D. Attali. r-Regular shape reconstruction from unorganized points. Computational Geometry (1997) 248-253.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....need not be a topologically correct surface. All these algorithms consider candidate triangles from the Delaunay complex by some criterion. In practice, these triangles are unlikely to form a topologically correct surface due to noise, undersampling or sharp surface features. Especially Attali [6] reports many missing triangles for her Delaunay based reconstruction algorithm. Throughout this paper, we assume that the sample points are not associated with additional information, the sampling need not be uniform, the surface need not be smooth, and is not restricted to any specific genus. ....

....the algorithm UMBREL LAFILTER performs quite well on smooth surfaces, it does not necessarily compute a topologically correct surface, i.e. there possibly exist vertices at which the umbrella condition is not satisfied. Due to noise, undersampling or sharp surface features, the algorithms [4, 6, 18] are also likely to remove some triangles necessary for the reconstruction or leave additional triangles. Hence, the topological methods we presented should be useful also for these algorithms. They build on the output of these algorithms and turn it into a topologically correct surface. ....

D. Attali. -regular shape reconstruction from unorganized points. Computational Geometry: Theory and Applications, 10:239--247, 1998.

....involved in this problem. A proper reconstruction of the surfaces is possible only if the surfaces are sufficiently sampled. However, sufficiency conditions like sampling theorems are fairly difficult to formulate and as a result, most of the existing reconstruction algorithms, excepting [Att97, ABK98, ACDL00] ignore this aspect of the problem. A common artifact when the surface is not sufficiently sampled is the presence of spurious surface boundaries in the model. Manual intervention or additional information about the sampled surface (for instance, that the surface is manifold ....

....of the point set. The cell selection scheme can be surface based or volume based. The surface based scheme proceeds by decomposing the space into cells, finding the cells that are traversed by the surface and finding the surface from the selected cells. The approaches of [HDD 92, EM94, BBX97, Att97] fall under this category. The differences in their methods lie in the cell selection strategy. The volume based scheme decomposes the space into cells, removes those cells that are not in the volume bounded by the sampled surface and creates the surface from the selected cells. Most algorithms ....

D. Attali. r-regular shape reconstruction from unorganized points. In ACM Sym. on Computational Geometry, pp 248--253, 1997.

....to formulate and as a result, most of the existing reconstruction algorithms ignore or do not specify their requirements on sampling for reliable reconstruction. Hence, these algorithms can be classified as surface reconstruction heuristics as opposed to algorithms. Exceptions include the work of [Attali97, Bernardini97, Amenta98b]. These algorithms that can reliably reconstruct surfaces (without boundaries) provide sufficiency conditions for sampling. Assuming that the set of sample points satisfies these sampling conditions, correctness of these algorithms are ensured by theoretical guarantees based on the sampling ....

....cells. Commonly used cell subdivision techniques include Delaunay tetrahedralization and voxelization. Once subdivided, the points in the adjoining cells are connected to arrive at the surface. These algorithms differ in the cell selection strategies for final reconstruction. The approaches of [Algorri96, Hoppe92, Edelsbrunner94, Bajaj95, Attali97] fall under this category. A few methods use distance functions to decide on the final connectivity between points. The distance function might measure the distance of points from a local approximation of a surface [Hoppe92, Hoppe93] from the medial axis [Roth97] or from any other convenient ....

[Article contains additional citation context not shown here]

D. Attali. -regular shape reconstruction from unorganized points. In ACM Symposium on Computational Geometry, pages 248--253, 1997.

....have well defined sampling requirements or performance guarantees. They are, however, very fast and robust and are well accepted in practice. There has a been a lot of closely related work on reconstructing curves in the plane using Delaunay triangulation, much of it recent. See [19] 14] 18] [4], 5] 9] 15] and [11] Many of these algorithms come with theoretical guarantees. 3 Good triangles and dense enough sampling In two dimensions, it is clear that the right answer to the reconstruction problem is a piecewise linear curve connecting points that are adjacent along the original ....

D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248--253.

....generates a dense set of discrete samples. Surface reconstruction is the problem of interpolating these samples with a piecewise linear surface that approximates the original surface. A number of algorithms with various guarantees and capabilities have been designed in recent years for the problem [1, 2, 3, 4, 5, 6, 7, 11, 14, 15, 17, 19]. Reconstructed surfaces are used for various purposes such as display in computer graphics, finite element methods in physical simulations or in computer aided manufacturing. Often the surface becomes unwieldy for these postprocessings because of their large combinatorial description. Naturally, ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th ACM Sympos. Comput. Geom., (1997), 248--253.

....under a general setting, where no additional information is available other than the space co ordinates of the sample points. The two dimensional version of the problem, namely the curve reconstruction in plane from sample co ordinates has been well researched. A variety of approaches [2, 5, 9, 10, 12, 15, 17] are known to work with theoretical guarantees. In three dimensions, very few algorithms are known that provide performance guarantees. Hoppe et. al [16] presented an algorithm based on zero sets of a signed distance function. A similar approach is taken by Curless and Levoy [8] Edelsbrunner ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th ACM Sympos. Comput. Geom., (1997), 248-253.

....X , we denote by Y e X one of its contact point other than X, and by j e X the minimum over all such points Y e X of kX GammaY e X k 2R e X . We borrow from Amenta and Bern [1] the notion of local feature size. A related notion is the r regularity introduced by Serra [18] see also [4, 7]) Denition 7 (Amenta Bern) The local feature size lfs(X) at a point X 2 S is the Euclidean distance from X to the medial axis of S. Lemma 9 For any X;Y 2 S, lfs(X) lfs(Y ) kX Gamma Y k: Proof. B(X; lfs(Y ) kX Gamma Y k) contains B(Y; lfs(Y ) Since, by denition of the local feature size, ....

D. Attali. r-regular shape reconstruction from unorganized points. Comput. Geom. Theory Appl., 10:239247, 1998.

....2D Delaunay triangulations to reconstruct the surface. Bernardini et al. 10] proposed a ball pivoting algorithm that reconstructs the surface incrementally by rolling a ball over the sample points. Kobbelt and Botsch [25] used hardware projections to reconstruct surfaces from large data. Attali [8] introduced normalized meshes to reconstruct surfaces. Very recently Amenta, Bern and Kamvysselis [2] proposed a Voronoi based surface reconstruction called CRUST and proved its theoretical guarantees. This algorithm was later improved by the COCONE algorithm in [3] and the POWER CRUST in [4] ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248--253.

....needs. If higher order continuity is required, various subdivision [13, 28] and fairing schemes [25] can be used on the initial control mesh generated by surface reconstruction. A number of algorithms have been proposed for the surface reconstruction problem in recent years. The results of [5, 6, 7, 10, 15, 18, 26, 27] provide the necessary foundation for the problem. Very recently, starting with the CRUST algorithm of [2] few other algorithms have been designed that provide theoretical guarantees with empirical support [1, 3, 4, 9, 11] All these new algorithms are based on Voronoi diagrams and their dual ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th ACM Sympos. Comput. Geom., (1997), 248--253.

....algorithm of Amenta et al. requires to add 2n so called poles to the initial sample points and to construct the Voronoi diagram of a set of points that is 3 times as big as the initial data. In two dimensions, theoretical results on the quality of these methods can be found in the work of Attali [3], Bernardini and Bajaj [6] The algorithm of Amenta et al. 2] is the rst one that has provable guarantees in 3 dimensions. These theoretical results hold when the sampling is suOEciently dense. However, these bounds are rarely met in practical applications and, although the algorithm appears to ....

D. Attali. r-regular shape reconstruction from unorganized points. Comput. Geom. Theory Appl., 10:239247, 1998.

....it with an appropriate algorithm. Our Contribution If the curve is closed, smooth, and uniformly sampled, several methods for the curve reconstruction problem are known to work ranging over minimum spanning trees [dFdMG95] # shapes [BB97, EKS83] # skeletons [KR85] and r regular shapes [Att97]. A survey of these techniques appears in [Ede98] The case of non uniformly sampled closed curves was first treated successfully by Amenta, Bern and Eppstein [ABE98] and subsequently improved algorithms such as [DK99, Gol99] appeared. Open non uniformly sampled curves were treated in [DMR99] All ....

....with reconstruction algorithms that come with a guarantee, i.e. under certain assumptions on # and the sample set S taken from #, they output the correct reconstruction as defined in section 1.1. The first algorithms like [dFdMG95] # shapes [BB97, EKS83] # skeleton [KR85] and r regular shapes [Att97] are known to work if the curve is closed, smooth and uniformly sampled, i.e. the distance between two adjacent samples must be less than some constant, which is determined by the most detailed area of the curve. A survey on these techniques appears in [Ede98] The case of non uniformly sampled ....

D. Attali. r-regular shape reconstruction from unorganized points. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 248--253, 1997.

....it is not possible to correctly reconstruct a given curve from an arbitrary sample set from it. Therefore, some restrictions are needed on the sample which specify how dense a sampling has to be to guarantee a correct output of the algorithm. The first algorithms for curve reconstruction [3, 4, 9, 10, 13] imposed a uniform sampling condition as they basically demanded that the distance between any two adjacent samples must be less than some constant. This is not satisfactory as it may require a dense sampling in areas where a sparse sampling is sufficient. Amenta, Bern, and Epstein [2] introduced ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248--253.

....of these surfaces is possible only if they are sufficiently sampled. However, sufficiency conditions like sampling theorems are fairly difficult to formulate and as a result, most of the existing reconstruction algorithms ignore this aspect of the problem. Exceptions include the works of [Att97, BB97, ABK98] If the surface is improperly sampled, the reconstruction algorithm can produce artifacts. A common artifact is the presence of spurious surface boundaries in the model. Manual intervention or additional information 2 about the sampled surface (for instance, that the surface is ....

....of the point set. The cell selection scheme can be surface based or volume based. The surface based scheme proceeds by decomposing the space into cells, finding the cells that are traversed by the surface and finding the surface from the selected cells. The approaches of [HDD 92, EM94, BBX95, Att97] fall under this category. The differences in their methods lie in the cell selection strategy. Hoppe et al. HDD 92, HDD 93, Hop94] use a signed distance function of the surface from any point to determine the selected cells. Bajaj and Bernardini [BBX95, BBX97, Ber96] construct an ....

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D. Attali. r-regular shape reconstruction from unorganized points. In ACM Symposium on Computationl Geometry, pages 248--253, 1997.

....suciently small , then the crust is homeomorphic to . Boissonnat and Cazals [12] and Hiyoshi and Sugihara [25] proposed algorithms to produce a smooth surface using natural coordinates, which are de ned and computed using the Voronoi diagram of the sample points. Further examples can be found in [5, 6, 11, 15]. In this section, we show that nice surface data can have complicated Delaunay triangulations, thereby showing that all these surface reconstruction algorithms can take quadratic time in the worst case. We will analyze our constructions in terms of the sample measure of a surface , de ned as ....

D. Attali. r-regular shape reconstruction from unorganized points. Comput. Geom. Theory Appl. 10:239-247, 1998.

....by Hoppe et al. 16] solutions to the general surface reconstruction problem can provide a baseline for solving and analyzing specialized problems. The two dimensional version of the problem, namely curve reconstruction in the plane, has received a lot of recent attention. Several algorithms [2, 4, 5, 9, 10, 14, 15, 18] with various theoretical guarantees have been proposed. The three dimensional problem has been addressed by researchers in computer graphics and computer vision. Hoppe et. al [16] presented an algorithm in which the surface is represented by the zero set of a signed distance function. Curless ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th ACM Sympos. Comput. Geom., (1997), 248-253.

....function on the entire space, without about the same amount of storage as the input data itself. Computational geometry The surface reconstruction problem has received a lot of recent attention in the computational geometry community. There have been several algorithms for reconstructing curves [19, 4, 6, 15, 21] including algorithms which handle plane curves with boundaries [16] and curves with sharp corners [20, 1] and an algorithm for space curves with a strong topological guarantee [ we give something similar in Section 7) In three dimensions, Amenta and Bern [3] gave an algorithm which selects a ....

.... If we could determine that two inner (outer) polar balls which induce a face of the power diagram must intersect deeply, then we could assign all power diagram two faces corresponding to shallowly intersection pairs of balls to the power crust, giving an algorithm analogous to that of Attali [6] in IR 2 . Unfortunately, we could not establish that adjacent inner (outer) polar balls intersect deeply. Instead, we have the following. Lemma 36 Two inside (resp. outside) polar balls inducing a face within the tubular neighborhood meet at an angle of at least =2, for small enough r. ....

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D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248-253.

....polygons [1] The polygonal reconstruction is the inscribed polygon through the sample points. For dense samplings the length and the total curvature of the polygonal reconstruction approximate the length and the total curvature of fl. This is no longer true if one considers polygons, as in Attali [3], that are only near to fl in the Hausdorff or Fr echet metric. Given the sample points and no other information the polygonal reconstruction is in general the best way to estimate the length and the total curvature of fl. Of course there is no algorithm that can reconstruct any curve from any ....

D. Attali r-Regular Shape Reconstruction from Unorganized Points, Proc. 13th Ann. ACM Symp. on Computational Geometry 1997, pp. 248-253 (1997)

....under certain assumptions on and V . Figure 1 illustrates the curve reconstruction problem. If the curve is closed, smooth, and uniformly sampled, several methods are known to work ranging over minimum spanning trees [FG94] shapes [BB97, EKS83] skeletons [KR85] and r regular shapes [Att97] A survey of these techniques appears in [Ede98] The case of non uniformly sampled closed curves was rst treated successfully by Amenta, Bern and Eppstein [ABE98] and subsequently improved algorithms such as [DK99, Gol99] appeared. Open non uniformly sampled curves were treated in [DMR99] All ....

D. Attali. r-regular shape reconstruction from unorganized points. In Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG'97), pages 248-253, 1997.

....algorithms which provably solve the reconstruction problem under certain assumptions on and V . If the curve is closed, smooth, and uniformly sampled, several methods are known to work ranging over minimum spanning tree [FG94] shapes [BB97; EKS83] skeleton [KR85] and r regular shapes [Att97]. A survey on these techniques appears in [Ede98] The case of non uniformly sampled closed curves was rst treated successfully by Amenta, Bern and Eppstein [ABE98] and subsequently improved algorithms such as [DK99; Gol99] appeared. Open non uniformly sampled curves were treated in [DMR99] ....

D. Attali. r-regular shape reconstruction from unorganized points. In Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG'97), pages 248-253, 1997. 12
E. Althaus, K. Mehlhorn, S. Naher, S. Schirra

....computer vision and intelligent systems, extracting information from aerial surveys in geographic information systems, and tting a spline through a set of points in mathematical modeling. As a result of this vast application domain, the problem has drawn attention of researchers for a long time [5, 6, 9, 10, 14, 15]. Recently, renewed interest in the problem has focused on its relation to the more demanding problem of surface reconstruction in CAD applications [1, 3, 13] Advances in laser technology have made it easier to obtain samples from the boundary of an object but these samples are useless without ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th ACM Sympos. Comput. Geom., (1997), 248-253.

.... morphology, relied on ad hoc heuristics (e.g. my own [OBW87] The heuristics were placed on a firmer footing with ff shapes [EKS83] and fi skeletons [KR85] and other structures, whose underlying proximity graphs were later shown to support accurate reconstruction from uniformly sampled curves [FMG95, Att98, BB97]. User selection of the ff or fi parameter is still necessary. A breakthrough was achieved by Amenta, Bern, and Eppstein [ABE98] who designed two algorithms that guarantee correct reconstruction of smooth closed curves even with (sufficiently dense) nonuniform samples, and which lift the burden ....

D. Attali. r-regular shape reconstruction from unorganized points. Comput. Geom. Theory Appl., 10:239--247, 1998.

....1997, Government of India and Max Planck Institut f ur Informatik, Germany. y Max Planck Institut f ur Informatik, D 66123 Saarbr ucken, Germany. E mail: fmehlhorn,ramosg mpi sb.mpg.de. Partially supported by esprit ltr project 28155 (GALIA) 1 [3, 7] skeleton [11] and r regular shapes [2]. A survey on these techniques appears in [6] The case of non uniformly sampled closed curves was rst treated successfully by Amenta, Bern and Eppstein [1] and subsequently improved algorithms such as [5, 9, 10] appeared. a) b) c) d) e) f) Figure 1: Reconstructions by NN Crust (a and ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248-253.

....the surface. These curves may form a tree structure if the surface resemble a tree of generalized cylinders . The method works independently of the bending of the surface. As a consequence it will return a correct result for the shape shown on Figure 2.b. Like in other reconstruction algorithms [4, 21, 2], we make some hypothesis on the input cluster of points. 1: The data points should be sampled on a certain (unknown) surface. 2: The sampling should be done in such a way that the distance between neighbor points is small with respect to the width of the tubular parts of the surface. The ....

D. Attali. r-regular shape reconstruction from unorganized points. In ACM Symposium on Computational Geometry, pages 248--253, Nice, France, 1997.

.... and pattern recognition has drawn a lot of attention from researchers over the last three decades [15, 16, 17] If the curve is closed and uniformly sampled, a number of methods is known to work ranging over minimum spanning tree [8] shapes [3, 7] skeleton [11] and r regular shapes [2]. A survey on these techniques appears in [6] The case of non uniformly sampled closed curves was rst treated successfully by Amenta, Bern and Eppstein [1] and subsequently improved algorithms such as [5, 9, 10] appeared. We need the following de nitions for further exposition. A single smooth ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248-253.

....defined family of fl neighborhood graphs, in which the angle between the two circles at the point of intersection (see Observation 16) is fixed at an optimal value, probably a bit more than =2. We have recently become aware of two concurrent independent research efforts related to ours. Attali [A97] proves that uniformly sampled curves can be reconstructed by (essentially) the above mentioned family of fl neighborhood graphs. She requires the sampling density be everywhere great enough to resolve the finest detail of the curve. Our results are better in that they allow the sampling density ....

Attali, Dominique. R-regular shape reconstruction from unorganized points, Proceedings of the ACM Symposium on Computational Geometry, (1997), pp. 248-253.

....and Eppstein [1] proposed a framework based on local feature size under which they show two graphs, crust and fi skeleton, coincide with G if the points are sufficiently sampled. Some of the other effective approaches include ff shapes by [6] which is analyzed later by [3] r regular shapes by [2], A shapes by [7] and a Delaunay based method by [4] A survey of these methods appear in [5] In this paper we show that a modified nearest neighbor graph also coincides with G. The algorithm and its analysis are simple. Nevertheless, it improves the sampling density to 1=3 from 0:252 as required ....

D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248--253.

....be extracted from their Delaunay triangulation. The notion of fl neighborhood graph unifies several graphs such as the Delaunay triangulation, the convex hull, the fi skeleton. Minimum spanning trees [HDD 92] ff shapes [Ede87, EM94] fl neighborhood graphs [Vel92a, Vel92b] and skeletons [Att97] have been used to reconstruct surfaces from sets of points, while Delaunay triangulations are used in volume based approaches [Boi84, BG93b] which can be interesting for some applications involving for example a further motion planning step [BG93a] In some special cases, more efficient methods ....

D. Attali. R-regular shape reconstruction from unorganized points. In Proc. 13th ACM Symposium on Computational Geometry, 1997, to appear

....well defined sampling requirements or performance guarantees. They are, however, very fast and robust and are well accepted in practice. There has a been a lot of closely related work on reconstructing curves in the plane using Delaunay triangulation, much of it recent. See [18] 13] 17] [4], 5] 9] 14] and [11] Many of these algorithms come with theoretical guarantees. 3 Good triangles and dense enough sampling In two dimensions, it is clear that the right answer to the reconstruction problem is a piecewise linear curve connecting points that are adjacent along the original ....

D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248--253.

....algorithms with provable guarantees. Figueiredo and Miranda Gomes [17] prove that the Euclidean minimum spanning tree can be used to reconstruct uniformly sampled curves in the plane. Bernardini and Bajaj [6] prove that ff shapes also reconstruct uniformly sampled curves in the plane. Attali [3] gives yet another provably correct reconstruction algorithm for uniformly sampled curves in the plane, using a subgraph of the Delaunay triangulation in which each edge is included or excluded according to the angle between the circumcircles on either side. Our previous paper showed that both the ....

D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248--253.

.... Delaunay sculpting heuristic of Boissonnat [6] which progressively eliminates tetrahedra from the Delaunay triangulation based on their circumspheres. In two dimensions, there are a number of recent theoretical results on various Delaunay based approaches to reconstructing smooth curves. Attali [3], Bernardini and Bajaj [5] Figueiredo and Miranda Gomes [11] and ourselves [1] have all given guarantees for different algorithms. A fundamentally different approach to reconstruction is to use the input points to define a signed distance function on IR 3 , and then polygonalize its zero set to ....

D. Attali. r-Regular Shape Reconstruction from Unorganized Points. In 13th ACM Symposium on Computational Geometry, pages 248--253, June 1997.

....in [15] The number of triangles is also about twice the number of points. Some algorithms take as input an arbitrary set of points to build a triangulation of the most probable surface passing through the points. Bittar et al. 3] uses implicit surfaces and medial axis transformation, and Attali [2] uses Delaunay simplicial decomposition. Other algorithms choose to match either globally or locally surface patches with the data points, minimizing a distance criterion. Taubin proposes in [33] an algorithm to fit an algebraic surface and a set of points with an Euclidean distance criterion. ....

D. Attali. r-regular shape reconstruction from unorganized set of points. In 13th ACM Symposium on Computational Geometry, Nice, June 1997.

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D. Attali. r-Regular shape reconstruction from unorganized points. Computational Geometry (1997) 248-253.

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D. Attali. r-regular shape reconstruction from unorganized points. Computational Geometry, pages 248--253, 1997.

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D. Attali. r-regular shape reconstruction from unorganized points. In Proceedings of the 13th Annual ACM Symposium on Computational Geometry (SCG'97), pages 248-253, 1997. 30

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ATTALI, D. r-regular shape reconstruction from unorganized points. Computational Geometry. Theory and Applications 10, 4 (July 1998), 239--247.

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D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248--253.

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D. Attali. r-regular shape reconstruction from unorganized points. Comput. Geom. Theory Appl., 10:239-247, 1998.

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Attali, D., 1997. r-regular shape reconstruction from unorganized points. Proc. 13th Annual ACM Symposium on Computational Geometry, pp. 248-253.

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D. Attali. r-regular shape reconstruction from unorganized points. In Proc. 13th ACM Sympos. Comput. Geom., pages 248--253, 1997.

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D. Attali, r-Regular shape reconstruction from unorganized points, in: 13th ACM Symp. on Computational GeometryissuenrJune (1997) 248--253.

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D. Attali. r-regular shape reconstruction from unorganized points. In ACM Sym. on Computational Geometry, pp 248--253, 1997.

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D. Attali. r-regular shape reconstruction from unorganized points. Proc. 13th Ann. Sympos. Comput. Geom., (1997), 248--253.

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D. Attali. r-regular shape reconstruction from unorganized points. In Proc. 13th Ann. Sympos. Comput. Geom., pages 248-253, 1997.

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D. Attali. r-Regular shape reconstruction from unorganized points. In Proc. 13th ACM Symp. Computational Geometry , 1997, 248--253.

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D. Attali. r-regular shape reconstruction from unorganized points. In ACM Symposium on Computational Geometry, pages 248--253, 1997.

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D. Attali. r-regular shape reconstruction from unorganized points. 13th ACM Symposium on Computational Geometry, pages 248-253, June 1997.

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D. Attali. r-regular shape reconstruction from unorganized points. In ACM Symposium on Computational Geometry, pages 248--253, 1997. Nice, France.

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D. Attali. r-regular shape reconstruction from unorganized points. In ACM Symposium on Computationl Geometry, pages 248--253, 1997.

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