## Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions (2000)

Citations: | 123 - 4 self |

### BibTeX

@INPROCEEDINGS{Boissonnat00smoothsurface,

author = {Jean-daniel Boissonnat and Frédéric Cazals},

title = {Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions},

booktitle = {},

year = {2000},

pages = {223--232}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through all the sample points. This surface is implicitly represented as the zero-set of some pseudo-distance function. It can be meshed so as to satisfy a user-defined error bound. Experimental results are presented for surfaces in R³.

### Citations

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Citation Context ...fore regarded as a level surface of an implicit function dened over the entire embedding space. Such methods have been applied to the surface reconstruction problem by Hoppe et al. [20], Bajaj et al. =-=[4, 5]-=-, and Curless and Levoy [12]. The algorithm proposed by Hoppe et al. [20] is related to ours. It estimates a tangent plane at the sample points using the k nearest neighbours and uses the distance to ... |

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Citation Context ...We have only considered surfaces, i.e. manifolds of codimension 1. It should be interesting to investigate other cases, most notably the case of curves in R 3 . For previous work on this problem, see =-=[14, 18, 28]-=-. Acknowledgements St#phane Nullans is acknowledged for preliminary contributions to this problem. Frank Da and Mariette Yvinec deserve special thanks for frequent discussions. Last but not the least,... |

5 |
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Citation Context ...s region is delimited by Voronoi centers in convex position, one could just collect them, compute the convex hull and its volume. But this requires a convex hull algorithm. Another method proposed in =-=[23]-=- consists of rst computing the Voronoi region of x, and second subdividing it into the natural neighbours sub-regions. This strategy requires intersection algorithms. To keep up with the Delaunay mach... |

3 |
Curves and Singularities (2nd edition
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Citation Context ...shows that h is continuously dioeerentiable. 2 By the implicit function theorem, h \Gamma1 (c) is continuously differentiable if c is a regular value which, by Sard's theorem is true for almost all c =-=[10, 17]-=-. 3. SURFACE RECONSTRUCTION 3.1 Interpolation of signed distance functions In the context of surface reconstruction, various functions can be used for the hp i (x). We follow Hoppe et al. [20] and use... |

2 |
Introduction to Implicit Surfaces, volume 391
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(Show Context)
Citation Context ...ped with. The surface is implicitly represented as the zero-set of a signed pseudo-distance function. Such a representation is attractive for computing ooesets or boolean operations and for rendering =-=[7]-=-. A polyhedral approximation of the implicit surface can also be provided. Third, theoretical guarantees can be derived for the quality of the reconstructed surface. Extensive tests in R 3 show that i... |

1 |
Natural coordinates on a surface. Rapport de recherche
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Citation Context ...f, for all x 2 S, there exists a point p i such that kxp i ks" lfs(x). When " ! 1, the sample is said to be a good sample. The following theorem 2 improves on a similar result by Amenta and =-=Bern. See [9] for a pro-=-of. Theorem 2. If P is a "-sample with "s1 4 , the surface facets form a polyhedron homeomorphic to S. As a consequence, when P is a good sample, the Delaunay simplices can be classied as in... |