#### DMCA

## Edge groups: An approach to understanding the mesh quality of marching methods

### Cached

### Download Links

- [www.sci.utah.edu]
- [www.sci.utah.edu]
- [www.sci.utah.edu]
- [www.sci.utah.edu]
- [www.sci.utah.edu]
- [www.sci.utah.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | IEEE Transactions on Visualization and Computer Graphics |

Citations: | 4 - 2 self |

### Citations

2695 | Marching Cubes: A high resolution 3D surface construction algorithm.
- Lorensen, Harvey
- 1987
(Show Context)
Citation Context ...of the resulting triangle mesh, including some that require only minor modifications of the original algorithm. Index Terms—Isosurface extraction, Marching Cubes. ✦ 1 INTRODUCTION Marching Cubes (MC) =-=[18]-=- became the most popular algorithm for isosurface extraction due to a powerful combination of simplicity, efficiency and robustness of implementation. There has been much work on improving the origina... |

440 | Introduction to Implicit Surfaces,
- Bloomenthal
- 1997
(Show Context)
Citation Context ...e dynamically generated MC tables [4]. Edge groups can be identified for any spatial subdivision that define cut points along edges of its cells, such as methods based on MC, like Marching Tetrahedra =-=[5,8]-=- and Marching Octahedra [7]. As stated before, the analysis of edge groups provides quality bounds for the triangles generated in each cell, and thus for the quality of the polygonization method itsel... |

322 | A.: Octrees for faster isosurface generation.
- WILHELMS, GELDER
- 1992
(Show Context)
Citation Context ...above 0.19. More importantly, our method retains most of the performance advantages and simplicity of Marching Cubes: in particular, we could take advantage of acceleration structures such as octrees =-=[37]-=-, interval trees [10] or span space methods [19]. On the other hand, our method is intrinsically based on Marching Cubes, and, as it is, incapable of generating meshes that adapt to the features in th... |

258 | Dual contouring of hermite data
- Ju, Losasso, et al.
- 2002
(Show Context)
Citation Context ... Spatial decomposition methods (introduced by [14]) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell =-=[7, 15, 18, 25, 33]-=-. Surface tracking methods place seed sampling points on the isosurface and trigger region growing-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. ... |

195 | A near optimal isosurface extraction algorithm using the span space.
- LIVNAT, SHEN, et al.
- 1996
(Show Context)
Citation Context ... More importantly, our method retains most of the performance advantages and simplicity of Marching Cubes: in particular, we could take advantage of acceleration structures such as span space methods =-=[17]-=-. On the other hand, our method is intrinsically based on Marching Cubes, and, as it is, incapable of generating meshes that adapt to the features in the surface such as curvature. One limitation of t... |

118 | a survey of unstructured mesh generation technology” in
- Owen
- 1998
(Show Context)
Citation Context ... generate the vertices. A survey of MC was recently presented by Newman and Yi [22]. Isosurface extraction methods are usually categorized by the general approach they use in computing the isosurface =-=[27]-=-. Spatial decomposition methods (introduced by [14]) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell... |

85 | Discretized marching cubes
- Montani, Scateni, et al.
- 1994
(Show Context)
Citation Context ...The opposing movements suggest that cut points are to be moved towards the center of each edge. (A similar movement, but for a different goal, was proposed in the Discretized Marching Cubes algorithm =-=[20]-=-.) Forcing intersection points to be placed at the middle of the edges is unnecessary in some situations. Therefore, we apply a symmetric non-linear displacement using a modulation function. On the x ... |

82 | On marching cubes.
- Nielson
- 2003
(Show Context)
Citation Context ...also have not pursued here is the influence of the underlying interpolant in the generation of MC case tables and their edge groups, and, consequently, on the quality of the generated meshes. Nielson =-=[24]-=- provides one of the few MC tables in the literature that respect a particular interpolation kernel. Smoother kernels will generate different reconstructions, and so we should use different case table... |

74 |
Three-Dimensional Display of Human Organs from Computer Tomograms," Computer Graphics and
- Herman, Liu
- 1979
(Show Context)
Citation Context ...that places sampling points at the center of each active cell (a cell crossed by the isosurface), and connects them to sampling points in adjacent cells. This procedure resembles the Cuberille method =-=[13]-=- and generates a dual of the MC mesh. A related technique is dual-contouring [15] which has been shown to generate higher quality meshes than MC. Bruin et al. [9] extended Gibson’s technique to couple... |

71 | Regularised marching tetrahedra: improved iso-surface extraction.
- Treece, Prager
- 1999
(Show Context)
Citation Context ... Spatial decomposition methods (introduced by [14]) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell =-=[7, 15, 18, 25, 33]-=-. Surface tracking methods place seed sampling points on the isosurface and trigger region growing-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. ... |

71 |
Data structures for soft objects. Visual Computer. 2:227--234. 540 VFC Morphology, Femininity, and Social Perception d Wood et al.
- Wyvill, McPheeters, et al.
- 1986
(Show Context)
Citation Context ... isosurface and trigger region growing-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. These algorithms trace their roots to work of Wyvill et al. =-=[35]-=- and have been recently extended [31] to generate higher quality triangulations. The divide-and-conquer nature of spatial decomposition methods often leads to robust and efficient methods, like MC [18... |

64 | Optimal isosurface extraction from irregular volume data
- Cignoni, Montani, et al.
- 1996
(Show Context)
Citation Context ...rtantly, our method retains most of the performance advantages and simplicity of Marching Cubes: in particular, we could take advantage of acceleration structures such as octrees [37], interval trees =-=[10]-=- or span space methods [19]. On the other hand, our method is intrinsically based on Marching Cubes, and, as it is, incapable of generating meshes that adapt to the features in the surface such as cur... |

59 | Isosurface stuffing: Fast tetrahedral meshes with good dihedral angles
- Labelle, Shewchuk
(Show Context)
Citation Context ...higher-quality meshes. In the past, efficiency and quality have been treated as orthogonal features, but a recent trend is to consider both aspects when designing an algorithm to improve mesh quality =-=[11, 16]-=-. Gibson [12] proposes a method based on MC that places sampling points at the center of each active cell (a cell crossed by the isosurface), and connects them to sampling points in adjacent cells. Th... |

57 | What is a good linear finite element? - interpolation, conditioning, anisotropy, and quality measures. Technical report
- Shewchuk
- 2002
(Show Context)
Citation Context ...ate step in many numerical codes. Because of this, there is a pressing need for algorithms that are fast and generate good meshes. Since good meshes make numerical processing faster and more accurate =-=[32]-=-, improving the quality of the meshes generated by Marching Cubes has become an important problem. Although much of the published work has involved post-processing and remeshing, there is also interes... |

50 | Constrained elastic surface nets: Generating smooth surfaces from binary segmented data. - Gibson - 1998 |

45 | Isosurfacing in higher dimensions
- Bhaniramka, Crawfis
- 2000
(Show Context)
Citation Context ... observed in MC. All triangles generated by MC come from one of these groups (which include symmetric or rotationally equivalent configurations). theory, and counting-cases for four-dimensional cases =-=[3]-=-. While they count cases that occur based on the sign of the vertices of the cell, we classify triangles inside each case by looking at the relative connectivity of the edges that generate the vertice... |

45 | A survey of the marching cubes algorithm,”
- Newman, Yi
- 2006
(Show Context)
Citation Context ...he vertices of the cell, we classify triangles inside each case by looking at the relative connectivity of the edges that generate the vertices. A survey of MC was recently presented by Newman and Yi =-=[22]-=-. Isosurface extraction methods are usually categorized by the general approach they use in computing the isosurface [27]. Spatial decomposition methods (introduced by [14]) subdivide the domain of th... |

31 | Isosurface construction in any dimension using convex hulls
- Bhaniramka, Wenger, et al.
- 2004
(Show Context)
Citation Context ...gons based on the barycentric coordinates of the cut points. This is an exciting avenue of research. More generally, our analysis of edge groups could be used to guide dynamically generated MC tables =-=[4]-=-. Edge groups can be identified for any spatial subdivision that define cut points along edges of its cells, such as methods based on MC, like Marching Tetrahedra [5,8] and Marching Octahedra [7]. As ... |

31 |
A New Tetrahedral Tessellation Scheme for Isosurface Generation.
- Chan
- 1998
(Show Context)
Citation Context ...e dynamically generated MC tables [4]. Edge groups can be identified for any spatial subdivision that define cut points along edges of its cells, such as methods based on MC, like Marching Tetrahedra =-=[5,8]-=- and Marching Octahedra [7]. As stated before, the analysis of edge groups provides quality bounds for the triangles generated in each cell, and thus for the quality of the polygonization method itsel... |

28 |
Simplical Mesh Generation with Applications
- Moore
- 1992
(Show Context)
Citation Context ... method itself. For example, tetrahedral cells with different shapes are obtained in the Delaunay triangulation of a BCC (body centered cubic) grid and from the Coxeter-Freudenthal-Kuhn triangulation =-=[21]-=- (or simply the Kuhn triangulation) subdivision scheme. The analysis of edge groups in tetrahedral cells is more involved than in cubic cells because we have edges with different sizes, and with varyi... |

18 |
B.: On histograms and isosurface statistics
- CARR, DUFFY, et al.
(Show Context)
Citation Context ...g the connectivity of the triangulation stored in the original MC table, and replacing edge groups associatedFig. 3. Box plots show the edge group distribution for 30 different datasets collected by =-=[6]-=-. The left plot shows the overall distribution of edge cases for the datasets, and the right plot shows the distribution of the worst 1000 triangles. Notice that case 2 dominates the bad triangles. to... |

15 | Edge transformations for improving mesh quality of marching cubes,
- Dietrich, Scheidegger, et al.
- 2009
(Show Context)
Citation Context ...der of magnitude in most cases we tested. We also apply a similar analysis to revisit Macet, a method that improves triangle quality by warping the locations of the MC grid before generating the mesh =-=[11]-=-. Edge groups help explain why that method performs well. In addition, edge groups naturally suggest a modification of the technique that further improves triangle quality in almost all datasets teste... |

15 | accuracy, and quality of isosurface meshes using dynamic particles
- Meyer, Kirby, et al.
(Show Context)
Citation Context ... isosurface mesh generation, to the best of our knowledge, are the works of Schreiner et al. [31] in advancing front triangulation, Dey and Levine [10] based on Delaunay refinements, and Meyer et al. =-=[19]-=-, which combines techniques from computational geometry with dynamic particle systems to sample an isosurface appropriately and then reconstruct the triangulation. They report worst triangle quality r... |

14 |
Theußl T, Möller T. Isosurfaces on Optimal Regular Samples
- Carr
- 2003
(Show Context)
Citation Context ... Spatial decomposition methods (introduced by [14]) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell =-=[7, 15, 18, 25, 33]-=-. Surface tracking methods place seed sampling points on the isosurface and trigger region growing-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. ... |

14 |
Approximating normals for marching cubes applied to locally supported isosurfaces
- Nielson, Huang, et al.
(Show Context)
Citation Context ...g combinatorial aspects of MC and related techniques. The original MC paper by Lorensen and Cline [18] enumerates the 15 cases by inspection of the possible 256 cases, without a formal proof. Nielson =-=[26]-=- demonstrates the existence of 23 cases by rotation only, despite mirroring and complementary operations, which can produce erroneous results. Banks et al. [1] present a formal proof based on group th... |

13 |
Delaunay meshing of isosurfaces
- Dey, Levine
(Show Context)
Citation Context ... tables. 6 DISCUSSION The state of the art in quality isosurface mesh generation, to the best of our knowledge, are the works of Schreiner et al. [31] in advancing front triangulation, Dey and Levine =-=[10]-=- based on Delaunay refinements, and Meyer et al. [19], which combines techniques from computational geometry with dynamic particle systems to sample an isosurface appropriately and then reconstruct th... |

13 | A comparison of triangle quality measures
- Pébay, Baker
- 2001
(Show Context)
Citation Context ...ach triangle. We chose as quality metric the radii-ratio, which computes the ratio of incircle to circumcircle, normalized to lie between zero and one; an equilateral triangle has maximum quality one =-=[28]-=-. The quality of triangles generated inside a cubic cell is hard to analyze. Each cell generates a set of triangles (up to five in MC), and the quality of each triangle is dictated by the position of ... |

10 | Improving triangle mesh quality with surfacenets
- Bruin, Vos, et al.
- 2000
(Show Context)
Citation Context ...edure resembles the Cuberille method [13] and generates a dual of the MC mesh. A related technique is dual-contouring [15] which has been shown to generate higher quality meshes than MC. Bruin et al. =-=[9]-=- extended Gibson’s technique to couple a gradient descent iteration to the mesh post-processing step, which reduces the distance between the mesh and the real isosurface. Dual MC techniques are also s... |

10 | Volume warping for adaptive isosurface extraction
- Balmelli, Morris, et al.
(Show Context)
Citation Context ... Spatial decomposition methods (introduced by [16]) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell =-=[1, 8, 17, 20, 27, 35]-=-. Surface tracking methods place seed sampling points on the isosurface and trigger region growing-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. ... |

9 | Counting cases in substitope algorithms
- Banks, Linton, et al.
- 2004
(Show Context)
Citation Context ... cases, without a formal proof. Nielson [26] demonstrates the existence of 23 cases by rotation only, despite mirroring and complementary operations, which can produce erroneous results. Banks et al. =-=[1]-=- present a formal proof based on group theory that also generalizes to higher dimensions and other polytopes. Other related papers include the follow-up to this work [2] that uses Pólya0 1 2 3 Fig. 2... |

9 | Quality isosurface mesh generation using an extended marching cubes lookup table
- RAMAN, WENGER
(Show Context)
Citation Context ...on. By carefully choosing the amount and direction of warping, together with the lattice in which the surface is extracted, they are able to prove lower bounds on tetrahedra quality. Raman and Wenger =-=[30]-=- propose both an extended lookup table to eliminate triangles degenerated to points or lines and a snapping technique to collapse bad-shaped triangles with cut points near to grid vertices. Extended l... |

4 |
Display of 3-D digital images: Computational foundations and medical applications
- Herman, Udupa
- 1983
(Show Context)
Citation Context ... presented by Newman and Yi [22]. Isosurface extraction methods are usually categorized by the general approach they use in computing the isosurface [27]. Spatial decomposition methods (introduced by =-=[14]-=-) subdivide the domain of the function f into smaller parts, often called cells, and generate local approximations to the isosurface inside each cell [7, 15, 18, 25, 33]. Surface tracking methods plac... |

4 |
Mc*: Star functions for marching cubes
- Nielson
- 2003
(Show Context)
Citation Context ... triangle meshes. To our knowledge there has been no discussion on a criteria to guide the way that the connectivity of the triangulation should be defined to improve the quality of the mesh. Nielson =-=[23]-=- proposes a connection table which leads to isosurfaces that are locally functions (each vertex star can be represented as a height field relative to one of the coordinate planes). There are also many... |

4 |
Warping cubes: Better triangles from marching cubes
- Tzeng
- 2004
(Show Context)
Citation Context ...es are also studied by Nielson [25] who proposes a method that leads to a polygon mesh surface which is the mathematical dual of a modified form of the MC surface called the “MC Patch” surface. Tzeng =-=[34]-=- proposes a post-processing step in which small edges are collapsed to eliminate poorly shaped triangles. Labelle and Shewchuk [16] propose warping of the sampling grid to eliminate poorly-shaped tetr... |

3 |
High quality extraction of isosurfaces from regular and irregular grids
- Schreiner, Scheidegger, et al.
(Show Context)
Citation Context ...g-like algorithms from the seeds, iteratively searching for optimal positions for new sampling points. These algorithms trace their roots to work of Wyvill et al. [35] and have been recently extended =-=[31]-=- to generate higher quality triangulations. The divide-and-conquer nature of spatial decomposition methods often leads to robust and efficient methods, like MC [18], while the optimal placing of each ... |

1 |
Debruijn Counting for Visualization Algorithms, chapter
- Banks, Stockmeyer
- 2008
(Show Context)
Citation Context ...rroneous results. Banks et al. [1] present a formal proof based on group theory that also generalizes to higher dimensions and other polytopes. Other related papers include the follow-up to this work =-=[2]-=- that uses Pólya0 1 2 3 Fig. 2. The quality of each triangle generated by Marching Cubes depends on the combination of edges that generate the triangle. 4 5 6 7 Fig. 1. The eight edge groups observed... |