M. Melkemi. A-shapes and their derivatives. In Proc. 13th ACM Sympos. Comput. Geom., pages 367--369, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....not 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 ....

M. Melkemi. A-shapes and their derivatives, manuscript, (1997).

....are the ff shapes of Edelsbrunner et al. 15, 16] and the sculpting method of Boissonnat [8] Recently, Amenta et al. 2] have proposed a new Voronoibased surface reconstruction algorithm that performs well in two and three dimensions. A similar idea has independently been proposed by Melkemi [22]. Since eOEcient and robust codes are now available to compute Voronoi diagrams and Delaunay triangulations [13] these methods are very fast. Notice however that the algorithm of Amenta et al. requires to add 2n so called poles to the initial sample points and to construct the Voronoi diagram of ....

M. Melkemi. A-shapes and their derivatives. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 367369, 1997.

....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 ....

M. Melkemi. A-shapes and their derivatives.

....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 to vary along with the level of detail. Melkemi [Mel97] defines an A shape on a set S of points as follows: let S 0 be the union of S with an arbitrary set of points A. An edge of the Delaunay triangulation of S 0 belongs to the A shape if both of its endpoints belong to S. Our crust is an A shape for which A is the set of Voronoi vertices. ....

Melkemi, Mahmoud, A-shapes and their derivatives, Proceedings of the ACM Symposium on Computational Geometry, (1997), pp. 367-369.

....not 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 [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 ....

M. Melkemi. A-shapes and their derivatives, manuscript, (1997).

....fails, both in theory and in practice. We believe, however, that there is a Voronoi based algorithm, perhaps combining aspects of crusts and ff shapes, that reconstructs noisy data into a thickened surface containing all the input points, some of them possibly in the interior. See Melkemi [15] for some suggestive experimental work in IR 2 . 7.2 Sharp Edges and Boundaries We would like to modify the crust algorithm to handle surfaces with sharp edges and to provide theoretical guarantees for the reconstruction of both sharp edges and boundaries. Interpolating reconstruction ....

M. Melkemi, A-shapes and their derivatives, In 13th ACM Symposium on Computational Geometry, pages 367--369, June 1997

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M. Melkemi. A-shapes and their derivatives. In Proc. 13th ACM Sympos. Comput. Geom., pages 367--369, 1997.

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