Fixing Geometric Errors on Polygonal Models: A Survey

Ju, Tao

doi:10.1007/s11390-009-9206-7

Cited by 89 publications

(41 citation statements)

References 77 publications

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“…Although many works in the literature proposed methods for fixing meshes (see [11] for an excellent survey), these are mainly focused on retrieving a valid manifold mesh. Topologically correct algorithms, on the other hand, require that the topology of the trilinear interpolant be preserved.…”

Section: Issue II -Non-manifold Surfacesmentioning

confidence: 99%

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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Section: Issue II -Non-manifold Surfacesmentioning

confidence: 99%

Practical considerations on Marching Cubes 33 topological correctness

Custódio

Etiene

Pesco

et al. 2013

Computers & Graphics

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“…Most methods available today for computing topology changes frame the problem in the context of mesh-repair [Attene et al 2013;Ju 2009]. After a surface is deformed, a mesh-repair-like algorithm is run on the surface at the final position.…”

Section: Prior Workmentioning

confidence: 99%

Putting holes in holey geometry

Bernstein

Wojtan

2013

ACM Trans. Graph.

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Figure 1: This zombie model (a) has numerous open surfaces, non-manifold edges, and self-intersections, displayed in red here (b). Nonethe-less, using the technique described in this paper, we are able to (c) poke through the zombie's chest and (d) create the desired tunnel/hole. AbstractThis paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces-that is, we prove a backwardscompatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors.

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“…The former operate directly on the input mesh, while the latter use an intermediate voxel representation. Note that comprehensive overviews of existing works can be found in [11] and [26].…”

Section: Combinatorial and Geometrical Singularity Removalmentioning

confidence: 99%

Mesh repair with user-friendly topology control

Hétroy

Rey

Andújar

et al. 2011

Computer-Aided Design

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Limitations of current 3D acquisition technology often lead to polygonal meshes exhibiting a number of geometrical and topological defects which prevent them from widespread use. In this paper we present a new method for model repair which takes as input an arbitrary polygonal mesh and outputs a valid two-manifold triangle mesh. Unlike previous work, our method allows users to quickly identify areas with potential topological errors and to choose how to fix them in a userfriendly manner. Key steps of our algorithm include the conversion of the input model into a set of voxels, the use of morphological operators to allow the user to modify the topology of the discrete model, and the conversion of the corrected voxel set back into a two-manifold triangle mesh. Our experiments demonstrate that the proposed algorithm is suitable for repairing meshes of a large class of shapes.

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Fixing Geometric Errors on Polygonal Models: A Survey

Cited by 89 publications

References 77 publications

Practical considerations on Marching Cubes 33 topological correctness

Practical considerations on Marching Cubes 33 topological correctness

Putting holes in holey geometry

Mesh repair with user-friendly topology control

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