The Experts below are selected from a list of 11022 Experts worldwide ranked by ideXlab platform
William Nicholls - One of the best experts on this subject based on the ideXlab platform.
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efficient minimum spanning tree construction without Delaunay Triangulation
Information Processing Letters, 2002Co-Authors: Hai Zhou, Narendra V Shenoy, William NichollsAbstract:Abstract Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least Ω(n 2 ) time. More efficient approaches find a minimum spanning tree only among edges in the Delaunay Triangulation of the points. However, Delaunay Triangulation is not well defined in rectilinear distance. In this paper, we first establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural definition and not necessarily a Delaunay Triangulation. Based on this framework, we then design an O(nlogn) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay Triangulation.
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efficient minimum spanning tree construction without Delaunay Triangulation
Asia and South Pacific Design Automation Conference, 2001Co-Authors: Hai Zhou, Narendra V Shenoy, William NichollsAbstract:Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least ω(n2) time. More efficient approaches find a minimum spanning tree only among edges in the Delaunay Triangulation of the points. However, Delaunay Triangulation is not well defined in rectilinear distance. In this paper, we first establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural definition and not necessarily a Delaunay Triangulation. Based on this framework, we then design an O(n log n) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay Triangulation.
Jeandaniel Boissonnat - One of the best experts on this subject based on the ideXlab platform.
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Delaunay Triangulation of manifolds
arXiv: Computational Geometry, 2013Co-Authors: Jeandaniel Boissonnat, Ramsay Dyer, Arijit GhoshAbstract:We present an algorithm for producing Delaunay Triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample points and an atlas on a compact manifold, a manifold Delaunay complex is produced provided the transition functions are bi-Lipschitz with a constant close to 1, and the sample points meet a local density requirement; no smoothness assumptions are required. If the transition functions are smooth, the output is a Triangulation of the manifold. The output complex is naturally endowed with a piecewise flat metric which, when the original manifold is Riemannian, is a close approximation of the original Riemannian metric. In this case the ouput complex is also a Delaunay Triangulation of its vertices with respect to this piecewise flat metric.
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Delaunay deformable models topology adaptive meshes based on the restricted Delaunay Triangulation
Computer Vision and Pattern Recognition, 2007Co-Authors: Jeanphilippe Pons, Jeandaniel BoissonnatAbstract:In this paper, we propose a robust and efficient Lagrangian approach, which we call Delaunay deformable models, for modeling moving surfaces undergoing large deformations and topology changes. Our work uses the concept of restricted Delaunay Triangulation, borrowed from computational geometry. In our approach, the interface is represented by a triangular mesh embedded in the Delaunay tetrahedralization of interface points. The mesh is iteratively updated by computing the restricted Delaunay Triangulation of the deformed objects. Our method has many advantages over popular Eulerian techniques such as the level set method and over hybrid Eulerian-Lagrangian techniques such as the particle level set method: localization accuracy, adaptive resolution, ability to track properties associated to the interface, seamless handling of triple junctions. Our work brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as T-snakes.
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a linear bound on the complexity of the Delaunay Triangulation of points on polyhedral surfaces
Discrete and Computational Geometry, 2004Co-Authors: Dominique Attali, Jeandaniel BoissonnatAbstract:Delaunay Triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay Triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay Triangulation of such point sets.Although the complexity of the Delaunay Triangulation of points in R3 may be quadratic in the worst case, we show in this paper that it is only linear when the points are distributed on a fixed set of well-sampled facets of R3 (e.g. the planar polygons in a polyhedron). Our bound is deterministic and the constants are explicitly given.
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complexity of the Delaunay Triangulation of points on surfaces the smooth case
Symposium on Computational Geometry, 2003Co-Authors: Dominique Attali, Jeandaniel Boissonnat, Andre LieutierAbstract:It is well known that the complexity of the Delaunay Triangulation of N points in R 3, i.e. the number of its faces, can be O (N2). The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay Triangulation of a set of points measured on a surface.In this paper, we bound the complexity of the Delaunay Triangulation of points distributed on generic smooth surfaces of R 3. Under a mild uniform sampling condition, we show that the complexity of the 3D Delaunay Triangulation of the points is O(N log N).
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a linear bound on the complexity of the Delaunay Triangulation of points on polyhedral surfaces
ACM Symposium on Solid Modeling and Applications, 2002Co-Authors: Dominique Attali, Jeandaniel BoissonnatAbstract:Delaunay Triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay Triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay Triangulation of such point sets. Although the complexity of the Delaunay Triangulation of points may be quadratic in the worst-case, we show in this paper that it is only linear when the points are distributed on a fixed number of well-sampled facets (e.g. the facets of a polyhedron). Our bound is deterministic and the constants are explicitly given.
Dimitri J Mavriplis - One of the best experts on this subject based on the ideXlab platform.
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an advancing front Delaunay Triangulation algorithm designed for robustness
AIAA Aerospace Sciences Meeting and Exhibit, 1993Co-Authors: Dimitri J MavriplisAbstract:A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting Triangulation constitutes the Delaunay Triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay Triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field.
Dominique Attali - One of the best experts on this subject based on the ideXlab platform.
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A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron
Discrete & Computational Geometry, 2012Co-Authors: Nina Amenta, Dominique Attali, Olivier DevillersAbstract:We show that the Delaunay Triangulation of a set of n points distributed nearly uniformly on a p -dimensional polyhedron (not necessarily convex) in d -dimensional Euclidean space is $O(n^{\frac{d-k+1}{p}})$ , where $k = \lceil\frac{d+1}{p+1} \rceil$ . This bound is tight in the worst case and improves on the prior upper bound for most values of p .
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complexity of Delaunay Triangulation for points on lower dimensional polyhedra
Symposium on Discrete Algorithms, 2007Co-Authors: Nina Amenta, Dominique Attali, Olivier DevillersAbstract:We show that the Delaunay Triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is O(n(d-1)/p). For all 2 ≤ p ≤ d - 1, this improves on the well-known worst-case bound of O(n⌈d/2⌉).
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a linear bound on the complexity of the Delaunay Triangulation of points on polyhedral surfaces
Discrete and Computational Geometry, 2004Co-Authors: Dominique Attali, Jeandaniel BoissonnatAbstract:Delaunay Triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay Triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay Triangulation of such point sets.Although the complexity of the Delaunay Triangulation of points in R3 may be quadratic in the worst case, we show in this paper that it is only linear when the points are distributed on a fixed set of well-sampled facets of R3 (e.g. the planar polygons in a polyhedron). Our bound is deterministic and the constants are explicitly given.
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complexity of the Delaunay Triangulation of points on surfaces the smooth case
Symposium on Computational Geometry, 2003Co-Authors: Dominique Attali, Jeandaniel Boissonnat, Andre LieutierAbstract:It is well known that the complexity of the Delaunay Triangulation of N points in R 3, i.e. the number of its faces, can be O (N2). The case of points distributed on a surface is of great practical importance in reverse engineering since most surface reconstruction algorithms first construct the Delaunay Triangulation of a set of points measured on a surface.In this paper, we bound the complexity of the Delaunay Triangulation of points distributed on generic smooth surfaces of R 3. Under a mild uniform sampling condition, we show that the complexity of the 3D Delaunay Triangulation of the points is O(N log N).
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a linear bound on the complexity of the Delaunay Triangulation of points on polyhedral surfaces
ACM Symposium on Solid Modeling and Applications, 2002Co-Authors: Dominique Attali, Jeandaniel BoissonnatAbstract:Delaunay Triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay Triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay Triangulation of such point sets. Although the complexity of the Delaunay Triangulation of points may be quadratic in the worst-case, we show in this paper that it is only linear when the points are distributed on a fixed number of well-sampled facets (e.g. the facets of a polyhedron). Our bound is deterministic and the constants are explicitly given.
Hai Zhou - One of the best experts on this subject based on the ideXlab platform.
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efficient minimum spanning tree construction without Delaunay Triangulation
Information Processing Letters, 2002Co-Authors: Hai Zhou, Narendra V Shenoy, William NichollsAbstract:Abstract Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least Ω(n 2 ) time. More efficient approaches find a minimum spanning tree only among edges in the Delaunay Triangulation of the points. However, Delaunay Triangulation is not well defined in rectilinear distance. In this paper, we first establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural definition and not necessarily a Delaunay Triangulation. Based on this framework, we then design an O(nlogn) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay Triangulation.
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efficient minimum spanning tree construction without Delaunay Triangulation
Asia and South Pacific Design Automation Conference, 2001Co-Authors: Hai Zhou, Narendra V Shenoy, William NichollsAbstract:Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least ω(n2) time. More efficient approaches find a minimum spanning tree only among edges in the Delaunay Triangulation of the points. However, Delaunay Triangulation is not well defined in rectilinear distance. In this paper, we first establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural definition and not necessarily a Delaunay Triangulation. Based on this framework, we then design an O(n log n) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay Triangulation.