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## Quality isosurface mesh generation using an extended marching cubes lookup table

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Venue: | Comput. Graph. Forum |

Citations: | 9 - 0 self |

### Citations

2695 | Marching Cubes: A high resolution 3D surface construction algorithm.
- Lorensen, Harvey
- 1987
(Show Context)
Citation Context ...lar to the one in [LS07], but it uses a lookup table for cubes not tetrahedra. It can also be modified for other convex mesh elements, such as pyramids or bipyramids. 2. Background Lorensen and Cline =-=[LC87]-=- published the Marching Cubes Algorithm in 1987. A year earlier, Wyvill et. al. [WMW86] published a somewhat similar isosurface extraction algorithm, but without the use of isosurface patch lookup tab... |

214 | Provably good mesh generation
- Bern, Eppstein, et al.
- 1994
(Show Context)
Citation Context ...ive, producing large triangles in flat, featureless regions and small triangles in regions with high curvature. We cite only the most relevant articles on mesh generation. Bernd, Eppstein and Gilbert =-=[BEG94]-=- introduced the idea of warping a background grid for mesh generation in 2D. Mitchell and Vavasis [MV00] generalized the algorithm to higher dimensions. Labelle and Shewchuk [LS07] applied the grid wa... |

123 | Tight cocone: a watertight surface reconstructor.
- Dey
- 2003
(Show Context)
Citation Context ...gulations. Meyer et. al. [MKW07] use a particle based system to construct a point sampling of the isosurface and then reconstruct the isosurface from the sample points using the TIGHT COCONE software =-=[DG03]-=-. All three algorithm are adaptive, producing large triangles in flat, featureless regions and small triangles in regions with high curvature. We cite only the most relevant articles on mesh generatio... |

59 | Isosurface stuffing: Fast tetrahedral meshes with good dihedral angles
- Labelle, Shewchuk
(Show Context)
Citation Context ...riangles, isosurface vertices located near grid vertices can create triangles with small areas, edges or angles. They can also create triangles with angles near 180 ◦ . Recently, Labelle and Shewchuk =-=[LS07]-=- presented an algorithm for constructing tetrahedral meshes with good dihedral angles. By combining their algorithm with the extended isosurface lookup table, we can modify Marching Cubes to produce a... |

50 |
Scopigno: Metro: Measuring error on simplified surfaces.
- Cignoni, Rocchini, et al.
- 1998
(Show Context)
Citation Context ... are quite close to the theoretical ones. To measure how much SnapMC modified the isosurface, we measured the difference between the SnapMC isosurface and the original isosurface using the tool METRO =-=[CRS98]-=-. METRO measures the Hausdorff distance between two surfaces. For technical reasons, we measured only the directed Hausdorff distance from the SnapMC surface to the original surface and used a slightl... |

50 | Quality mesh generation in higher dimensions
- Mitchell, Vavasis
(Show Context)
Citation Context ...ature. We cite only the most relevant articles on mesh generation. Bernd, Eppstein and Gilbert [BEG94] introduced the idea of warping a background grid for mesh generation in 2D. Mitchell and Vavasis =-=[MV00]-=- generalized the algorithm to higher dimensions. Labelle and Shewchuk [LS07] applied the grid warping to a body centered lattice and combined it with a Marching Cubes style lookup table to quickly gen... |

45 | Isosurfacing in higher dimensions - Bhaniramka, Crawfis - 2000 |

31 | Isosurface construction in any dimension using convex hulls - Bhaniramka, Wenger, et al. - 2004 |

31 |
What is a Good Linear Element
- Shewchuk
(Show Context)
Citation Context ....3.) ing, but not a major visualization problem. However, when isosurface triangulations are used for modeling and simulation, small or large triangle angles can create significant numerical problems =-=[She02]-=-. SnapMC produces an isosurface triangulation with guaranteed upper and lower bounds on the angles of any triangle in the triangulation. SnapMC has two drawbacks. First, it can change isosurface topol... |

31 | High-quality extraction of isosurfaces from regular and irregular grids
- Schreiner, Scheidegger, et al.
- 2006
(Show Context)
Citation Context ...ng Cubes Algorithm. Their algorithms apply to generating lookup tables for other convex mesh elements such as tetrahedra or pyramids and to mesh elements in dimension R 4 or higher. Schreiner et. al. =-=[SSS06]-=- gave an advancing front method for constructing isosurfaces with good triangles. However, the method has difficulties in a few cases where the front meets itself. Dey and Levine [DL07] gave an isosur... |

28 |
Continuous analogs of digital boundaries: A topological approach to iso-surfaces. Graphical Models,
- Lachaud, Montanvert
- 2000
(Show Context)
Citation Context ...e construction based on the extended isosurface lookup table is exactly the same as the Marching Cubes Algorithm. The challenge is in constructing the extended lookup table. Lachaud and Montanvert in =-=[LM00]-=- and independently Bhaniramka et. al. in [BWC00,BWC04] gave convex hull based algorithms for automatically generating isosurface lookup tables. We show how to modify those algorithms to generate exten... |

26 |
WYVILL B.: Data Structure for Soft Objects
- WYVILL, MCPHEETERS
- 1986
(Show Context)
Citation Context ...also be modified for other convex mesh elements, such as pyramids or bipyramids. 2. Background Lorensen and Cline [LC87] published the Marching Cubes Algorithm in 1987. A year earlier, Wyvill et. al. =-=[WMW86]-=- published a somewhat similar isosurface extraction algorithm, but without the use of isosurface patch lookup tables. Marching Cubes is a fast, efficient, easily implementable algorithm because of its... |

15 | accuracy, and quality of isosurface meshes using dynamic particles
- Meyer, Kirby, et al.
(Show Context)
Citation Context ...ficulties in a few cases where the front meets itself. Dey and Levine [DL07] gave an isosurface construction and meshing algorithm based on Voronoi diagrams and Delaunay triangulations. Meyer et. al. =-=[MKW07]-=- use a particle based system to construct a point sampling of the isosurface and then reconstruct the isosurface from the sample points using the TIGHT COCONE software [DG03]. All three algorithm are ... |

13 |
Delaunay meshing of isosurfaces
- Dey, Levine
(Show Context)
Citation Context ...einer et. al. [SSS06] gave an advancing front method for constructing isosurfaces with good triangles. However, the method has difficulties in a few cases where the front meets itself. Dey and Levine =-=[DL07]-=- gave an isosurface construction and meshing algorithm based on Voronoi diagrams and Delaunay triangulations. Meyer et. al. [MKW07] use a particle based system to construct a point sampling of the iso... |