arxiv: 2604.20002 · v1 · submitted 2026-04-21 · ❄️ cond-mat.soft

Recognition: unknown

multisphere: a Python implementation of the Multi Sphere Shape generator (MSS) for DEM simulations

Felix Buchele , Patric M\"uller , Thorsten P\"oschel

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:51 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords multisphereDEM simulationsmulti-sphere particlesPython packagetriangulated meshesvoxelized volumesparticle shape generation

0 comments

The pith

multisphere is a Python package that converts triangulated meshes and voxel volumes into sets of intersecting spheres for DEM particle simulations.

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

The paper presents an open-source tool that reconstructs complex particle geometries as clusters of overlapping spheres. This enables discrete element method users to simulate irregular shapes without writing custom geometry code. The package accepts surface meshes or voxel data, generates the sphere sets, and supplies evaluation, visualization, and export functions. A sympathetic reader would care because many DEM studies rely on simplified particle models yet lack ready access to reliable conversion utilities.

Core claim

The package implements the Multi Sphere Shape generator to approximate arbitrary particle shapes by placing and overlapping spheres so that their union matches a given triangulated surface mesh or voxelized volume, while also offering built-in tools to assess the quality of the approximation, visualize the result, and export the sphere data for use in DEM codes.

What carries the argument

The multi-sphere reconstruction routine that places intersecting spheres to match input geometry from meshes or voxels.

If this is right

Users can import existing triangulated particle models directly into DEM workflows.
Voxel-based particle descriptions from imaging can be turned into sphere clusters without additional coding.
Evaluation and visualization tools allow quick checking of how well the spheres fill the original volume.
Export functions let the sphere sets be loaded into standard DEM software packages.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Wider adoption could reduce the barrier to simulating non-spherical particles in granular flow studies.
The open-source release invites community extensions such as new input formats or optimization criteria for sphere placement.
Integration with existing DEM frameworks might become a standard preprocessing step for irregular grains.

Load-bearing premise

That the sphere clusters produced will be accurate enough in both geometry and dynamics to be useful in actual DEM simulations.

What would settle it

A side-by-side DEM run comparing the motion or collision outcomes of the generated multi-sphere particles against either the original mesh-based particles or an independent reference method, revealing large discrepancies in macroscopic behavior.

Figures

Figures reproduced from arXiv: 2604.20002 by Felix Buchele, Patric M\"uller, Thorsten P\"oschel.

**Figure 1.** Figure 1: Mesh model of a cow [11] and its multisphere representation with n = 2000. Color indicates sphere sizes. introduced as a theoretical concept in [16]. MSS requires fewer spheres than other particle generators to achieve a given mismatch value. Unlike other particle generators, MSS preserves symmetry properties, such that the generated particle model S˜ exhibits the same symmetries as the target shape S. MS… view at source ↗

**Figure 2.** Figure 2: High-level architecture of the multisphere package. There are three main stages of the workflow involving public functions. minimum admissible sphere radius, and a maximum number of spheres. At least one of these criteria must be specified. The reconstruction accuracy is expressed through the DiceSørensen coefficient [17] (as cited in [18]), D ≡ 2 P i,j,k [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: shows multi-sphere models of the Stanford Bunny [19] reconstructed with n = {10, 50, 629} spheres. The corresponding Python script is shown in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 6.** Figure 6: Dice coefficient and multisphere runtime for the reconstruction of all 402 particles from the Sand Atlas [20] as a function of the number of spheres. ⟨D⟩ over all grains, and the shaded region indicates the standard deviation [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗

**Figure 4.** Figure 4: multisphere script to create the multisphere model of the Stanford Bunny shown in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Sample grains from the Sand Atlas [20]. Top row: surface meshes of Hamburg sand [20], couscous grains [21], Hostun sand [22], Ottawa sand [23], and Alveolinella quoyi [24]. Bottom row: corresponding multi-sphere models generated with multisphere. 10 20 30 number of spheres 0.0 0.2 0.4 0.6 0.8 dice coefficient 10 20 30 number of spheres 0 20 40 60 time [s] [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

read the original abstract

multisphere is an open-source Python package for generating multi-sphere representations of complex particles for use in DEM simulations. It reconstructs triangulated surface meshes and voxelized volumes as sets of intersecting spheres and provides tools for evaluation, visualization, and export.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a software announcement for a Python package implementing known multi-sphere generation for DEM, with no new results or validation shown.

read the letter

The main takeaway is that this paper describes the release of an open-source Python package for generating multi-sphere representations of complex shapes intended for discrete element method simulations. It handles conversion from triangulated meshes and voxelized volumes into sets of intersecting spheres, along with basic tools for assessment and output. On the positive side, providing this as a free, Python-based implementation fills a gap for users who need non-spherical particle models but don't have the resources to develop their own shape approximation code. The inclusion of evaluation and visualization features is a good touch, as it helps users check the quality without extra work. If the code is robust, it could see adoption in the granular simulation community where such tools are often shared informally. The approach builds on the multi-sphere method that's been around, so the novelty is in the packaging and accessibility rather than any algorithmic breakthrough. That's fine for a tool paper, but it means the contribution is incremental. The weaker part is the absence of supporting evidence in the write-up. There are no reported benchmarks for how well the generated spheres approximate the original geometry, no measures of computational cost, and no validation against known test cases or other generators. This makes it difficult to assess whether the package delivers reliable results for typical DEM applications or if there are limitations in accuracy or efficiency that users would encounter. Overall, this work targets researchers and engineers using DEM for soft matter or granular systems who might benefit from an easy way to create multi-sphere particles. It could be worth a quick look for anyone in that area looking for practical tools. For broader interest, the lack of quantitative results limits its appeal. I think it deserves peer review in the right context, such as a journal with a software or computational methods focus, where referees can check the code and documentation. In a more theoretical physics venue, it might not warrant full review.

Referee Report

1 major / 2 minor

Summary. The manuscript describes 'multisphere', an open-source Python package implementing the Multi Sphere Shape generator (MSS) for DEM simulations. It converts triangulated surface meshes and voxelized volumes into sets of intersecting spheres, and supplies accompanying tools for evaluation, visualization, and export to common DEM formats.

Significance. If the implementation is reliable, the package addresses a recurring practical need in the DEM community: rapid generation of multi-sphere approximations for non-spherical particles. Open-source release with evaluation utilities is a clear strength that can support reproducibility and community adoption.

major comments (1)

Abstract and §2 (Implementation): the central claim that the package 'reconstructs' meshes and voxels as sphere sets is not accompanied by any error metrics, overlap-volume statistics, or comparison against reference methods or ground-truth particle shapes. Without such quantitative validation the functionality claim cannot be assessed.

minor comments (2)

The manuscript would benefit from a short table or figure showing runtime and sphere-count scaling for a few benchmark meshes/voxels of varying complexity.
Add explicit citation of the original MSS algorithm paper and at least two other open multi-sphere generators to place the contribution in context.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and positive evaluation of the package's potential utility in the DEM community. We address the major comment point by point below.

read point-by-point responses

Referee: Abstract and §2 (Implementation): the central claim that the package 'reconstructs' meshes and voxels as sphere sets is not accompanied by any error metrics, overlap-volume statistics, or comparison against reference methods or ground-truth particle shapes. Without such quantitative validation the functionality claim cannot be assessed.

Authors: We agree that the current manuscript does not present quantitative error metrics, overlap statistics, or direct comparisons, which limits the ability to assess reconstruction fidelity from the text alone. The manuscript's emphasis is on documenting the open-source implementation of the established MSS algorithm together with user-facing evaluation and export utilities. In the revised version we will add a dedicated validation subsection (likely within §2 or as a new §3) that reports concrete metrics for representative test cases, including volume overlap fractions, surface deviation measures (e.g., Hausdorff distance), and comparisons against both ground-truth particle volumes and at least one alternative multi-sphere generation approach from the literature. These additions will be supported by the evaluation tools already present in the package. revision: yes

Circularity Check

0 steps flagged

Software package description with no derivations or predictions

full rationale

The manuscript is a descriptive announcement of an open-source Python package that converts triangulated meshes and voxel data into intersecting sphere sets for DEM use, along with evaluation, visualization, and export utilities. No equations, fitted parameters, predictions, uniqueness theorems, or ansatzes are present. The central claim is simply that the tool exists and performs the stated conversions, which is a factual software description with no internal derivation chain that could reduce to its own inputs or self-citations. This is a self-contained implementation report with no opportunity for circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced; the central claim concerns the existence and basic capabilities of a computational tool.

pith-pipeline@v0.9.0 · 5333 in / 1022 out tokens · 40275 ms · 2026-05-10T00:51:08.276239+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 15 canonical work pages

[1]

P. A. Cundall, O. D. L. Strack, A discrete numerical model for granular assemblies, Géotechnique 79 (1979) 47–65.doi:10.1680/geot.1979.29.1.47

work page doi:10.1680/geot.1979.29.1.47 1979
[2]

Pöschel, T

T. Pöschel, T. Schwager, Computational Granular Dynamics: Models and Algorithms, Springer, Berlin, Heidelberg, 2005.doi:10.1007/3-540-27720-X

work page doi:10.1007/3-540-27720-x 2005
[3]

Matuttis, J

H.-G. Matuttis, J. Chen, Understanding the Discrete Element Method: Simulation of Non-Spherical Par- ticles for Granular and Multi-body Systems, Wiley, 2014.doi:10.1002/9781118567210

work page doi:10.1002/9781118567210 2014
[4]

G. Lu, J. Third, C. Müller, Discrete element models for non-spherical particle systems: From theoretical de- velopments to applications, Chemical Engineering Sci- ence 127 (2015) 425–465.doi:10.1016/j.ces.2014. 11.050. 4

work page doi:10.1016/j.ces.2014 2015
[5]

J. Zhao, S. Zhao, S. Luding, The role of particle shape in computational modelling of granular mat- ter, Nature Reviews Physics 5 (2023).doi:10.1038/ s42254-023-00617-9

2023
[6]

Pöschel, V

T. Pöschel, V. Buchholtz, Static friction phenomena in granular materials: Coulomb law versus particle geometry, Physical Review Letters 71 (1993) 3963– 3966.doi:10.1103/PhysRevLett.71.3963

work page doi:10.1103/physrevlett.71.3963 1993
[7]

Buchholtz, T

V. Buchholtz, T. Pöschel, Numerical investigations of the evolution of sandpiles, Physica A-Statistical Mechanics and Its Applications 202 (1994) 390–401. doi:10.1016/0378-4371(94)90467-7

work page doi:10.1016/0378-4371(94)90467-7 1994
[8]

Buchholtz, T

V. Buchholtz, T. Pöschel, Avalanche statistics of sand heaps, Journal of Statistical Physics 84 (1996) 1373–1378.doi:10.1007/BF02174136

work page doi:10.1007/bf02174136 1996
[9]

P. M. Hubbard, Approximating polyhedra with spheres for time-critical collision detection, ACM Transactions on Graphics 15 (1996) 179–210.doi: 10.1145/231731.231732

work page doi:10.1145/231731.231732 1996
[10]

Favier, M

J. Favier, M. Abbaspour-Fard, M. Kremmer, A. O. Raji, Shape representation of axi-symmetrical, non- spherical particles in discrete element simulation using multi-element model particles, Engineering Computations 16 (1999) 467–480. doi:10.1108/ 02644409910271894

1999
[11]

Viewpoint Animation Engineering, Sun Microsystems, cow2 [3d model] from the princeton suggestive con- tour gallery,https://gfx.cs.princeton.edu/proj/ sugcon/models/, accessed: 2026-01-26 (n.d.)

2026
[12]

Angelidakis, S

V. Angelidakis, S. Nadimi, M. Otsubo, S. Utili, CLUMP: A code library to generate universal multi- sphere particles, SoftwareX 15 (2021) 100735.doi: 10.1016/j.softx.2021.100735

work page doi:10.1016/j.softx.2021.100735 2021
[13]

A. U. Canbolat, S. Nadimi, V. Angelidakis, A Python implementation of CLUMP, the code library to gen- erate universal multi-sphere particles, SoftwareX 29 (2025) 101957.doi:10.1016/j.softx.2024.101957

work page doi:10.1016/j.softx.2024.101957 2025
[14]

Amberger, M

S. Amberger, M. Friedl, C. Goniva, S. Pirker, C. Kloss, Approximation of objects by spheres for multisphere simulations in DEM, 2012

2012
[15]

Ferellec, G

J.-F. Ferellec, G. R. McDowell, A method to model realistic particle shape and inertia in DEM, Gran- ular Matter 12 (2010) 459–467. doi:10.1007/ s10035-010-0205-8

2010
[16]

Felix, T

B. Felix, T. Pöschel, P. Müller, Multi-sphere shape generator for dem simulations of complex-shaped par- ticles, Powder Technology, submitted (2026). doi: 10.48550/arXiv.2603.05877

work page doi:10.48550/arxiv.2603.05877 2026
[17]

L. R. Dice, Measures of the amount of ecologic associ- ation between species, Ecology 26 (3) (1945) 297–302. doi:10.2307/1932409

work page doi:10.2307/1932409 1945
[18]

A. Levy, B. R. Shalom, M. Chalamish, A guide to similarity measures and their data science applications, Journal of Big Data 12 (1) (2025) 188.doi:10.1186/ s40537-025-01227-1

2025
[19]

stanford.edu/data/3Dscanrep/, Stanford Bunny Model, accessed: 2026-03-19 (1994)

Stanford Computer Graphics Laboratory, The stan- ford 3d scanning repository, http://graphics. stanford.edu/data/3Dscanrep/, Stanford Bunny Model, accessed: 2026-03-19 (1994)

2026
[20]

Milatz, N

M. Milatz, N. Hüsener, E. Andò, G. Viggiani, J. Grabe, Quantitative 3D imaging of partially saturated gran- ular materials under uniaxial compression, Acta Geotechnica 16 (2021) 3573–3600. doi:10.1007/ s11440-021-01315-5

2021
[21]

Vego, Multi-modal investigation of hygroscopic gran- ular media at high relative humidity, Ph.D

I. Vego, Multi-modal investigation of hygroscopic gran- ular media at high relative humidity, Ph.D. thesis, Université Grenoble Alpes (2023)

2023
[22]

Wiebicke, E

M. Wiebicke, E. Andò, I. Herle, G. Viggiani, On the metrology of interparticle contacts in sand from x-ray tomography images, Meas. Sci. Technol. 28 (12) (2017) 124007.doi:10.1088/1361-6501/aa8dbf

work page doi:10.1088/1361-6501/aa8dbf 2017
[23]

Saadatfar, N

M. Saadatfar, N. Francois, A. Arad, M. Madadi, R. Cruikshank, M. Alizadeh, A. Sheppard, A. Kingston, A. Limay, T. Senden, M. Knack- stedt, 3D mapping of deformation in an uncon- solidated sand: A micro mechanical study, in: SEG Technical Program Expanded Abstracts 2012, Society of Exploration Geophysicists, 2012, pp. 1–6. doi:10.1190/segam2012-1263.1

work page doi:10.1190/segam2012-1263.1 2012
[24]

Luijmes, T

J. Luijmes, T. van Leeuwen, W. Renema, Foram- etcetera, a novel ct scan dataset to expedite classi- fication research of (non-)foraminifera, Scientific Data 11 (2024) 642.doi:10.1038/s41597-024-03476-w. 5

work page doi:10.1038/s41597-024-03476-w 2024