## Recent advances in remeshing of surfaces (2008)

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Venue: | Shape Analysis and Structuring, Mathematics and Visualization |

Citations: | 33 - 1 self |

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@INPROCEEDINGS{Alliez08recentadvances,

author = {Pierre Alliez and Giuliana Ucelli and Craig Gotsman and Marco Attene},

title = {Recent advances in remeshing of surfaces},

booktitle = {Shape Analysis and Structuring, Mathematics and Visualization},

year = {2008},

publisher = {Springer}

}

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### Abstract

Summary. Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and error-driven remeshing. We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research. 1

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Citation Context ...division surfaces [Sch98, ZS00], geometric modeling [KBB + 00], digital geometry processing [Tau00, SS01] morphing [Ale02], simplification and compression [LRC + 02, GGK02, AG03] and parameterization =-=[FH04]-=-.2 Pierre Alliez, Giuliana Ucelli, Craig Gotsman, and Marco Attene Fig. 1. Uniform remeshing of the Digital Michelangelo David model. Figure reproduced from [SAG03]. 1.1 Remeshing There is no precise... |

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Citation Context ... sampling. Over-sampling, however, will significantly increase the number of vertices, and thus the associated complexity, transmission and processing cost. Furthermore, as observed by Kobbelt et al. =-=[KBSS01]-=-, the associated aliasing problem will not be solved by over-sampling, since the surface normals in the reconstructed model will not converge to the normal field of the original object. To cope with s... |

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Citation Context ...lobally uniform edges in the simple case, and locally uniform edges (i.e. isotropic sampling) if weights are assigned to edges [VRS03]. The interactive remeshing technique introduced by Alliez et al. =-=[AMD02]-=- is based on global parameterization. It represents the original mesh by a series of 2D maps in parameter space, and allows the user to control the sampling density over the surface patch using a so-c... |

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Citation Context ...ing algorithm is used to remove the discontinuities across chart boundaries and create a watertight surface. Another way to minimize seams due to cutting is to first parameterize the mesh to a sphere =-=[GGS03]-=-, which is then mapped in a highly structured way to the square. Fig. 7. Construction of a Geometry Image: Original mesh (70k faces, genus 0), original mesh with cut, parameterization and Geometry Ima... |

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Citation Context ... this. More importantly, a model that contains features interior to the base mesh triangles will require a very dense subdivision mesh over the entire model. Inter-Surface Mapping Kraevoy and Sheffer =-=[KS04]-=- developed a technique for joint parameterization and compatible remeshing of two genus-0 meshes with a partial correspondence (Fig.10). The input of the algorithm is a pair of triangle meshes and a s... |

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Citation Context ...a global optimum, and to accelerate convergence. Another promising direction for efficient isotropic sampling is the hierarchical Penrose-based importance sampling technique developed by Ostromoukhov =-=[ODJ04]-=-, which is deterministic and several orders of magnitude faster than relaxation methods. 2.4 Feature Remeshing Definitions Assume that a triangle mesh is an approximation of a curved shape, possibly w... |

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Citation Context ... embedding is computed for each mesh. Second, the initial subdivision is deformed such that the common features coincide on the spheres. The two connectivities are then merged. Figure reproduced from =-=[Ale99]-=-. A more general approach is to parameterize the models over a common base mesh [LDSS99, LCLC03, MKFC01, PSS01]. This approach splits the meshes into matching patches with an identical inter-patch con... |

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Citation Context ...nsitive to the patch structure (see example Fig.5). The vertex sampling is also delicate to control. The second class of techniques does not rely on any parameterization but instead uses ray shooting =-=[KVLS99]-=- to find correspondences for shrink wrapping the new mesh onto the input mesh (Fig.6). Shape compression techniques employing semi-regular remeshing are among the best reported to date. The main idea ... |

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Citation Context ...and parameterization) are not important for the representation of the geometry. The goal is therefore to reduce the “volume” of these two components as much as possible by semi-regular remeshing (see =-=[AG03]-=- for a more detailed description of this shape compression technique). Discussion In all mapping-based methods, the parameterization plays a critical role, and any deficiencies in it will be amplified... |

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Citation Context ...terested in related topics to read several comprehensive courses and tutorials on subdivision surfaces [Sch98, ZS00], geometric modeling [KBB + 00], digital geometry processing [Tau00, SS01] morphing =-=[Ale02]-=-, simplification and compression [LRC + 02, GGK02, AG03] and parameterization [FH04].2 Pierre Alliez, Giuliana Ucelli, Craig Gotsman, and Marco Attene Fig. 1. Uniform remeshing of the Digital Michela... |

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Citation Context ...ended using an approximation of the geodesic distance for remeshing byRecent Advances in Remeshing of Surfaces 15 Sifri et al. [SSG03]. A more general approach was recently introduced by Dong et al. =-=[DKG05]-=-, who compute two orthogonal harmonic Morse functions on the mesh surface. Drawing contours of each results in a good quad remesh (Fig.11). Another quasi-uniform remeshing approach based on an advanci... |

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Citation Context ...ring4 Pierre Alliez, Giuliana Ucelli, Craig Gotsman, and Marco Attene to a reference smooth approximation of the original geometry (e.g. by using triangular cubic Bézier patches such as PN triangles =-=[VPBM01]-=- or continuous patches [WM96]). We now list some general desirable algorithmic functionalities of a remeshing algorithm: • • • Levels of detail. Support for continuous Levels-of-Detail (i.e., continuo... |

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Citation Context ...ncident triangles [SG03]. This technique has been recently extended to local equalization of the Voronoi areas of the vertices in order to symmetrize a linear system used for multiresolution modeling =-=[BK04]-=-. The system is solved efficiently using a Cholesky-based solver that takes advantage of symmetric band-limited matrices. Although efficient and robust, these area equalization techniques do not provi... |

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Citation Context ...t void. Its main advantage is in retaining the uniformity while increasing the density. In contrast to stochastic approaches, it can guarantee some uniformity by bounding the distance between samples =-=[BO03]-=-. This paradigm, also called Delaunay refinement [Che93, Rup95, Mil04] or sink insertion [EG01] has proven particularly effective in producing uniform as well as isotropic sample placements. It has be... |

36 | Geodesic remeshing using front propagation - Peyré, Cohen |

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Citation Context ... mesh surface. Drawing contours of each results in a good quad remesh (Fig.11). Another quasi-uniform remeshing approach based on an advancing front is implicit in the SwingWrapper compression scheme =-=[AFSR03]-=-. In order to reduce the number of bits to encode the vertex locations, SwingWrapper partitions the surface into geodesic triangles that, when flattened, constitute a new mesh which is strongly compre... |

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Citation Context ...composed solely of triangles and quadrilaterals. Figure reproduced from [DKG05]. Attraction-repulsion. One of the first remeshing techniques to surface in the graphics community was described by Turk =-=[Tur92]-=-. It places a (user defined) number of new vertices on the input mesh, and arranges the new vertices with the help of an attraction-repulsion particle relaxation procedure, followed by an intermediate... |

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Citation Context ... sampling is even more restricting by dictating the sampling to be uniform over the entire mesh. Smooth gradation means that if the sampling density is not uniform - it should vary in a smooth manner =-=[BHP97]-=-. Motivation High quality remeshing is motivated by numerical stability and reliability of computations for simulation. Efficient rendering, interactive free-form shape modeling, as well as a few geom... |

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Citation Context ...em may be avoided by snapping some of the evenly distributed vertices onto sharp creases, as proposed in [VRKS01]. Feature-enhancing When the original shape is not available, the EdgeSharpener method =-=[AFRS03]-=- provides an automatic procedure for identifying and sharpening the chamfered edges and corners. In a first step, the mesh is analyzed and the average dihedral angle at edges is computed. Based on thi... |