O. Devillers. Improved incremental randomized delaunay triangulation. In 14th Annu. ACM Sympos. Comput. Geom., pages 106--115, 1998. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Fully Dynamic Constrained Delaunay Triangulations - Kallmann, Bieri, Thalmann (2003) (Correct)
....4 3 ) for randomly distributed points. Simple incremental algorithms can thus be competitive with optimal (but more complex) O(n log n) approaches. Note that, if dedicated data structures are maintained to optimize point location, the incremental algorithm reaches the expected time of O(n log n) [6]. Along this paper we mainly discuss complexity analysis results from existing incremental DT algorithms, expecting that similar asymptotic times are obtained for CDTs without special cases . Therefore, constraints should have few intersections and not make the CDT become too di#erent from the ....
....CDT, the locate point routine searches where in the triangulation p is. Point location is an important issue for any incremental algorithm, and several approaches have been proposed. Most e#cient methods rely on dedicated data structures, reaching the expected time of O(log n) to locate one point [6] [4] 11] Alternatively, bucketing has also been used [16] with good performances for well distributed points. We follow the simpler jump and walk approach [14] which takes expected O(n ) time (in DTs) It has the advantage that no additional data structures are needed, which is an important ....
Devillers, O. (1998): Improved incremental randomized Delaunay triangulation. Proc. of the 14th ACM Symposium on Computational Geometry, 106--115
An Experimental Comparison of Two-Dimensional Triangulation.. - Zlotowski, Bäsken (Correct)
....for many problem instances. Implementations of such algorithms (especially Dwyer s divide and conquer algorithm) can be found in LEDA and triangle. Another successful strategy is the combination of randomized incremental algorithms with a hierarchical data structure used for point location [2]. An implementation using hierarchies can be found in CGAL. We combine in our implementations ideas of the known divide and conquer based algorithms with the simple local transformation strategies. In this way we achieve good performance for randomly distributed input. The reason for this ....
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106-115, 1998.
Smooth Surface Reconstruction via Natural Neighbour.. - Boissonnat, Cazals (2000) (25 citations) (Correct)
....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 a set of points that is 3 times as big as the initial data. In two dimensions, theoretical results on the ....
....2.1 f 13 operator (vector , vector ) 2.1 f 14 mixed(vector , vector , vector ) 2.0 f 15 Tetra: resetFlags(void) Table 2: Prole over a sequence of simulateInsert( 5. 3 About the Delaunay triangulation used Practically, we use the randomised Delaunay triangulation algorithm of Devillers [13]. This code processes about 500,000 points randomly distributed in the unit cube per minute on an Intel i686 processor with 256MB of RAM. Notice however that when the points are not distributed in a volume but on a surface, which is the case in the reconstruction context, the performances are ....
[Article contains additional citation context not shown here]
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
Three Dimensional Triangulations in CGAL - Teillaud (1999) (2 citations) (Correct)
....class, where the user can specify the type of points he wants to use as well as the elementary operations on them (predicates, the triangulation data structure class of the middle level, described in Section 3. Delaunay triangulations as well as hierarchical Delaunay triangulations [Dev98] are also implemented in the package but not presented here. 2 Triangulation of points in 3D space The basic triangulation class of Cgal is primarily designed to represent the triangulations of a set S of points in the space. A 3D triangulation can be seen as a partition of the space into ....
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
The Shuffling Buffer - Devillers, Guigue Self-citation (Devillers) (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
Efficient Exact Geometric Predicates for Delaunay Triangulations - Devillers, Pion (2003) (1 citation) Self-citation (Devillers) (Correct)
No context found.
Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106-115, 1998.
The Shuffling Buffer - Devillers, Guigue Self-citation (Devillers) (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
On Deletion in Delaunay Triangulations - Devillers (1999) (10 citations) Self-citation (Devillers) (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106--115, 1998.
On Deletion in Delaunay Triangulation - Devillers (1998) (10 citations) Self-citation (Devillers) (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
Efficient Exact Geometric Predicates for Delaunay Triangulations - Devillers (2003) (1 citation) Self-citation (Devillers) (Correct)
No context found.
Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
Walking in a Triangulation - Devillers, Pion, al. (2001) (2 citations) Self-citation (Devillers) (Correct)
No context found.
Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
The Shuffling Buffer - Devillers, Guigue Self-citation (Devillers) (Correct)
....located point; this yields to a (disastrous) O(n 3 ) complexity which is improved in O( n 3 log k k ) by the shuing buoeer. Some other location techniques based on a hierarchy of random samples independent from the insertion order (similarly to skip lists) such as the Delaunay hierarchy [5] gives an expected linear location time for a non random order. 4 The shuing buoeer technique improves it by the log k k factor getting a location time of the same order as the insertion time. The whole complexity of constructing the Delaunay triangulation of points in the plane with the ....
....145300 and 407500 3D points. Such a measuring system really matches the context of that paper, data are measured by moving a scanning system around the object and thus data are not all known in advance and they are not coming in a random order. We use an implementation of the Delaunay Hierarchy [5]. The results indicate a signicant reduction in the running time of the program. As Figure 4 testies, experimental results indicate a factor of 2 in the running time of the shufAEing buoeer over the deterministic version of the algorithm for k 90, indicating that the shuing buoeer version is ....
[Article contains additional citation context not shown here]
Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
The Shuffling Buffer - Devillers, Guigue Self-citation (Devillers) (Correct)
....of m points and walking from there to nd R(M) Choosing m = p n and k = p n log n gives the same complexity O(n p n) in the randomized and shuing buoeer analysis, this is the best randomized complexity without hypotheses on the point distribution. In the case of the Delaunay Hierarchy [4], we achieve optimal randomized complexity of O(n 2 ) in the worst case and O( n 2 log k k ) with the shuing buoeer technique. 3.4 Experimental results We performed experimental testing on real data provided by a 3D scanning system measuring real objects having respectively 145300 and ....
....Courtesy of Kreon Industry. Such a measuring system really matches the context of that paper, data are measured by moving a scanning system around the object and thus data are not all known in advance and they are not coming in a random order. We use an implementation of the Delaunay Hierarchy [4]. As Figure 2 testies, experimental results, obtained by averaging on about 50 dioeerent executions, indicate that the shuing buoeer version is eOEcient in practice. 4 Conclusion We have shown that the shuing buoeer permits to improve the incremental construction cost of structures such as ....
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
The Shuffling Buffer - Devillers, Guigue Self-citation (Devillers) (Correct)
....the located point; this yields to a (disastrous) O(n 3 ) complexity which is improved in O( n 3 log k k ) by the shuing buoeer. Some other location techniques based on a hierarchy of random samples independent from the insertion order (similarly to skip lists) such as the Delaunay hierarchy [4] gives an expected linear location time for a non random order. The shuing buoeer technique improves it by the log k k factor getting a location time of the same order as the insertion time. The whole complexity of constructing the Delaunay triangulation of points in the plane with the Delaunay ....
....Sec. 2 3 7 9 10 11 12 13 14 15 16 17 18 19 Size of Buffer 160 180 200 220 240 260 280 300 320 340 360 Sec. 20 40 60 80 100 120 140 160 180 200 Size of Buffer Figure 5: Running time of the Delaunay tetrahedrization. Courtesy of Kreon Industry. We use an implementation of the Delaunay Hierarchy [4]. As Figure 5 testies, experimental results, obtained by averaging on about 50 dioeerent executions, indicate that the shuing buoeer version is eOEcient in practice. 4 Trapezoidal diagrams and line segment intersections For S a set of n straight line segments in the plane, what are the pairs of ....
[Article contains additional citation context not shown here]
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106115, 1998.
On Deletion in Delaunay Triangulations - Devillers (1999) (10 citations) Self-citation (Devillers) (Correct)
....algorithms have the two following properties: they are incremental and they do not used complicated data structures in addition to the triangulation itself. Among these algorithms, let us mention the historical algorithm of Green and Sibson [GS78] or some other variants [MSZ96, BD95, Dev98, DLM98, Lem97]. All perform a walk in the triangulation to accelerate point location. The advantage of that category of incremental Delaunay algorithms is that they may easily be turned into fully dynamic Delaunay algorithms. Since there is no complicated data structure for point location, the deletion of a ....
....easiest method to generalize. Furthermore, the increase in the average value of k with the dimension reinforces its advantage over alternative candidates in higher dimensions. 4. 3 Experimental results Code and data This algorithm was implemented within the author s simple hierarchical structure [Dev98]. Robustness issues are solved using 24 bits integers to store points coordinates. Geometric predicates are computed with approximate arithmetic and the exactness of the result can be ensured by static and semi static filters 2 . The filters failure are backed up by exact computations. ....
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106--115, 1998.
Regular Triangulations of Dynamic Sets of Points - Marc Vigo Uria (Correct)
No context found.
O. Devillers. Improved incremental randomized delaunay triangulation. In 14th Annu. ACM Sympos. Comput. Geom., pages 106--115, 1998.
Reinforcement Learning in the Joint Space: Value Iteration in.. - Monson (2003) (Correct)
No context found.
O. Devillers, Improved incremental randomized Delaunay triangulation, Proceedings of the Fourteenth Annual Symposium on Computational Geometry (Minneapolis, Minnesota), ACM Press, 1998, pp. 106--115. 78
Unknown - Ist- Effective Computational (Correct)
No context found.
Olivier Devillers. Improved incremental randomized Delaunay triangulation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 106--115, 1998.
Provably Good Surface Sampling and Approximation - Oudot, Boissonnat (2003) (1 citation) (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. Proc. 14th Annu. ACM Sympos. Comput. Geom., pp 106-115.
Computing Polygonal Surfaces from Unions of Balls - Tam, Heidrich (Correct)
No context found.
O. Devillers. Improved incremental randomized Delaunay triangulation. In Proc. Symposium on Computational Geometry, pages 106--115, 1998.
Reinforcement Learning in the Joint Space: Value Iteration in.. - Monson (2003) (Correct)
No context found.
O. Devillers, Improved incremental randomized Delaunay triangulation, Proceedings of the Fourteenth Annual Symposium on Computational Geometry (Minneapolis, Minnesota), ACM Press, 1998, pp. 106--115. 78
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