Pith. sign in

REVIEW 1 major objections 5 minor 80 references

Fast Tetrahedral Meshing in the Wild

T0 review · 1 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read fTetWild converts messy triangle soups into valid floating-point tetrahedral meshes about seven times faster than TetWild, with similar quality.

desk verdict fTetWild is a genuine step forward in robust tetrahedral meshing — fast, well-evaluated, and honestly disclosed — but its advertised 'always valid' guarantee leans on an unverified subdivision-table enumeration. read the letter →

arxiv 1908.03581 v2 pith:23AAK3VA submitted 2019-08-09 cs.GR

Yixin Hu , Teseo Schneider , Bolun Wang , Denis Zorin , Daniele Panozzo This is my paper · ORCID
classification cs.GR
keywords tetrahedralmeshingtrianglesoupsfloating-pointrobustnessincrementalinsertionsubdivisiontableepsilon-envelopeAMIPSenergymeshrepair
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 presents fTetWild, a tetrahedral meshing algorithm that turns imperfect triangle soups—inputs with gaps, self-intersections, and degenerate faces—into high-quality volumetric tetrahedral meshes. Its central claim is that, by inserting one input triangle at a time into a floating-point background mesh and rejecting any local operation that would invert an element, the algorithm can guarantee a valid floating-point tetrahedral mesh at every stage, something the rational-number-based TetWild could only achieve up to a final rounding step. The payoff is practical: average running time on the Thingi10k dataset drops from 360 to 49.8 seconds, comparable to Delaunay-based meshers that cannot handle such inputs. The trade-off is that the algorithm no longer formally guarantees every input triangle is present in the output, although in all tested cases it inserted every triangle.

What carries the argument

The engine is the incremental triangle-insertion routine. Each input triangle is inserted into the current tetrahedral mesh one at a time: the algorithm finds the set of tetrahedra the triangle cuts, snaps nearby vertices onto the triangle's plane when this does not invert elements, computes plane-edge intersections, and subdivides all affected tetrahedra using a precomputed subdivision table. The table encodes 41 realizable edge-cut configurations (falling into 7 symmetry classes), and a vertex-ordering rule chooses which secondary triangulation to use so that adjacent tetrahedra agree on shared faces, preserving mesh topology. Exact orientation predicates are used only for the robust predicates, not for coordinate construction. Mesh improvement uses the conformal AMIPS energy, with a hybrid rational evaluation only for energy values above 1e8 to avoid numerical instability that caused over-refinement.

What would settle it

Instrument fTetWild to log every edge-cut configuration encountered on the Thingi10k dataset and on adversarial inputs; finding a single realizable configuration outside the 41 listed cases—for example, a tetrahedron with five cut edges after snapping—would break the subdivision table and the validity guarantee.

Watch

Extended reading notes

Core claim

The paper's discovery is that rational arithmetic is not needed for robust tetrahedral meshing in the wild. By interleaving incremental triangle insertion with local mesh optimization, fTetWild maintains a mesh that is valid (all tetrahedra have positive volume) and whose tracked surface stays within an epsilon-envelope of the input, using only floating-point coordinates. Because the mesh is always valid, any stopping point yields a usable mesh, and the output is guaranteed to be a valid floating-point tetrahedral mesh regardless of stopping criteria. The paper reports 100% success on all 10,000 Thingi10k models within 11 hours, an average 7x speedup over TetWild, and output quality statistically similar to TetWild.

Load-bearing premise

The validity guarantee rests on the assumption that the 41-entry subdivision table, combined with the vertex-ordering rule, covers every realizable way a plane can cut a tetrahedron's edges after snapping; this is asserted by enumeration but not formally verified.

Editorial extensions

If this is right

  • Any user-specified stopping criterion (quality threshold or iteration cap) produces a valid mesh, so meshing can be tuned against simulation accuracy rather than against validity.
  • Because no exact rational construction is needed, the core routine parallelizes more easily; the paper reports an additional speedup from shared-memory parallelization of preprocessing and smoothing.
  • The same pipeline gives an approximate mesh arrangement and Boolean-operation method for non-PWN, self-intersecting, non-manifold triangle soups, where CGAL and Mesh Arrangements fail.
  • Mesh repair can extract a manifold boundary surface from the tet mesh, with controllable geometric error given by the envelope size.
  • On the Thingi10k dataset, fTetWild averages 49.8 seconds per model versus 360 seconds for TetWild, with 98.7% of models finishing in under two minutes.

Reading between the lines

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

  • If the table-completeness claim were formally verified (for example, machine-checked), the 'always valid' guarantee would become a fully rigorous theorem; currently it rests on enumeration plus an unverified ordering rule.
  • The incremental insertion strategy suggests a natural dynamic remeshing use: start from an existing mesh and insert new constraint triangles only in regions where the geometry changed, which the authors note but do not develop.
  • The same table-based subdivision could be reused as a general routine for cutting a tetrahedral mesh by an arbitrary plane in other applications, since it handles both cut and neighbor tetrahedra.
  • Because validity is guaranteed at every stage, one could adaptively decide on the fly whether to improve the mesh further based on downstream simulation needs, without risking the loss of the mesh.
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

1 major / 5 minor

Summary. This paper introduces fTetWild, a tetrahedral meshing algorithm for imperfect triangle soups. It follows the TetWild pipeline (envelope preprocessing, background Delaunay mesh, incremental input-triangle insertion, AMIPS-based mesh optimization, and winding-number filtering) but replaces rational triangle insertion with a floating-point insertion procedure. Each inserted triangle is handled by finding cut tetrahedra, optional snapping with tolerance delta, and a table-based subdivision of affected tetrahedra; invalid operations are rejected and rolled back. The paper claims that fTetWild always maintains a valid floating-point tetrahedral mesh regardless of stopping criteria, that it is roughly 4x7x faster than TetWild on Thingi10k while producing comparable element quality, and that it supports mesh repair, approximate Boolean operations, and simulation-ready meshes.

Significance. If the guarantees hold, this is a significant practical contribution: it removes the rational-arithmetic bottleneck of TetWild and gives a floating-point validity guarantee that TetWild cannot provide. The evaluation is unusually strong: 100% success on all 10,000 Thingi10k models, transparent caveats about average-time comparisons over different subsets, a released implementation and reproduction scripts, and demonstrations on challenging industrial and architectural models. The central gap is the formal verification of the 41-case subdivision table and the secondary-index rule, which support the unconditional validity claim; because the code is provided, this gap is checkable and could be closed by an exhaustive or machine-checked enumeration.

major comments (1)
  1. [Section 3.4.2; Appendix C; Appendix E] The central guarantee that fTetWild always produces a valid floating-point tetrahedral mesh depends on two assertions in Section 3.4.2: that the 41 listed edge-cut configurations 'cover all subdivision cases,' and that the vertex-ordering rule 'completely identifies a secondary index and preserves the topology of the mesh.' The paper states that a direct enumeration eliminates 23 configurations, leaving 41, but it does not provide the enumeration, a proof, or a machine-checked certificate. Appendix C only rules out two decompositions requiring an internal vertex; it does not prove that the 41 configurations are exhaustive after the snapping operations described in Section 3.4.2, whose interaction with edge cuts is only tabulated (Appendix E), not derived. If a realizable configuration were missing, or if the secondary-index rule ever produced incompatible triangulations on a face shared by two subdivided tetrahedra, adjacent tetrahedra would become non-conforming and the claimed validity guarantee would fail. Because the guarantee is universal, this is a load-bearing point rather than a presentation detail. I ask the authors to provide either a machine-checked exhaustive enumeration of all snapping configurations and all secondary-index choices, or a formal argument that the triangulation rule is consistent on shared faces. If this cannot be supplied, the unconditional wording of the guarantee should be weakened to a statement conditional on the table being complete, with the relevant experiments reported as supporting evidence.
minor comments (5)
  1. [Figure 5] The caption and labels contain a typo ('Traingle Insertion') and the rightmost panel is unlabeled; please correct these presentation issues.
  2. [Figure 1 caption] The caption writes 'fTeWild' where 'fTetWild' is meant; please fix the typo.
  3. [Section 3.4.2] The phrase 'pre-computedtet-subdivision table' is missing a space; more importantly, Table 1 shows only a subset, so the complete table and the list of all 41 configurations should be included in the manuscript or referenced with a stable identifier in the supplementary material.
  4. [Section 4, Table 2] The note that average times are computed over different per-method success sets is helpful; I suggest also reporting the median and 95th percentile since the means may be dominated by long tails.
  5. [Appendix B] The example of AMIPS instability is useful; consider stating explicitly which permutation-invariance property of the energy is being demonstrated, since the four listed values are all from different vertex orders.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: fTetWild's validity guarantee and benchmark claims rest on an independent construction and external data, not on self-citation or fitted inputs.

full rationale

The claimed derivation chain is self-contained rather than circular. fTetWild's validity guarantee is maintained as an algorithmic invariant: every triangle insertion is checked with exact predicates (Shewchuk 1997; Levy 2019), rejected if it would create inverted or degenerate tetrahedra, and rolled back otherwise (Sections 3.1 and 3.4.2), so the claim that a valid floating-point mesh is always produced is not equivalent to any fitted parameter or input quantity. The tet-subdivision table is an original enumeration of 41 realizable edge-cut configurations; the statement that these cover all subdivision cases is a combinatorial assertion that can be checked independently, and it does not reduce to the inputs or to a prior self-citation. The paper's performance comparisons use the external Thingi10k dataset and the same stopping criteria and input parameters as TetWild (Section 4), so the observed speed and success-rate numbers are not self-predictions. The paper does cite the authors' own TetWild for the envelope construction, preprocessing, and mesh improvement framework, but those citations are appropriate lineage references to a released, externally benchmarked system; the central novelty, floating-point incremental insertion with table-based subdivision, does not reduce to those citations. Appendix C and E provide enumerative arguments about unused decompositions and snapping, and their lack of machine-checking is a rigor concern rather than a circularity concern. No self-definitional, fitted-input-called-prediction, or self-citation-chain circularity is present.

Assumptions & free parameters 6 free parameters · 3 assumptions · 0 invented entities

The central claims depend on a small set of hand-chosen algorithm parameters (envelope size, snapping tolerance, stopping criteria) and on the correctness of inherited components (exact predicates, envelope tests) and on the completeness of the paper-specific subdivision table enumeration. No invented physical or mathematical entities are introduced.

free parameters (6)
  • envelope size epsilon = 10^-3 d (default)
    User-controlled geometric tolerance; bounds how far the output surface may deviate from the input. Set to the same value as TetWild in all experiments.
  • target edge length l = d/20 (default)
    User-controlled target resolution; same as TetWild. Affects mesh density and runtime.
  • snapping tolerance delta = 10^-3*epsilon for first pass, 10^-8 afterwards
    Heuristic chosen to improve insertion success with floating point arithmetic; not fitted to a target scientific outcome.
  • preprocessing envelope ratio = 0.8
    Hand-chosen from range 0.7 to 0.999; authors report minor impact on runtime and negligible effect on output.
  • epsilon_zero = 10^-8
    Numerical tolerance for distances, areas, and volumes; authors state performance is insensitive above 10^-20.
  • stopping criteria = max AMIPS energy < 10 or 80 iterations
    Terminates mesh improvement; same as TetWild; affects final quality and runtime.
assumptions (3)
  • domain assumption The envelope containment test by sampling with conservative compensation (Hu et al. 2018) correctly keeps the tracked surface within the epsilon-envelope.
    Used in preprocessing (Section 3.3) and throughout; inherited without modification from TetWild.
  • ad hoc to paper The enumeration of 41 realizable tetrahedron edge-cut configurations and the vertex-ordering rule cover all snapping cases and preserve mesh topology.
    Asserted by direct enumeration (Section 3.4.2, Appendix C); not machine-checked in the paper.
  • standard math Exact orientation predicates (Shewchuk; Levy/Geogram) are correct and are used for all decisions that determine mesh validity.
    Assumed correctness of well-established robust predicates; the validity guarantee relies on these checks.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Fast Tetrahedral Meshing in the Wild." pith.science (2026). https://pith.science/paper/23AAK3VA

@misc{pith2026190803581,
  author       = {Pith},
  title        = {Pith review of: Fast Tetrahedral Meshing in the Wild},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23AAK3VA}},
  note         = {Machine review of arXiv:1908.03581}
}
read the original abstract

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.

Figures

Figures reproduced from arXiv: 1908.03581 by the authors.

Figure 1
Figure 1. The bar charts show the percentage of models requiring more than the indicated time for the different approaches over 4 540 inputs (the subset of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Example of an input surface mesh with self-intersections and a bad triangulation on the base. fTetWild converts this model into a high-quality tetrahedral mesh. eliminating near-degenerate or overly refined triangles in the input model, which [Zhou et al. 2016] cannot do. We also make fewer assumptions on the inputs, allowing gaps, self-intersections, and degeneracies. 3 METHOD fTetWild takes as input a 3D triangle … view at source ↗
Figure 3
Figure 3. Overview of our algorithm. From left to right, the input mesh is simplified, a background mesh is created and the input faces are inserted, the mesh [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (22 more)
Figure 5
Figure 5. Figure 5: Segment insertion into a triangle mesh (a 2D analog of triangle insertion) with and without snapping. (a) Insertion of segment pq into mesh M. (b) Identification of cut triangles TI (in red). (c) Snapping vertex v to line pq and updating TI , where v is δ -close to pq.…
Figure 6
Figure 6. Figure 6: Examples of tetrahedra T included into, or excluded from, TI . The intersections are shown in red. Left two:T intersects a face of T at a segment ([p1, p2]) or a polygon ([p1, p2, p3]) that contains interior points of both T and the intersected face of T. In this case,…
Figure 7
Figure 7. Figure 7: Plane P intersects TI (T ∈ TI ). (a) The faces of F (marked in yellow) are the covering of triangle T . (b) Snapping v to its closest point on P and expanding F to include red triangles makes F safely covering T . (c) Snapping a boundary vertex p1 of F to v changes the…
Figure 8
Figure 8. Figure 8: 2D illustration of step (1) to (3) of snapping when inserting segment [p, q]. The cut triangles in TI are marked in red. (1) Vertex v is within δ distance to segment [p, q]. (2) Check the effect of moving v to line [p, q]. (Vertex v cannot be moved to [p, q] in this ca…
Figure 9
Figure 9. Figure 9: 7 symmetry classes of edge-cut configurations. (4) and (6) can only happen on neighboring tetrahedra of TI with only certain edges cut by P. We retrieve a list of decompositions of T corresponding to a primary index; we now need to select a secondary index corre￾spondi…
Figure 10
Figure 10. Figure 10: Example of model where the numerical instability of the AMIPS energy causes over-refinement (middle). By evaluating the energy using rational numbers (when it is above 108 ) the issue disappears (right). 3.5 Mesh Improvement We adapt the mesh improvement framework pro…
Figure 11
Figure 11. Figure 11: Input with open boundary on the bottom (left). The output tetrahe￾dral mesh preserves the input geometry and closes the open side (middle). Users can choose to enable an additional smoothing process for smoothing the open region (right). the vertices of T, however its…
Figure 12
Figure 12. Figure 12: 1000 random samples of fTetWild output on Thingi10k dataset. Memory usage of fTetWild (MB) [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 15
Figure 15. Figure 15: Example of a challenging model where fTetWild is 17 times faster than TetWild. of TetWild ( [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]
Figure 16
Figure 16. Figure 16: Our method (right) produces high-quality tet-meshes that are [PITH_FULL_IMAGE:figures/full_fig_p011_16.png]
Figure 17
Figure 17. Figure 17: shows the histograms of worst and average element quality of 10 000 output meshes of TetWild and our method. The quality of our outputs are quite similar to TetWild’s output. We refer to the study in [Hu et al. 2018, [PITH_FULL_IMAGE:figures/full_fig_p011_17.png]
Figure 18
Figure 18. Figure 18: Histograms of number of tetrahedra in log scale for the output meshes of Thingi10k dataset. Input #F = 16 248 MeshFix 23s #F = 13 486 Our 129s #F = 31 348 [PITH_FULL_IMAGE:figures/full_fig_p012_18.png]
Figure 20
Figure 20. Figure 20: Example of a non-manifold surface mesh (left) which is automati￾cally repaired by our algorithm (right second). used to repair triangle meshes, guaranteeing the extraction of an high-quality, manifold boundary surface mesh within the prescribed distance from the input…
Figure 19
Figure 19. Figure 19: Example of repairing an invalid triangular mesh (left) with MeshFix [PITH_FULL_IMAGE:figures/full_fig_p012_19.png]
Figure 21
Figure 21. Figure 21: Meshing a complex model with 93 million vertices and 31 million [PITH_FULL_IMAGE:figures/full_fig_p013_21.png]
Figure 22
Figure 22. Figure 22: Example of an architectural application with 80 999 self-intersecting faces. The cylinders in the input are intersecting with each other as shown in the closeup. fTetWild successfully cleaned and tetrahedralized this input. Here we stop mesh optimization when maximum …
Figure 23
Figure 23. Figure 23: Three Boolean operations computed on non-manifold, self-intersecting, and non-PWN input surface meshes. The left are two objects for Boolean [PITH_FULL_IMAGE:figures/full_fig_p014_23.png]
Figure 24
Figure 24. Figure 24: Four Boolean operations among 5 objects. fTetWild takes 34s and products output with #T = 8 060 and max energy = 7.2. Input #F = 8 436 Time 58s #T = 16 291 Max energy = 7.9 Elastic deformation [PITH_FULL_IMAGE:figures/full_fig_p014_24.png]
Figure 25
Figure 25. Figure 25: Example of non-linear elastic deformation of a body (right). Input #F = 30 580 Max energy ≤ 10, 107s #T = 90 438 Max energy = 8.0 p ≤ 4, 69s #T = 41 735 Max energy = 32.4 [PITH_FULL_IMAGE:figures/full_fig_p014_25.png]
Figure 26
Figure 26. Figure 26: Two different stopping criteria of our algorithm. The full optimiza [PITH_FULL_IMAGE:figures/full_fig_p014_26.png]
Figure 28
Figure 28. Figure 28: Two unused configurations requiring an additional vertex. T T P p1 p2 p3 p4 e (1) (2) (3) [PITH_FULL_IMAGE:figures/full_fig_p017_28.png]
Figure 29
Figure 29. Figure 29: Example for preserving an open-boundary edge e of triangle T . (1) Insert T and TI = {T } in this case. (2) The sub-tetrahedra of T after subdi￾vision. (Only sub-tetrahedra behind T are shown for better visualization.) (3) Inserting edge e and get the intersection poi…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

80 extracted references · 61 canonical work pages

  1. [1]

    1531381 G

    https://doi.org/10.1145/1531326. 1531381 G. Varadhan, S. Krishnan, T. Sriram, and D. Manocha

    doi:10.1145/1531326

  2. [8]

    Direct Repair of Self-intersecting Meshes. Graph. Models 76, 6 (Nov. 2014), 658–668. https://doi.org/10.1016/j.gmod.2014.09.002 M. Attene

    work page doi:10.1016/j.gmod.2014.09.002 2014

  3. [9]

    To preserve them, we subdivide the tetrahedra once more

    Before 1 vertex snapped 2 vertices snapped 3 vertices snapped (2) (1) (2) (1) (3) (1)(2) (1)(2) (1) (5) (1)(3) (1)(2) (1)(2) (7) (3) (1)(3) (1) not preserved. To preserve them, we subdivide the tetrahedra once more. In Figure 29(1),T first get decomposed into sub-tetrahedra (Fig- ure 29(2)). Then the faces coveringT areF ={[p1, p2, p3],[p4, p2, p3]} Figur...

    work page 2020

  4. [16]

    https: //doi.org/10.1145/2983621 J.-F. Remacle

    doi:10.1145/2983621

  5. [21]

    InProceedings of the 21st International Meshing Roundtable

    Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains With Bounded Quality. InProceedings of the 21st International Meshing Roundtable . Springer Berlin Heidelberg, Berlin, Heidelberg, 191–209. https://doi.org/10.1007/978-3-642-33573-0_12 O. Busaryev, T. K. Dey, and J. A. Levine

    work page doi:10.1007/978-3-642-33573-0_12

  6. [22]

    In 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling (SPM ’09)

    Repairing and Meshing Imperfect Shapes with Delaunay Refinement. In 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling (SPM ’09) . ACM, New York, NY, USA, 25–33. https://doi.org/10. 1145/1629255.1629259 M. Campen and L. Kobbelt

    work page arXiv 2009

  7. [23]

    Exact and Robust (self-)intersections for Polygonal Meshes. Comput. Graph. Forum 29, 2 (2010), 397–406. S. A. Canann, S. N. Muthukrishnan, and R. K. Phillips

    work page 2010

  8. [26]

    The full optimiza- tion (middle) improves the mesh to high quality, while using the criterion in [Schneider et al

    Two different stopping criteria of our algorithm. The full optimiza- tion (middle) improves the mesh to high quality, while using the criterion in [Schneider et al. 2018] (right) results in lower mesh quality but faster meshing and smaller mesh size. The color shows the solution of the volu- metric Laplace equation. M. Alexa

    work page 2018

Show all 80 references
  1. [27]

    The background mesh (middle) is obtained by subtracting the obstacle from a cylinder using our method

    Streamlines of a fluid (right) moving in a cylindrical pipe (left top) with a complicated obstacle (left bottom) in the center. The background mesh (middle) is obtained by subtracting the obstacle from a cylinder using our method. P. Alliez, D. Cohen-Steiner, M. Yvinec, and M....

    2005

  2. [30]

    In Pro- ceedings of the ninth annual symposium on Computational geometry - SCG ’93

    Guaranteed-Quality Mesh Generation for Curved Surfaces. In Pro- ceedings of the ninth annual symposium on Computational geometry - SCG ’93 . ACM Press, New York, NY, USA, 274–280. https://doi.org/10.1145/160985.161150 D. Cohen-Steiner, E. C. de Verdière, and M. Yvinec

  3. [32]

    In Proceedings of the 21st International Meshing Roundtable

    Automatic 3D Mesh Generation of Multiple Domains for Topology Optimization Methods. In Proceedings of the 21st International Meshing Roundtable. Springer Berlin Heidelberg, Berlin, Heidelberg, 243–259. https://doi.org/10.1007/978-3-642-33573-0_15 T. K. Dey and J. A. Levine

    doi

  4. [33]

    In Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG ’08

    Delpsc: A Delaunay Mesher for Piecewise Smooth Complexes. In Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG ’08 . ACM Press, New York, NY, USA, 220–221. https://doi.org/10. 1145/1377676.1377712 A. Doi and A. Koide

  5. [34]

    IEICE TRANSACTIONS on Information and Systems 74, 1 (1991), 214–224

    An efficient method of triangulating equi-valued surfaces by using tetrahedral cells. IEICE TRANSACTIONS on Information and Systems 74, 1 (1991), 214–224. C. Doran, A. Chang, and R. Bridson

    1991

  6. [35]

    In ACM SIGGRAPH 2013 Talks on - SIGGRAPH ’13

    Isosurface Stuffing Improved: Acute Lattices and Feature Matching. In ACM SIGGRAPH 2013 Talks on - SIGGRAPH ’13 . ACM Press, New York, NY, USA, 38:1–38:1. https://doi.org/10.1145/2504459.2504507 M. Douze, J.-S. Franco, and B. Raffin

    2013

  7. [37]

    ACM Trans

    Curved Optimal Delaunay Triangulation. ACM Trans. Graph. 37, 4 (2018), 61:1–61:16. X.-M. Fu, Y. Liu, and B. Guo

    2018

  8. [39]

    Internat

    ’Ultimate’ robust- ness in meshing an arbitrary polyhedron. Internat. J. Numer. Meth- ods Engrg. 58, 7 (2003), 1061–1089. https://doi.org/10.1002/nme.808 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.808 M. Granados, P. Hachenberger, S. Hert, L. Kettner, K. Mehlhor...

    2003 doi

  9. [40]

    Journal of graphics tools 8, 1 (2003), 39–52

    Fast and Robust Triangle-Triangle Overlap Test Using Orientation Predicates. Journal of graphics tools 8, 1 (2003), 39–52. https: //doi.org/10.1080/10867651.2003.10487580 P. Hachenberger and L. Kettner

    2003

  10. [41]

    In Proceedings of the 22nd International Meshing Roundtable

    MOSS: Multiple Orthogonal Strand System. In Proceedings of the 22nd International Meshing Roundtable. Springer International Publishing, Cham, 75–91. https://doi.org/10.1007/978-3-319-02335-9_5 K. Hu, D. Yan, D. Bommes, P. Alliez, and B. Benes

    doi

  11. [43]

    ACM Trans

    TriWild: Robust Triangulation with Curve Constraints. ACM Trans. Graph. (2019). Y. Hu, Q. Zhou, X. Gao, A. Jacobson, D. Zorin, and D. Panozzo

    2019

  12. [44]

    ACM Trans

    Tetrahedral Meshing in the Wild. ACM Trans. Graph. 37, 4, Article 60 (July 2018), 14 pages. https://doi.org/10.1145/3197517.3201353 C. Jamin, P. Alliez, M. Yvinec, and J.-D. Boissonnat

    2018

  13. [45]

    ACM Trans

    CGALmesh: A Generic Framework for Delaunay Mesh Generation. ACM Trans. Math. Software 41, 4 (10 2015), 1–24. https://doi.org/10.1145/2699463 F. Labelle and J. R. Shewchuk

    2015 doi

  14. [50]

    ACM Trans

    Isotopic Approximation Within a Tolerance Volume. ACM Trans. Graph. 34, 4, Article 64 (July 2015), 12 pages. https://doi.org/10.1145/2766950 A. Masoud

    2015 doi

  15. [52]

    ACM Trans

    Level set surface editing operators. ACM Trans. Graph. 21, 3 (2002), 330–338. B. Naylor, J. Amanatides, and W. Thibault

    2002

  16. [53]

    CoRR abs/1704.00142 (2017)

    Arrangements of cellular complexes. CoRR abs/1704.00142 (2017). arXiv:1704.00142 http://arxiv.org/abs/1704.00142 D. Pavic, M. Campen, and L. Kobbelt

    2017 arXiv

  17. [54]

    Hybrid Booleans. Comput. Graph. Forum 29 (2010), 75–87. J. Peraire, M. Vahdati, K. Morgan, and O. C. Zienkiewicz

    2010

  18. [55]

    Adaptive Remeshing for Compressible Flow Computations. J. Comput. Phys. 72, 2 (Oct. 1987), 449–466. https://doi.org/10.1016/0021-9991(87)90093-3 M. Rabinovich, R. Poranne, D. Panozzo, and O. Sorkine-Hornung

    1987 doi

  19. [56]

    ACM Trans

    Scalable Locally Injective Mappings. ACM Trans. Graph. 36, 2 (April 2017),

    2017

  20. [57]

    https://doi.org/10.1145/1275808.1276448 B. Lévy

  21. [58]

    Computer-Aided Design 85 (04 2017), 2–9

    A Two-Level Multithreaded Delaunay Kernel. Computer-Aided Design 85 (04 2017), 2–9. https://doi.org/10.1016/j.cad.2016.07.018 J. Ruppert

    2017 doi

  22. [60]

    et al jagm.1995.1021 E

    16 • Hu, Y. et al jagm.1995.1021 E. A. Sadek

    1995

  23. [62]

    In ACM SIGGRAPH 2010 Talks

    Meshmixer: an interface for rapid mesh composition. In ACM SIGGRAPH 2010 Talks. ACM, ACM, New York, NY, USA,

    2010

  24. [63]

    ACM Transactions on Graphics 37, 6 (dec 2018), 1–14

    Decoupling simulation accuracy from mesh quality. ACM Transactions on Graphics 37, 6 (dec 2018), 1–14. https://doi.org/10.1145/3272127.3275067 M. Schweiger and S. Arridge

    2018

  25. [64]

    Internat

    Basis mapping methods for forward and inverse problems: BASIS MAPPING METHODS. Internat. J. Numer. Methods Engrg. 109 (05 2016). https://doi.org/10.1002/nme.5271 D. R. Sheehy

    2016 doi

  26. [65]

    Computer Graphics Forum 31, 5 (08 2012), 1627–1635

    New Bounds on the Size of Optimal Meshes. Computer Graphics Forum 31, 5 (08 2012), 1627–1635. https://doi.org/10.1111/j.1467-8659.2012.03168.x B. Sheng, P. Li, H. Fu, L. Ma, and E. Wu. 2018a. Efficient non-incremental constructive solid geometry evaluation for triangular meshe...

    2018

  27. [67]

    In Proceedings of the fourteenth annual symposium on Computational geometry - SCG ’98

    Tetrahedral Mesh Generation by Delaunay Refinement. In Proceedings of the fourteenth annual symposium on Computational geometry - SCG ’98. ACM Press, New York, NY, USA, 86–95. https://doi.org/10.1145/276884.276894 J. R. Shewchuk

  28. [69]

    TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator.ACM Trans. Math. Softw. 41, 2, Article 11 (Feb. 2015), 36 pages. https://doi.org/10.1145/2629697 H. Si and K. Gartner

    2015 doi

  29. [70]

    Engineering with Computers 30, 2 (04 2014), 253–269

    Incrementally Constructing and Updating Constrained Delaunay Tetrahedralizations With Finite-Precision Coordinates. Engineering with Computers 30, 2 (04 2014), 253–269. https://doi.org/10.1007/s00366-013-0331-0 A. Tabatabaei Ghomi, M. Bolhassan, A. Nejur, and M. Akbarzadeh

    2014 doi

  30. [71]

    InProceedings of the IASS Symposium 2018, Creativity in Structural Design

    Effect of Subdivision of Force Diagrams on the Local Buckling, Load-Path and Material Use of Founded Forms. InProceedings of the IASS Symposium 2018, Creativity in Structural Design. MIT, Boston, USA. W. C. Thibault and B. F. Naylor

    2018

  31. [72]

    ACM Transactions on Graphics 28, 3 (07 2009),

    Interleaving Delaunay Refinement and Optimization for Practical Isotropic Tetrahedron Mesh Generation. ACM Transactions on Graphics 28, 3 (07 2009),

    2009

  32. [75]

    Internat

    Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Internat. J. Numer. Methods Engrg. 37, 12 (1994), 2005–2039. https://doi.org/10.1002/nme.1620371203 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620...

    1994 doi

  33. [77]

    The Visual Computer 27, 6-8 (2011), 507–517

    Parallel and efficient Boolean on polygonal solids. The Visual Computer 27, 6-8 (2011), 507–517. Q. Zhou, E. Grinspun, D. Zorin, and A. Jacobson

    2011

  34. [78]

    ACM Transactions on Graphics (TOG) 35, 4 (2016),

    Mesh Arrangements for Solid Geometry. ACM Transactions on Graphics (TOG) 35, 4 (2016),

    2016

  35. [79]

    CoRR abs/1605.04797 (2016)

    Thingi10K: A Dataset of 10, 000 3D-Printing Models. CoRR abs/1605.04797 (2016). arXiv:1605.04797 A A BRIEF DESCRIPTION OF THE TETWILD ALGORITHM The TetWild algorithm [Hu et al . 2018] takes a 3D triangle soup as input and generates a tetrahedral mesh that (1) has no inverted o...

    2016 arXiv

  36. [190]

    Chen and J.-c

    https://doi.org/10.1016/0168-874X(93)90056-V L. Chen and J.-c. Xu

    doi

  37. [233]

    Cuilliere, V

    https: //doi.org/10.1145/513400.513425 J.-C. Cuilliere, V. Francois, and J.-M. Drouet

  38. [409]

    Bernstein

    https://doi.org/10.1016/S0022-0000(05)80059-5 G. Bernstein

    doi

  39. [617]

    1145/1073204.1073238 P

    https://doi.org/10. 1145/1073204.1073238 P. Alliez, D. Cohen-Steiner, M. Yvinec, and M. Desbrun. 2005b. Variational Tetrahedral Meshing. ACM Trans. Graph. 24, 3 (July 2005), 617–625. https://doi.org/10.1145/ 1073204.1073238 M. Attene

    2005

  40. [864]

    Aurenhammer

    https://doi.org/10.1016/j.cagd.2009.06.002 F. Aurenhammer

    2009 doi

  41. [1980]

    Internat

    A scheme for the automatic generation of tri- angular finite elements. Internat. J. Numer. Methods Engrg. 15, 12 (1980), 1813–1822. https://doi.org/10.1002/nme.1620151206 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620151206 R. Schmidt and K. Singh

    1980 doi

  42. [1983]

    IEEE Computer Graphics and Applications 3, 1 (Jan 1983), 39–46

    A Modified Quadtree Approach To Finite Element Mesh Generation. IEEE Computer Graphics and Applications 3, 1 (Jan 1983), 39–46. https://doi.org/10.1109/MCG.1983.262997 H. Zhao, C. C. Wang, Y. Chen, and X. Jin

    1983

  43. [1987]

    SIGGRAPH Comput

    Marching Cubes: A High Resolution 3D Surface Construction Algorithm. SIGGRAPH Comput. Graph. 21, 4 (Aug. 1987), 163–169. https://doi.org/10.1145/37402.37422 S. V. Magalhães, W. R. Franklin, and M. V. Andrade

    1987

  44. [1988]

    Discrete & Computational Geometry 3, 2 (01 Jun 1988), 147–168

    Nonobtuse triangulation of polygons. Discrete & Computational Geometry 3, 2 (01 Jun 1988), 147–168. https://doi.org/10. 1007/BF02187904 G. Barill, N. Dickson, R. Schmidt, D. I. Levin, and A. Jacobson

    1988

  45. [1989]

    Algorithmica 4, 1 (01 Jun 1989), 97–108

    Constrained delaunay triangulations. Algorithmica 4, 1 (01 Jun 1989), 97–108. https://doi.org/10.1007/BF01553881 L. P. Chew

    1989 doi

  46. [1991]

    ACM Comput

    Voronoi Diagrams&Mdash;a Survey of a Fundamental Geo- metric Data Structure. ACM Comput. Surv. 23, 3 (Sept. 1991), 345–405. https: //doi.org/10.1145/116873.116880 F. Aurenhammer, R. Klein, and D.-T. Lee. 2013.Voronoi Diagrams and Delaunay Trian- gulations. WORLD SCIENTIFIC, Ri...

    1991

  47. [1993]

    Finite Elements in Analysis and Design 13, 2 (1993), 185 –

    Optismoothing: An optimization- driven approach to mesh smoothing. Finite Elements in Analysis and Design 13, 2 (1993), 185 –

    1993

  48. [1994]

    Provably good mesh generation. J. Comput. System Sci. 48, 3 (1994), 384 –

    1994

  49. [1995]

    Journal of Algorithms 18, 3 (05 1995), 548–585

    A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation. Journal of Algorithms 18, 3 (05 1995), 548–585. https://doi.org/10.1006/ , Vol. 1, No. 1, Article . Publication date: January

    1995

  50. [1996]

    Engineering with Computers 12, 3 (01 Sep 1996), 243–255

    Topological refinement procedures for triangular finite element meshes. Engineering with Computers 12, 3 (01 Sep 1996), 243–255. https://doi.org/10.1007/BF01198738 S. A. Canann, M. B. Stephenson, and T. Blacker

    1996 doi

  51. [1997]

    Discrete & Computational Geometry 18, 3 (Oct

    Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. Discrete & Computational Geometry 18, 3 (Oct. 1997), 305–363. J. R. Shewchuk

    1997

  52. [1998]

    Internat

    Tetrahedral Mesh Improvement Using Swapping and Smoothing. Internat. J. Numer. Methods Engrg. 40 (05 1998). https: //doi.org/10.1002/(SICI)1097-0207(19971115)40:213.0.CO;2-9 F. Alauzet and D. Marcum

    1998 doi

  53. [1999]

    Lecture Notes on Delaunay Mesh Generation. (1999). J. R. Shewchuk. 2002a. Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. In Eleventh International Meshing Roundtable . Sandia National Laboratories, 193–204. J. R. Shewchuk. 2002b. What is a good l...

    1999

  54. [2001]

    International Journal of Compu- tational Geometry & Applications 11, 06 (12 2001), 669–682

    A Point-Placement Strategy for Conforming Delaunay Tetrahedralization. International Journal of Compu- tational Geometry & Applications 11, 06 (12 2001), 669–682. https://doi.org/10.1142/ s0218195901000699 K. Museth, D. E. Breen, R. T. Whitaker, and A. H. Barr

    2001

  55. [2002]

    Computational Geometry 22 (2002), 5–19

    Triangulations in CGAL. Computational Geometry 22 (2002), 5–19. J.-D. Boissonnat and S. Oudot

    2002

  56. [2003]

    International journal for numerical methods in engineering 56, 9 (2003), 1355–1373

    Tetrahedral Mesh Generation and Optimization Based on Centroidal Voronoi Tessellations. International journal for numerical methods in engineering 56, 9 (2003), 1355–1373. N. Faraj, J.-M. Thiery, and T. Boubekeur

    2003

  57. [2004]

    Journal of Computational Mathematics 22, 2 (2004), 299–308

    Optimal Delaunay Triangulations. Journal of Computational Mathematics 22, 2 (2004), 299–308. S.-W. Cheng, T. K. Dey, and J. A. Levine

    2004

  58. [2005]

    Graphical Models 67, 5 (09 2005), 405–451

    Provably Good Sampling and Meshing of Surfaces. Graphical Models 67, 5 (09 2005), 405–451. https://doi.org/10.1016/j.gmod.2005.01.004 R. Bridson and C. Doran

    2005 doi

  59. [2007]

    In ACM SIGGRAPH 2007 papers on - SIGGRAPH ’07

    Isosurface Stuffing: Fast Tetrahedral Meshes With Good Dihedral Angles. In ACM SIGGRAPH 2007 papers on - SIGGRAPH ’07 . ACM Press, New York, NY, USA,

    2007

  60. [2008]

    In Proceedings of the 16th International Meshing Roundtable

    A Practical Delaunay Meshing Algorithm for a Large Class of Domains. In Proceedings of the 16th International Meshing Roundtable. Springer, Springer Berlin Heidelberg, Berlin, Heidelberg, 477–494. S.-W. Cheng, T. K. Dey, and J. Shewchuk. 2012.Delaunay Mesh Generation. Chapman ...

    2012

  61. [2009]

    Computer Aided Geometric Design 26, 8 (2009), 850 –

    On converting sets of tetrahedra to combinatorial and PL manifolds. Computer Aided Geometric Design 26, 8 (2009), 850 –

    2009

  62. [2010]

    The Visual Computer 26, 11 (01 Nov 2010), 1393–1406

    A lightweight approach to repairing digitized polygon meshes. The Visual Computer 26, 11 (01 Nov 2010), 1393–1406. https://doi.org/10.1007/ s00371-010-0416-3 M. Attene

    2010

  63. [2011]

    IEEE Trans

    Approximate Boolean Operations on Large Polyhedral Solids with Partial Mesh Reconstruction. IEEE Trans. Vis. Comput. Graph. 17, 6 (2011), 836–849. N. P. Weatherill and O. Hassan

    2011

  64. [2012]

    ACM Trans

    Bounded Distortion Mapping Spaces for Triangular Meshes. ACM Trans. Graph. 31, 4 (2012),

    2012

  65. [2013]

    ACM Comput

    Polygon Mesh Repairing: An Application Perspective. ACM Comput. Surv. 45, 2, Article 15 (March 2013), 33 pages. https: //doi.org/10.1145/2431211.2431214 M. Attene, D. Giorgi, M. Ferri, and B. Falcidieno

    2013

  66. [2014]

    In Proceedings of the 22nd International Meshing Roundtable

    A Closed Advancing-Layer Method With Changing Topology Mesh Movement for Viscous Mesh Generation. In Proceedings of the 22nd International Meshing Roundtable. Springer International Publishing, Cham, 241–261. https://doi.org/10.1007/978-3-319-02335-9_14 , Vol. 1, No. 1, Articl...

    doi

  67. [2015]

    ACM Trans

    Computing Locally Injective Mappings by Advanced MIPS. ACM Trans. Graph. 34, 4, Article 71 (July 2015), 12 pages. https://doi.org/10. 1145/2766938 J. A. George

    2015

  68. [2016]

    Discrete & Computational Geometry 56, 1 (2016), 43–92

    Nonobtuse Triangulations of PSLGs. Discrete & Computational Geometry 56, 1 (2016), 43–92. J.-D. Boissonnat, O. Devillers, S. Pion, M. Teillaud, and M. Yvinec

    2016

  69. [2017]

    https://doi

    Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement.IEEE Transactions on Visualization and Computer Graphics 23, 12 (Dec 2017), 2560–2573. https://doi. org/10.1109/TVCG.2016.2632720 Y. Hu, T. Schneider, X. Gao, Q. Zhou, A. Jacobson, D. Zorin, ...

    2017

  70. [2018]

    ACM Transactions on Graphics 37, 4 (2018), 43:1– 43:12

    Fast Winding Numbers for Soups and Clouds. ACM Transactions on Graphics 37, 4 (2018), 43:1– 43:12. H. Barki, G. Guennebaud, and S. Foufou

    2018

  71. [2019]

    ACM Transactions on Graphics (Proceedings of SIGGRAPH) 38, 4 (2019),

    Harmonic Triangulations. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 38, 4 (2019),

    2019

  72. [2020]

    • 15 6 (2015), 1235–1254. M. Bern, D. Eppstein, and J. Gilbert

    2015

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.