A survey of the marching cubes algorithm

Newman, Timothy S.; Hong, Yi

doi:10.1016/j.cag.2006.07.021

Cited by 432 publications

(246 citation statements)

References 87 publications

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“…To calculate n T n ðzÞ, Singular Value Decomposition (SVD) 17 of D/ T ðzÞ is used. To identify the zero level set of L T ðzÞ, Marching Cube algorithm 18 is used. Specifically, one of the simplest variants of Marching Cube algorithms 19 that was originally developed by Doi.…”

Section: Application a Abc Flowmentioning

confidence: 99%

Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

Teramoto

Haller

Komatsuzaki

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Normally hyperbolic invariant manifolds (NHIMs) are well-known organizing centers of the dynamics in the phase space of a nonlinear system. Locating such manifolds in systems far from symmetric or integrable, however, has been an outstanding challenge. Here, we develop an automated detection method for codimension-one NHIMs in autonomous dynamical systems. Our method utilizes Stationary Lagrangian Coherent Structures (SLCSs), which are hypersurfaces satisfying one of the necessary conditions of a hyperbolic LCS, and are also quasi-invariant in a well-defined sense. Computing SLCSs provides a quick way to uncover NHIMs with high accuracy. As an illustration, we use SLCSs to locate two-dimensional stable and unstable manifolds of hyperbolic periodic orbits in the classic ABC flow, a three-dimensional solution of the steady Euler equations. Invariant manifolds play an important role in transport phenomena that range from chemical reactions through fluid mixing to celestial mechanics. Such manifolds, however, are often challenging to locate in multi-dimensional systems that are far from integrable and possess no special symmetries. Among these invariant manifolds, normally hyperbolic invariant manifolds are particularly important due to their persistence under small perturbations. This renders them robust with respect to modeling errors and numerical inaccuracies. Here, we develop a method to detect codimension-one, normally hyperbolic invariant manifolds in general autonomous systems. We approximate such manifolds as zero level sets of a scalar function derived from the recent variational theory of hyperbolic Lagrangian Coherent Structures (LCSs). This approximation converges exponentially fast to a true invariant manifold as longer and longer flow-map samples are used in its construction. We illustrate this method on the classic steady ABC flow, revealing some of its two-dimensional invariant manifolds at a previously unseen level of detail.

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Section: Application a Abc Flowmentioning

confidence: 99%

Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

Teramoto

Haller

Komatsuzaki

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The algorithm that generates surfaces according to such grid units mostly involve Marching Cubes [13] used in volume modeling, while research on expanding the range, limitations, and properties of calculation of various figures is being carried out [14]. Creating sharp edges that cannot be created through the Marching Cubes algorithm can be implemented by using internal vertices within the specific grids in the Expended Marching Cubes [15] and the intersection points and normal vectors between the grids and the input isosurfaces in the Dual Contouring [16].…”

Section: Spatial Grid-based Modeling Algorithmmentioning

confidence: 99%

Real-Time Spatial Surface Modeling System Using Wand Traversal Patterns of Grid Edges

Kim

Lee

et al. 2011

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper presents a grid-based, real-time surface modeling algorithm in which the generation of a precise 3D model is possible by considering the user's intention during the course of the spatial input. In order to create the corresponding model according to the user's input data, plausible candidates of wand traversal patterns of grid edges are defined by considering the sequential and directional characteristics of the wand input. The continuity of the connected polygonal surfaces, including the octree space partitioning, is guaranteed without the extra crack-patching algorithm and the pre-defined patterns. Furthermore, the proposed system was shown to be a suitable and effective surface generation tool for the spatial sketching system. It is not possible to implement the unusual input intention of the 3D spatial sketching system using the conventional Marching Cubes algorithm.

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“…This algorithm defines a type of triangulation for each cell in the volume or space given the values of the vertices, given a desired iso-value the vertices are compair against this value and then a triangulation case is selected ( Figure 2) and then a triangulation is generated for each cell. The algorithm has been widely studied (Newman and Yi, 2006) and several extensions had been made to solve topological problems with techniques (Chernyaev, 1995), (Lewiner et al, 2003) also methodologies to obtain more accurate representations were studied (Congote et al, 2009). One of the biggest advantages of the algorithm is their complexity O(n) where n is the number of cells in the volume, so the time taken by the algorithm to the process could be easily controlled in real time process because it is constant and can be modified changing the number of cells.…”

Section: Related Workmentioning

confidence: 99%

Marching Cubes in an Unsigned Distance Field for Surface Reconstruction From Unorganized Point Sets

Congote¹,

Moreno²,

Barandiarán³

et al. 2010

Proceedings of the International Conference on Computer Graphics Theory and Applications

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Abstract:Surface reconstruction from unorganized point set is a common problem in computer graphics. Generation of the signed distance field from the point set is a common methodology for the surface reconstruction. The reconstruction of implicit surfaces is made with the algorithm of marching cubes, but the distance field of a point set can not be processed with marching cubes because the unsigned nature of the distance. We propose an extension to the marching cubes algorithm allowing the reconstruction of 0-level iso-surfaces in an unsigned distance field. We calculate more information inside each cell of the marching cubes lattice and then we extract the intersection points of the surface within the cell then we identify the marching cubes case for the triangulation. Our algorithm generates good surfaces but the presence of ambiguities in the case selection generates some topological mistakes.

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A survey of the marching cubes algorithm

Cited by 432 publications

References 87 publications

Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

Real-Time Spatial Surface Modeling System Using Wand Traversal Patterns of Grid Edges

Marching Cubes in an Unsigned Distance Field for Surface Reconstruction From Unorganized Point Sets

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