Results 1 - 10
of
32
An Empirical Comparison of Techniques for Updating Delaunay Triangulations
, 2004
"... The computation of Delaunay triangulations from static point sets has been extensively studied in computational geometry. When the points move with known trajectories, kinetic data structures can be used to maintain the triangulation. However, there has been little work so far on how to maintain the ..."
Abstract
-
Cited by 29 (2 self)
- Add to MetaCart
The computation of Delaunay triangulations from static point sets has been extensively studied in computational geometry. When the points move with known trajectories, kinetic data structures can be used to maintain the triangulation. However, there has been little work so far on how to maintain the triangulation when the points move without explicit motion plans, as in the case of a physical simulation. In this paper we examine how to update Delaunay triangulations after small displacements of the defining points, as might be provided by a physics-based integrator. We have implemented a variety of update algorithms, many new, toward this purpose. We ran these algorithms on a corpus of data sets to provide running time comparisons and determined that updating Delaunay can be significantly faster than recomputing.
Lecture Notes on Delaunay Mesh Generation
, 1999
"... purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ..."
Abstract
-
Cited by 23 (0 self)
- Add to MetaCart
(Show Context)
purposes notwithstanding any copyright annotation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the
I/O-Efficient Construction of Constrained Delaunay Triangulations
"... In this paper, we designed and implemented an I/O-efficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( N B logM/B N B) I/Os for triangulating N points in the plane, where M ..."
Abstract
-
Cited by 18 (5 self)
- Add to MetaCart
In this paper, we designed and implemented an I/O-efficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( N B logM/B N B) I/Os for triangulating N points in the plane, where M is the memory size and B is the disk block size. If there are more constraining segments, the theoretical bound does not hold, but in practice the performance of our algorithm degrades gracefully. Through an extensive set of experiments with both synthetic and real data, we show that our algorithm is significantly faster than existing implementations.
Incremental Construction of the Delaunay Triangulation and the Delaunay Graph in Medium Dimension
, 2009
"... We describe a new implementation of the well-known incremental algorithm for constructing Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons show that our implementation outperforms the best currently available ..."
Abstract
-
Cited by 13 (1 self)
- Add to MetaCart
(Show Context)
We describe a new implementation of the well-known incremental algorithm for constructing Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons show that our implementation outperforms the best currently available codes for exact convex hulls and Delaunay triangulations, compares very well to the fast non-exact Qhull implementation and can be used for quite big input sets in spaces of dimensions up to 6. To circumvent prohibitive memory usage, we also propose a modi cation of the algorithm that uses and stores only the Delaunay graph (the edges of the full triangulation). We show that a careful implementation of the modi ed algorithm performs only 6 to 8 times slower than the original algorithm while drastically reducing memory usage in dimension 4 or above.
Delaunay Triangulations in O(sort(n)) Time and More
"... We present several results about Delaunay triangulations (DTs) and convex hulls in transdichotomous and hereditary settings: (i) the DT of a planar point set can be computed in expected time O(sort(n)) on a word RAM, where sort(n) is the time to sort n numbers. We assume that the word RAM supports ..."
Abstract
-
Cited by 12 (6 self)
- Add to MetaCart
(Show Context)
We present several results about Delaunay triangulations (DTs) and convex hulls in transdichotomous and hereditary settings: (i) the DT of a planar point set can be computed in expected time O(sort(n)) on a word RAM, where sort(n) is the time to sort n numbers. We assume that the word RAM supports the shuffle-operation in constant time; (ii) if we know the ordering of a planar point set in x- and in y-direction, its DT can be found by a randomized algebraic computation tree of expected linear depth; (iii) given a universe U of points in the plane, we construct a data structure D for Delaunay queries: for any P ⊆ U, D can find the DT of P in time O(|P | log log |U|); (iv) given a universe U of points in 3-space in general convex position, there is a data structure D for convex hull queries: for any P ⊆ U, D can find the convex hull of P in time O(|P |(log log |U|) 2); (v) given a convex polytope in 3-space with n vertices which are colored with χ> 2 colors, we can split it into the convex hulls of the individual color classes in time O(n(log log n) 2). The results (i)–(iii) generalize to higher dimensions. We need a wide range of techniques. Most prominently, we describe a reduction from DTs to nearest-neighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling.
MEIJERS M.: Topologically consistent 3D city models obtain by extrusion
- International Journal of Geographical Information Science, In Press, LEE J., ZLATANOVA S.: A
, 2008
"... One of the simplest methods to construct a 3D city model is to extrude building footprints to obtain “block-shaped ” polyhedra representing buildings. While the method is well-known and easy to implement, if the 2D topological relationships between the footprints are not taken into account, the resu ..."
Abstract
-
Cited by 9 (2 self)
- Add to MetaCart
One of the simplest methods to construct a 3D city model is to extrude building footprints to obtain “block-shaped ” polyhedra representing buildings. While the method is well-known and easy to implement, if the 2D topological relationships between the footprints are not taken into account, the resulting 3D city models will not necessarily be topologically consistent (i.e. primitives shared by 3D buildings will be duplicated and/or intersect each others). As a result, the model will be of little use for most applications, besides visualisation that is. In this paper, we present a new extrusion procedure to construct topologically correct 3D city models. It is based on the use of a constrained triangulation, is conceptually simple, and offers great flexibility to create city models in different formats (e.g. CityGML or a surface-based representation). We have implemented the procedure, tested it with real-world datasets, and validated it. 1
DELAUNAY TRIANGULATION OF IMPRECISE POINTS: PREPROCESS AND ACTUALLY GET A FAST QUERY TIME
- JOURNAL OF COMPUTATIONAL GEOMETRY
, 2011
"... We propose a new algorithm to preprocess a set of n disjoint unit disks in O(n log n) expected time, allowing to compute the Delaunay triangulation of a set of n points, one from each disk, in O(n) expected time. Our algorithm has the same asymptotic complexity as previous ones for this problem, bu ..."
Abstract
-
Cited by 8 (0 self)
- Add to MetaCart
We propose a new algorithm to preprocess a set of n disjoint unit disks in O(n log n) expected time, allowing to compute the Delaunay triangulation of a set of n points, one from each disk, in O(n) expected time. Our algorithm has the same asymptotic complexity as previous ones for this problem, but our algorithm is much simpler and it runs faster in practice than a direct computation of the Delaunay triangulation.
Simple and Fast Nearest Neighbor Search
- IN: 2010 PROCEEDINGS OF THE TWELFTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS
, 2010
"... We present a simple randomized data structure for two-dimensional point sets that allows fast nearest neighbor queries in many cases. An implementation outperforms several previous implementations for commonly used benchmarks. ..."
Abstract
-
Cited by 8 (2 self)
- Add to MetaCart
(Show Context)
We present a simple randomized data structure for two-dimensional point sets that allows fast nearest neighbor queries in many cases. An implementation outperforms several previous implementations for commonly used benchmarks.
Parallel Geometric Algorithms for Multi-Core Computers
- COMPUTATIONAL GEOMETRY
, 2010
"... ..."
(Show Context)
Deterministic Galois: On-demand, Portable and Parameterless
- In Proc. of ASPLOS
, 2014
"... Non-determinism in program execution can make program development and debugging difficult. In this paper, we argue that solutions to this problem should be on-demand, portable and parameterless. On-demand means that the programming model should permit the writing of non-deterministic pro-grams since ..."
Abstract
-
Cited by 7 (0 self)
- Add to MetaCart
(Show Context)
Non-determinism in program execution can make program development and debugging difficult. In this paper, we argue that solutions to this problem should be on-demand, portable and parameterless. On-demand means that the programming model should permit the writing of non-deterministic pro-grams since these programs often perform better than de-terministic programs for the same problem. Portable means that the program should produce the same answer even if it is run on different machines. Parameterless means that if there are machine-dependent scheduling parameters that must be tuned for good performance, they must not affect the output. Although many solutions for deterministic program exe-cution have been proposed in the literature, they fall short along one or more of these dimensions. To remedy this, we propose a new approach, based on the Galois programming model, in which (i) the programming model permits the writing of non-deterministic programs and (ii) the runtime system executes these programs deterministically if needed. Evaluation of this approach on a collection of benchmarks from the PARSEC, PBBS, and Lonestar suites shows that it delivers deterministic execution with substantially less over-head than other systems in the literature.
