Efficient Implementation of Marching Cubes' Cases with Topological Guarantees

Lewiner, Thomas; Lopes, Hélio; Vieira, Antônio Wilson; Tavares, Geovan

doi:10.1080/10867651.2003.10487582

Cited by 434 publications

(274 citation statements)

References 8 publications

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“…Bobzin et al generate 3D-voxel volumes by combining randomly selected windows of a single cross-sectional image instead of using multiple cross-sectional images, which may be more representative for the computation of homogenization properties and eliminates the need for the majority of grinding and polishing steps (Ref 16). A standard method to convert segmented voxel volumes to the required boundary representation is given by the marching cubes algorithm or enhancements thereof (Ref 17,18).…”

Section: Related Workmentioning

confidence: 99%

Efficient Large-Scale Coating Microstructure Formation Using Realistic CFD Models

Wiederkehr

Müller

2014

J Therm Spray Tech

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For the understanding of physical effects during the formation of thermally sprayed coating layers and the deduction of the macroscopic properties of a coating, microstructure modeling and simulation techniques play an important role. In this contribution, a coupled simulation framework consisting of a detailed, CFD-based single splat simulation, and a large-scale coating build-up simulation is presented that is capable to compute large-scale, three-dimensional, porous microstructures by sequential drop impingement of more than 10,000 individual particles on multicore workstation hardware. Due to the geometry-based coupling of the two simulations, the deformation, cooling, and solidification of every particle is sensitive to the hit surface area and thereby pores develop naturally in the model. The single splat simulation employs the highly parallel Lattice-Boltzmann method, which is well suited for GPUacceleration. In order to save splat calculations, the coating simulation includes a database-driven approach that re-uses already computed splats for similar underground shapes at the randomly chosen impact sites. For a fast database search, three different methods of efficient pre-selection of candidates are described and compared against each other.

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Section: Related Workmentioning

confidence: 99%

Efficient Large-Scale Coating Microstructure Formation Using Realistic CFD Models

Wiederkehr

Müller

2014

J Therm Spray Tech

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“…He used the Asymptotic Decider and a new interior ambiguity test to discriminate among subcases. Lewiner et al [15] provided a practical open-source implementation of the Chernyaev algorithm. It is worth noting that some of the configurations shown in Chernyaev's work [2] may have been inspired by personal communication with Nielson [22].…”

Section: Related Workmentioning

confidence: 99%

“…The latter topic is of special interest in this work. We focus on the problem of MC interior ambiguity and, in particular, on the topological correctness of Chernyaev's Marching Cubes 33 (MC33) [2,15].…”

Section: Introductionmentioning

confidence: 99%

“…Throughout years of research, it has been shown that some supposedly topologically correct techniques, including MC33, have issues that prevent correctness [7,16,21]. In particular, the work of Etiene et al [7] shows that the MC33 implementation by Lewiner et al [14,15], fails to produce topologically correct isosurfaces. Alas, the authors do not provide an explanation for the problem source, let alone fix the problem.…”

Section: Introductionmentioning

confidence: 99%

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Practical considerations on Marching Cubes 33 topological correctness

Custódio

Etiene

Pesco

et al. 2013

Computers & Graphics

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Chernyaev's Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5. This work closes an existing gap in the topological correctness of Marching Cubes 33. Furthermore, we make our results reproducible, meaning that examples provided in this work can be easily explored and studied. Finally, as part of the philosophy of reproducibility, we provide a corrected version of the Marching Cubes 33 open-source implementation and access to datasets that can be used to verify the correctness of any available topologically correct isosurface extraction implementation that preserves the topology of the trilinear interpolant.

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“…For future work, we plan to extend this approach for working with other variants of MC, in particular, variants that provide topological guarantees, are able to keep sharp corners, and adaptive versions of MC [17], [19]. In addition, we want to investigate the effect of warping the cells and active edges on the reconstructed surface on a theoretical level and, in particular, try to provide formal theoretical bounds on the quality of the triangles.…”

Section: Tablementioning

confidence: 99%

Edge Transformations for Improving Mesh Quality of Marching Cubes

Dietrich¹,

Scheidegger

Schreiner

et al. 2009

IEEE Trans. Visual. Comput. Graphics

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Abstract-Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through postprocessing operations such as smoothing. As we demonstrate in experiments with several data sets, while these improve the mesh, they do not remove all degeneracies and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as out-of-core and acceleration structures).

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Efficient Implementation of Marching Cubes' Cases with Topological Guarantees

Cited by 434 publications

References 8 publications

Efficient Large-Scale Coating Microstructure Formation Using Realistic CFD Models

Efficient Large-Scale Coating Microstructure Formation Using Realistic CFD Models

Practical considerations on Marching Cubes 33 topological correctness

Edge Transformations for Improving Mesh Quality of Marching Cubes

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