## Computing and Rendering Point Set Surfaces (2002)

Citations: | 167 - 20 self |

### BibTeX

@MISC{Alexa02computingand,

author = {Marc Alexa and Tu Darmstadt and Johannes Behr and Shachar Fleishman and David Levin and Claudio T. Silva and Zgdv Darmstadt and Daniel Cohen-or},

title = {Computing and Rendering Point Set Surfaces},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can handle any point set.

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Citation Context ...lly interpolate a smooth surface. We call consolidation the process of “massaging” the point set into a surface. Some techniques, such as Hoppe et al. [23], Curless and Levoy [12], and Wheeler et al. =-=[55]-=- consolidate their sampled data by using an implicit representation based on a distance function defined on a volumetric grid. In [23], the distances are taken as the signed distance to a locally defi... |

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Citation Context ... detailed versions of a surface from one point set (see, for example, Fig. 4). A set of different versions could be used as a smooth-to-detailed hierarchy and would allow for multiresolution modeling =-=[27]-=-. Of course, h is not necessarily a global parameter and could be adapted to the local feature size. Varying h has several implications and utility in handling point sets (see [30] for a nice introduc... |

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Citation Context ...simplification technique which transitions triangles into (possibly multiple) points for faster rendering. Their system uses an extension of Floriani et al.’s Multi-Triangulation data structure [15], =-=[16]-=-. A similar system has been developed by Chen and Nguyen [8] as an extension of QSplat. 3 DEFINING THE SURFACE—PROJECTING Our approach relies on the idea that the given point set implicitly defines a ... |

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Citation Context ...uce a simplification technique which transitions triangles into (possibly multiple) points for faster rendering. Their system uses an extension of Floriani et al.’s Multi-Triangulation data structure =-=[15]-=-, [16]. A similar system has been developed by Chen and Nguyen [8] as an extension of QSplat. 3 DEFINING THE SURFACE—PROJECTING Our approach relies on the idea that the given point set implicitly defi... |

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Citation Context ...e systems to sample an implicit surface [56], [13]. Crossno and Angel [11] describe a system for sampling isosurfaces, where they use the curvature to automatically modulate the repulsive forces. Lee =-=[30]-=- uses a moving-least squares approach to the reconstruction of curves from unorganized and noisy points. He proposes a solution for reconstructing two and three-dimensional curves by thinning the poin... |

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Citation Context ...g bumps and other kinds of undesirable features, such as holes and tunnels, and be nonmanifold. Further processing of the triangulated models, such as smoothing [51], [14] or manifold conversion cite =-=[20]-=-, becomes necessary. The prominent difficulty is that the point set might not actually interpolate a smooth surface. We call consolidation the process of “massaging” the point set into a surface. Some... |

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Citation Context ...e, surface simplification algorithms [9] sample surfaces in different ways to optimize rendering performance. Related to our work are algorithms which use particle systems for sampling surfaces. Turk =-=[52]-=- proposes a technique for computing level of details of triangular surfaces by first randomly spreading points on a triangular surface, then optimizing their positions by letting each point repel thei... |

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Citation Context ...ed.sALEXA ET AL.: COMPUTING AND RENDERING POINT SET SURFACES 5 Another approach to defining surfaces from the data points is to perform some type of surface fitting [18], such as fitting a polynomial =-=[31]-=- or an algebraic surface [42] to the data. In general, it is necessary to know the intrinsic topology of the data and (sometimes) have a parametrization before surface fitting can be applied. Since th... |

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Citation Context ...ssibly multiple) points for faster rendering. Their system uses an extension of Floriani et al.’s Multi-Triangulation data structure [15], [16]. A similar system has been developed by Chen and Nguyen =-=[8]-=- as an extension of QSplat. 3 DEFINING THE SURFACE—PROJECTING Our approach relies on the idea that the given point set implicitly defines a surface. We build upon recent work by Levin [33]. The main i... |

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Citation Context ... fitting smooth surfaces to dense polygon meshes created by Curless and Levoy [12]. Another form of surface fitting algorithms couples some form of high-level model recognition with a fitting process =-=[44]-=-. The process of sampling (or resampling) surfaces has been studied in different settings. For instance, surface simplification algorithms [9] sample surfaces in different ways to optimize rendering p... |