor (green) PSLs in the solid object [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: Material fields generated with TO (a) and porous infill [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Same designs as in Fig. 1 but with lower material budget of roughly 0.22. [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: High resolution results using the same boundary conditions [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: A clip plane reveals the interior structure of different [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: Variable load structural analysis. Top row: All infills are optimized for the same boundary conditions (see inset with downward [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 14
Figure 14. Figure 14: Stress-to-stress alignment. High (white) to low (brown) alignment between stresses in the solid and the optimized infill with [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 58 canonical work pages

  1. [1]

    Optimal shape design as a material distribution problem,

    M. P. Bendsøe, “Optimal shape design as a material distribution problem,” Structural Optimization, vol. 1, no. 4, pp. 193–202, 1989

    work page 1989

  2. [2]

    Structural optimization using sensitivity analysis and a level-set method,

    G. Allaire, F. Jouve, and A.-M. Toader, “Structural optimization using sensitivity analysis and a level-set method,” Journal of Computational Physics, vol. 194, no. 1, pp. 363–393, 2004

    work page 2004

  3. [3]

    Topology optimization of multi-scale structures: a review,

    J. Wu, O. Sigmund, and J. P. Groen, “Topology optimization of multi-scale structures: a review,” Structural and Multidisciplinary Optimization , pp. 1–26, 2021

    work page 2021

  4. [4]

    On optimal orientation of orthotropic materials,

    P. Pedersen, “On optimal orientation of orthotropic materials,” Structural optimization, vol. 1, no. 2, pp. 101–106, 1989

    work page 1989

  5. [5]

    Lviii. the limits of economy of material in frame- structures,

    A. G. M. Michell, “Lviii. the limits of economy of material in frame- structures,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , vol. 8, no. 47, pp. 589–597, 1904

    work page 1904

  6. [6]

    Design and optimization of conforming lattice structures,

    J. Wu, W. Wang, and X. Gao, “Design and optimization of conforming lattice structures,” IEEE Transactions on Visualization and Computer Graphics, vol. 27, no. 1, pp. 43–56, 2021

    work page 2021

  7. [7]

    Review on design and structural optimisation in additive manufacturing: Towards next-generation lightweight structures,

    J. Plocher and A. Panesar, “Review on design and structural optimisation in additive manufacturing: Towards next-generation lightweight structures,” Materials & Design , vol. 183, p. 108164, 2019

    work page 2019

  8. [8]

    Reinforcement of general shell structures,

    F. Gil-Ureta, N. Pietroni, and D. Zorin, “Reinforcement of general shell structures,” ACM Transactions on Graphics (TOG) , vol. 39, no. 5, pp. 1–19, 2020

    work page 2020

Show all 61 references
  1. [9]

    A systematic review of voxelization method in additive manufacturing,

    A. Bacciaglia, A. Ceruti, and A. Liverani, “A systematic review of voxelization method in additive manufacturing,” Mechanics & Industry , vol. 20, no. 6, p. 630, 2019

    2019

  2. [10]

    The topology of symmetric, second- order tensor fields,

    T. Delmarcelle and L. Hesselink, “The topology of symmetric, second- order tensor fields,” in Proceedings Visualization’94. IEEE, 1994, pp. 140–147

    1994

  3. [11]

    A globally conforming lattice structure for 2D stress tensor visualization,

    J. Wang, J. Wu, and R. Westermann, “A globally conforming lattice structure for 2D stress tensor visualization,” Computer Graphics F orum, vol. 39, no. 3, pp. 417–427, 2020

    2020

  4. [12]

    Visualization of tensor fields in mechanics,

    C. Hergl, C. Blecha, V . Kretzschmar, F. Raith, F. G¨unther, M. Stommel, J. Jankowai, I. Hotz, T. Nagel, and G. Scheuermann, “Visualization of tensor fields in mechanics,” in Computer Graphics F orum, vol. 40, no. 6. Wiley Online Library, 2021, pp. 135–161

    2021

  5. [13]

    Global topology of 3d symmetric tensor fields,

    S.-H. Hung, Y . Zhang, and E. Zhang, “Global topology of 3d symmetric tensor fields,” IEEE Transactions on Visualization and Computer Graphics, 2023

    2023

  6. [14]

    Singularity aware de-homogenization for high-resolution topology optimized struc- tures,

    F. C. Stutz, J. P. Groen, O. Sigmund, and J. A. Bærentzen, “Singularity aware de-homogenization for high-resolution topology optimized struc- tures,” Structural and Multidisciplinary Optimization , aug 2020

    2020

  7. [15]

    Benchmarking optimization solvers for structural topology optimization,

    S. Rojas-Labanda and M. Stolpe, “Benchmarking optimization solvers for structural topology optimization,” Structural and Multidisciplinary Optimization, vol. 52, no. 3, pp. 527–547, 2015

    2015

  8. [16]

    Topology optimization benchmarks in 2d: results for minimum com- pliance and minimum volume in planar stress problems,

    S. I. Valdez, S. Botello, M. A. Ochoa, J. L. Marroqu´ın, and V . Cardoso, “Topology optimization benchmarks in 2d: results for minimum com- pliance and minimum volume in planar stress problems,” Archives of Computational Methods in Engineering , vol. 24, pp. 803–839, 2017

    2017

  9. [17]

    On benchmarking and good scientific practise in topology optimization,

    O. Sigmund, “On benchmarking and good scientific practise in topology optimization,” Structural and Multidisciplinary Optimization , vol. 65, no. 11, p. 315, 2022

    2022

  10. [18]

    Compressive strength assessment of 3d printing infill patterns,

    B. Pernet, J. K. Nagel, and H. Zhang, “Compressive strength assessment of 3d printing infill patterns,” Procedia CIRP , vol. 105, pp. 682–687, 2022, the 29th CIRP Conference on Life Cycle Engineering, April 4 – 6, 2022, Leuven, Belgium. [Online]. Available: https://www.science...

    2022

  11. [19]

    Multidisciplinary design optimization: a survey of architectures,

    J. R. Martins and A. B. Lambe, “Multidisciplinary design optimization: a survey of architectures,” AIAA journal, vol. 51, no. 9, pp. 2049–2075, 2013

    2013

  12. [20]

    The design process of additively manufactured mesoscale lattice structures: a review,

    F. Tamburrino, S. Graziosi, and M. Bordegoni, “The design process of additively manufactured mesoscale lattice structures: a review,” Journal of Computing and Information Science in Engineering , vol. 18, no. 4, p. 040801, 2018

    2018

  13. [21]

    Design and optimization of lattice structures: A review,

    C. Pan, Y . Han, and J. Lu, “Design and optimization of lattice structures: A review,” Applied Sciences, vol. 10, no. 18, p. 6374, 2020

    2020

  14. [22]

    A review on integration of lightweight gradient lattice structures in additive manufacturing parts,

    A. Seharing, A. H. Azman, and S. Abdullah, “A review on integration of lightweight gradient lattice structures in additive manufacturing parts,” Ad- vances in Mechanical Engineering , vol. 12, no. 6, p. 1687814020916951, 2020

    2020

  15. [23]

    Slm lattice structures: Properties, performance, applica- tions and challenges,

    T. Maconachie, M. Leary, B. Lozanovski, X. Zhang, M. Qian, O. Faruque, and M. Brandt, “Slm lattice structures: Properties, performance, applica- tions and challenges,” Materials & Design , vol. 183, p. 108137, 2019

    2019

  16. [24]

    A novel lattice structure topology optimization method with extreme anisotropic lattice properties,

    C. Zhang, J. Liu, Z. Yuan, S. Xu, B. Zou, L. Li, and Y . Ma, “A novel lattice structure topology optimization method with extreme anisotropic lattice properties,” Journal of Computational Design and Engineering , vol. 8, no. 5, pp. 1367–1390, 2021

    2021

  17. [25]

    Two-scale topology optimization with microstructures,

    B. Zhu, M. Skouras, D. Chen, and W. Matusik, “Two-scale topology optimization with microstructures,” ACM Transactions on Graphics (TOG), vol. 36, no. 4, p. 1, 2017

    2017

  18. [26]

    A real-time multigrid finite hexahedra method for elasticity simulation using cuda,

    C. Dick, J. Georgii, and R. Westermann, “A real-time multigrid finite hexahedra method for elasticity simulation using cuda,” Simulation Modelling Practice and Theory , vol. 19, no. 2, pp. 801–816, 2011

    2011

  19. [27]

    A system for high-resolution topology optimization,

    J. Wu, C. Dick, and R. Westermann, “A system for high-resolution topology optimization,” IEEE transactions on visualization and computer graphics, vol. 22, no. 3, pp. 1195–1208, 2015

    2015

  20. [28]

    Narrow-band topology optimization on a sparsely populated grid,

    H. Liu, Y . Hu, B. Zhu, W. Matusik, and E. Sifakis, “Narrow-band topology optimization on a sparsely populated grid,”ACM Transactions on Graphics (TOG), vol. 37, no. 6, pp. 1–14, 2018

    2018

  21. [29]

    Giga-voxel computational morphogenesis for structural design,

    N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature, vol. 550, no. 7674, pp. 84–86, 2017

    2017

  22. [30]

    A 99 line topology optimization code written in Matlab,

    O. Sigmund, “A 99 line topology optimization code written in Matlab,” Structural and multidisciplinary optimization , vol. 21, no. 2, pp. 120–127, 2001

    2001

  23. [31]

    Infill optimization for additive manufacturing – approaching bone-like porous structures,

    J. Wu, N. Aage, R. Westermann, and O. Sigmund, “Infill optimization for additive manufacturing – approaching bone-like porous structures,” IEEE Transactions on Visualization and Computer Graphics , vol. 24, no. 2, pp. 1127–1140, 2018

    2018

  24. [32]

    Build-to-last: Strength to weight 3d printed objects,

    L. Lu, A. Sharf, H. Zhao, Y . Wei, Q. Fan, X. Chen, Y . Savoye, C. Tu, D. Cohen-Or, and B. Chen, “Build-to-last: Strength to weight 3d printed objects,” ACM Transactions on Graphics (ToG), vol. 33, no. 4, pp. 1–10, 2014

    2014

  25. [33]

    Stress trajectory guided structural design and topology optimization,

    J. Wang, J. Wu, and R. Westermann, “Stress trajectory guided structural design and topology optimization,” in International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 1. American Society of Mechanical Engineers, 2022, p. 1

    2022

  26. [34]

    Robust hex-dominant mesh generation using field-guided polyhedral agglomeration,

    X. Gao, W. Jakob, M. Tarini, and D. Panozzo, “Robust hex-dominant mesh generation using field-guided polyhedral agglomeration,” ACM Transactions on Graphics (TOG) , vol. 36, no. 4, pp. 1–13, 2017. 13

    2017

  27. [35]

    V olumetric michell trusses for parametric design & fabrication,

    R. Arora, A. Jacobson, T. R. Langlois, Y . Huang, C. Mueller, W. Matusik, A. Shamir, K. Singh, and D. I. Levin, “V olumetric michell trusses for parametric design & fabrication,” in Proceedings of the ACM Symposium on Computational Fabrication. ACM, 2019, pp. 1–13

    2019

  28. [36]

    3D-TSV: The 3D trajectory-based stress visualizer,

    J. Wang, C. Neuhauser, J. Wu, X. Gao, and R. Westermann, “3D-TSV: The 3D trajectory-based stress visualizer,” Advances in Engineering Software , vol. 170, p. 103144, 2022

    2022

  29. [37]

    A. H. Aitkenhead. (2013) Mesh voxelisation. [On- line]. Available: https://www.mathworks.com/matlabcentral/fileexchange/ 27390-mesh-voxelisation

    2013

  30. [38]

    Simple and efficient gpu accelerated topology optimisation: Codes and applications,

    E. A. Tr ¨aff, A. Rydahl, S. Karlsson, O. Sigmund, and N. Aage, “Simple and efficient gpu accelerated topology optimisation: Codes and applications,” Computer Methods in Applied Mechanics and Engineering , vol. 410, p. 116043, 2023

    2023

  31. [39]

    An efficient 3d topology optimization code written in matlab,

    K. Liu and A. Tovar, “An efficient 3d topology optimization code written in matlab,” Structural and multidisciplinary optimization , vol. 50, pp. 1175–1196, 2014

    2014

  32. [40]

    On projection methods, convergence and robust formulations in topology optimization,

    F. Wang, B. S. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Structural and Multidisciplinary Optimization , vol. 43, no. 6, pp. 767–784, 2011

    2011

  33. [41]

    The method of moving asymptotes—a new method for structural optimization,

    K. Svanberg, “The method of moving asymptotes—a new method for structural optimization,” International journal for numerical methods in engineering, vol. 24, no. 2, pp. 359–373, 1987

    1987

  34. [42]

    Procedural voronoi foams for additive manufacturing,

    J. Mart´ınez, J. Dumas, and S. Lefebvre, “Procedural voronoi foams for additive manufacturing,” ACM Transactions on Graphics (TOG) , vol. 35, no. 4, pp. 1–12, 2016

    2016

  35. [43]

    Orthotropic k-nearest foams for additive manufacturing,

    J. Mart´ınez, H. Song, J. Dumas, and S. Lefebvre, “Orthotropic k-nearest foams for additive manufacturing,” ACM Trans. Graph., vol. 36, no. 4, Jul. 2017. [Online]. Available: https://doi.org/10.1145/3072959.3073638

    2017

  36. [44]

    Robust inside-outside segmentation using generalized winding numbers,

    A. Jacobson, L. Kavan, and O. Sorkine-Hornung, “Robust inside-outside segmentation using generalized winding numbers,” ACM Transactions on Graphics (TOG), vol. 32, no. 4, pp. 1–12, 2013

    2013

  37. [45]

    Reentrant polygon clipping,

    I. E. Sutherland and G. W. Hodgman, “Reentrant polygon clipping,” Communications of the ACM , vol. 17, no. 1, pp. 32–42, 1974

    1974

  38. [46]

    Triangulating topological spaces,

    H. Edelsbrunner and N. R. Shah, “Triangulating topological spaces,” in Proceedings of the tenth annual symposium on Computational geometry , 1994, pp. 285–292

    1994

  39. [47]

    Polyhedral voronoi diagrams for additive manufacturing,

    J. Mart´ınez, S. Hornus, H. Song, and S. Lefebvre, “Polyhedral voronoi diagrams for additive manufacturing,” ACM Transactions on Graphics (TOG), vol. 37, no. 4, pp. 1–15, 2018

    2018

  40. [48]

    Scipy 1.0: fundamental algorithms for scientific computing in python,

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright et al., “Scipy 1.0: fundamental algorithms for scientific computing in python,” Nature methods, vol. 17, no. 3, pp. 261–272, 2020

    2020

  41. [49]

    The quickhull algorithm for convex hulls,

    C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The quickhull algorithm for convex hulls,” ACM Transactions on Mathematical Software (TOMS) , vol. 22, no. 4, pp. 469–483, 1996

    1996

  42. [50]

    A structural topology design method based on principal stress line,

    T.-H. Kwok, Y . Li, and Y . Chen, “A structural topology design method based on principal stress line,”Computer-Aided Design, vol. 80, pp. 19–31, 2016

    2016

  43. [51]

    Trajectory-based stress tensor visualization and its application in structural design and optimization,

    J. Wang, “Trajectory-based stress tensor visualization and its application in structural design and optimization,” Ph.D. dissertation, Technische Universit¨at M¨unchen, 2023

    2023

  44. [52]

    A post-treatment of the homogenization method for shape optimization,

    O. Pantz and K. Trabelsi, “A post-treatment of the homogenization method for shape optimization,” SIAM Journal on Control and Optimization , vol. 47, no. 3, pp. 1380–1398, 2008

    2008

  45. [53]

    Homogenization-based topology optimiza- tion for high-resolution manufacturable microstructures,

    J. P. Groen and O. Sigmund, “Homogenization-based topology optimiza- tion for high-resolution manufacturable microstructures,” International Journal for Numerical Methods in Engineering , vol. 113, no. 8, pp. 1148– 1163, 2018

    2018

  46. [54]

    Topology optimization of modulated and oriented periodic microstructures by the homogenization method,

    G. Allaire, P. Geoffroy-Donders, and O. Pantz, “Topology optimization of modulated and oriented periodic microstructures by the homogenization method,” Computers & Mathematics with Applications , vol. 78, no. 7, pp. 2197–2229, 2019

    2019

  47. [55]

    Continuous stress fields in finite element analysis,

    G. Loubignac, G. Cantin, and G. Touzot, “Continuous stress fields in finite element analysis,” AIAA journal, vol. 15, no. 11, pp. 1645–1647, 1977

    1977

  48. [56]

    A fast voxel traversal algorithm for ray tracing

    J. Amanatides and A. Woo, “A fast voxel traversal algorithm for ray tracing.” in Eurographics, vol. 87, no. 3. Citeseer, 1987, pp. 3–10

    1987

  49. [57]

    Worst-case structural analysis

    Q. Zhou, J. Panetta, and D. Zorin, “Worst-case structural analysis.” ACM Trans. Graph., vol. 32, no. 4, pp. 137–1, 2013

    2013

  50. [58]

    Large-scale worst- case topology optimization,

    D. Zhang, X. Zhai, X.-M. Fu, H. Wang, and L. Liu, “Large-scale worst- case topology optimization,” in Computer Graphics F orum, vol. 41, no. 7. Wiley Online Library, 2022, pp. 529–540

    2022

  51. [59]

    Tetgen, a delaunay-based quality tetrahedral mesh generator,

    S. Hang, “Tetgen, a delaunay-based quality tetrahedral mesh generator,” ACM Trans. Math. Softw , vol. 41, no. 2, p. 11, 2015

    2015

  52. [60]

    Fast tetrahedral meshing in the wild,

    Y . Hu, T. Schneider, B. Wang, D. Zorin, and D. Panozzo, “Fast tetrahedral meshing in the wild,” ACM Transactions on Graphics (ToG) , vol. 39, no. 4, pp. 117–1, 2020

    2020

  53. [61]

    Parallel framework for topology optimization using the method of moving asymptotes,

    N. Aage and B. S. Lazarov, “Parallel framework for topology optimization using the method of moving asymptotes,” Structural and multidisciplinary optimization, vol. 47, no. 4, pp. 493–505, 2013. Junpeng Wang is a Post-doc in the Computer Graphics and Visualization Group at Tec...

    2013

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.