J.-D. Boissonnat, F. Cazals, Smooth surface reconstruction via natural neighbour interpolation of distance functions, in: Proc. 16th Annual ACM Sympos. Comput. Geom., 2000, pp. 223--232.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... in the study of dynamical systems, the quasiperiodic and chaotic orbits can be automatically recognized from sample points in the phase portraits if automatic shape recognition can be performed; see [23] To this end one may try reconstruction algorithms for curves [2, 11, 17] and for surfaces [1, 3, 6, 8, 12, 18]. Unfortunately, these reconstruction algorithms are of no use if the dimension of the shape is not determined a priori. For example, a surface reconstruction algorithm cannot produce a curve out of a sample that has been derived from a curve. The situation becomes worse when data have samples ....

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance functions. Proc. 16th Ann. Sympos. Comput. Geom., (2000), 223--232.

....is. In order to alleviate this problem in the context of surface reconstruction, Amenta and Bern [1] identify some Voronoi vertices called poles that remain far from the surface. These poles are the farthest Voronoi vertices from the sample points in their Voronoi cells. Boissonnat and Cazals [7] and Amenta, Choi and Kolluri [4] show that the poles indeed lie close to the medial axis and converge to it as the sample density approaches infinity. The convergence result of poles to the medial axis is a significant progress in the medial axis approximation in 3D. However, many applications ....

....require much smaller values. The Voronoi diagram and its dual, the Delaunay triangulation, play a key role in capturing information about shapes. This observation has led to a number of algorithms for the related problem of surface reconstruction which exploit the structures of these diagrams [1, 3, 7, 14, 15]. The Voronoi diagram V P for a point set P is a cell complex consisting of Voronoi cells P and their facets, edges and vertices, where V p x x q . The dual complex, D P , called the Delaunay triangulation of P, consists of Delaunay tetrahedra and their incident ....

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance functions. Proc. 16th. ACM Sympos. Comput. Geom., (2000), 223--232.

....DMR 0121695 and CCR 0219594. 1 Introduction Delaunay triangulations and their dual Voronoi diagrams are among the most commonly used and thoroughly studied structures in combinatorial geometry. One application that has received considerable attention recently is curve and surface reconstruction [1, 2, 3, 4, 12, 18, 19, 23, 29, 30]. The input to the surface reconstruction problem is a set of unorganized points from an unknown surface # in IR , and the goal is to construct a geometric approximation of # with the correct topology. Most recent reconstruction algorithms begin by constructing the Delaunay triangulation or ....

....input points. The recent work of Dey, Funke, and Ramos [18, 23] is a notable exception. Since three dimensional Delaunay triangulations can have complexity # n in the worst case, these algorithms have worst case running time# ) However, this behavior is almost never observed in practice [12, 17] except for highly contrived inputs [21] For all practical purposes, Delaunay triangulations of surface points appear to have linear complexity. The first subquadratic complexity bound for Delaunay triangulations of surface points was obtained by Golin and Na [25, 26, 27] They proved that if n ....

[Article contains additional citation context not shown here]

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Proc. 16th Annu. ACM Sympos. Comput. Geom., 223--232, 2000.

....Amenta, Bern and Kamvysselis [1] This algorithm called CRUST exploits the structures of the Voronoi diagram of the input point set to reconstruct the surface. Amenta, Choi, Dey and Leekha [2] introduced the COCONE algorithm which improved CRUST both in theory and practice. Boissonnat and Cazals [7] designed another algorithm based on natural neighbors following the development of CRUST. Funke and Ramos improved the theoretical complexity of the COCONE algorithm [15] Recently Cohen Steiner and Da have designed another Delaunay based surface reconstruction algorithm [10] All these ....

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance functions. Proc. 16th. Annu. Sympos. Comput. Geom., (2000), 223--232.

....neighbors; moving least squares. 1 Introduction We consider the problem of surface reconstruction and refinement from scattered data points without normals. Several algorithms are known for this important problem [4 13] including a number of recent algorithms with theoretical guarantees [4 7]. Those algorithms use a 3D Delaunay triangulation of the original point cloud to compute a triangular surface mesh. Computing the Delaunay triangulation can be slow and susceptible to numerical errors. Gopi, Krishnan, and Silva [12] proposed an algorithm based on Differential Geometry that ....

J. D. Boissonnat, F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance function. Computational Geometry: T&A 22(1--3):185--203, 2002.

....and arithmetic coding. Khodakovsky et al. 13] point out the great importance of normal versus tangent decomposition of the relative position for bit allocation in geometry. Devillers and Gandoin [8] totally suppress the order of the vertices, assuming that a geometry centered triangulation [3] is later able to progressively rebuild the connectivity from the regularity of the point cloud transmitted. Snoyeink et al. 23] and Denny and Solher [7] stress that any data already transmitted have defined an implicit order which can be used to save significant entropy. Since compression ....

J-D. Boissonnat and F. Cazals. Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions. In ACM Symposium on Computational Geometry, 2000.

....into Delaunay tetrahedra. Di erent approaches have been proposed to constrain surfaces. One approach re nes surfaces, by adding points until every boundary triangles are forced into the Delaunay triangulation [10,26] Some reconstruction methods produce directly Delaunay conforming surfaces [2,6,11]. In this paper, we use the fact that we are considering iso surfaces. Therefore, we propose a di erent approach. We build iso surfaces that are directly included in the Delaunay tetrahedrization of their vertices. The proposed method is performed locally and remains valid, whatever is the size ....

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. In Proc. 16th Annu. ACM Sympos. Comput. Geom., 2000.

....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 Delaunay triangulations. If the input is equipped with additional information such as the estimation of surface normals, or matrix adjacency among the sample points from range scanners, efficient algorithms exploiting these ....

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance functions. Proc. 16th. ACM Sympos. Comput. Geom., (2000), 223--232.

.... and Voronoi diagrams are one of the most thoroughly studies objects in computational geometry, with applications to nearest neighbor searching [3, 21, 25, 43] clustering [1, 46, 48, 54] niteelement mesh generation [20, 32, 49, 56] deformable surface modeling [19] and surface reconstruction [4, 5, 6, 7, 12, 45]. Many algorithms in these application domains begin by constructing the Delaunay triangulation or Voronoi diagram of a set of points in IR 3 . Since three dimensional Delaunay triangulations can have complexity (n 2 ) in the worst case, these algorithms have worst case running time (n 2 ) ....

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Proc. 16th Annu. ACM Sympos. Comput. Geom., 223-232, 2000.

....an algorithm to extract a certain manifold subcomplex of the Delaunay triangulation, called the crust. Amenta et al. 4] simpli ed the crust algorithm and proved that if S is an sample of a smooth surface , for some 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 ....

....vertices called poles in order to estimate surface normals. Boissonnat and Cazals (personal communication) report that adding a small subset of the poles can signi cantly reduce the complexity of the Voronoi diagram with only minimal changes to the smooth surface constructed by their algorithm [12]. How few poles can we add to an sample so that the resulting Delaunay triangulation has only linear complexity, and how quickly can we nd those poles quickly Acknowledgments. I thank Herbert Edelsbrunner for asking the (still open ) question that started this work, Kim Whittlesey for ....

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Proc. 16th Annu. ACM Sympos. Comput. Geom., pp. 223-232. 2000.

No context found.

J.-D. Boissonnat, F. Cazals, Smooth surface reconstruction via natural neighbour interpolation of distance functions, in: Proc. 16th Annual ACM Sympos. Comput. Geom., 2000, pp. 223--232.

No context found.

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. In SCG '00: Proceedings of the pages 223--232. ACM Press, 2000.

No context found.

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comp. Geometry Theory and Applications, 2003. to appear.

No context found.

J-D. BOISSONNAT F. C.: Smooth surface reconstruction via natural neighbour interpolation of distance functions. In Computational Geometry - Theory and Application (

No context found.

J.D. Boissonnat, F. Cazals. Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions. Sixteenth ACM Symposium on Computational Geometry, 2000

No context found.

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comp. Geometry Theory and Applications, 2003. to appear.

No context found.

J.-D. Boissonnat, F. Cazals, Smooth surface reconstruction via natural neighbour interpolation of distance functions, in: Proc. 16th Annual Symp. on Computational Geometry, ACM Press, 2000, pp. 223--232. 2

No context found.

J. D. Boissonnat, F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance function. Computational Geometry 22(1--3):185--203, 2002.

No context found.

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance function. In 16th Proc. Annu. ACM Symposium on Computer Geometry, pages 185--203, 2000.

No context found.

J. D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance function. In 16th Proc. Annu. ACM Symposium on Computer Geometry, pages 185-- 203, 2000.

No context found.

Boissonnat J.-D., Cazals F.: Smooth surface reconstruction via natural neighbor interpolation of distance function. Computational Geometry 22(1--3):185--203, 2002. 1

No context found.

J. D. Boissonnat, F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance function. Computational Geometry 22(1--3):185--203, 2002.

No context found.

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Proc. 16th Annu. ACM Sympos. Comput. Geom., 223--232, 2000.

No context found.

J.-D. Boissonnat and F. Cazals. Smooth surface reconstruction via natural neighbor interpolation of distance functions. In Proc. 16th Ann. Sympos. Comput. Geom., pages 223-232, 2000.

No context found.

J.-D. Boissonnat, F. Cazals, Smooth surface reconstruction via natural neighbor interpolation of distance functions, in: Proc. of SCG'00 (ACM Symposium on Computational Geometry), 2000, pp. 223--232.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC