5,797 research outputs found
Towards a Scalable Dynamic Spatial Database System
With the rise of GPS-enabled smartphones and other similar mobile devices,
massive amounts of location data are available. However, no scalable solutions
for soft real-time spatial queries on large sets of moving objects have yet
emerged. In this paper we explore and measure the limits of actual algorithms
and implementations regarding different application scenarios. And finally we
propose a novel distributed architecture to solve the scalability issues.Comment: (2012
Localization in Unstructured Environments: Towards Autonomous Robots in Forests with Delaunay Triangulation
Autonomous harvesting and transportation is a long-term goal of the forest
industry. One of the main challenges is the accurate localization of both
vehicles and trees in a forest. Forests are unstructured environments where it
is difficult to find a group of significant landmarks for current fast
feature-based place recognition algorithms. This paper proposes a novel
approach where local observations are matched to a general tree map using the
Delaunay triangularization as the representation format. Instead of point cloud
based matching methods, we utilize a topology-based method. First, tree trunk
positions are registered at a prior run done by a forest harvester. Second, the
resulting map is Delaunay triangularized. Third, a local submap of the
autonomous robot is registered, triangularized and matched using triangular
similarity maximization to estimate the position of the robot. We test our
method on a dataset accumulated from a forestry site at Lieksa, Finland. A
total length of 2100\,m of harvester path was recorded by an industrial
harvester with a 3D laser scanner and a geolocation unit fixed to the frame.
Our experiments show a 12\,cm s.t.d. in the location accuracy and with
real-time data processing for speeds not exceeding 0.5\,m/s. The accuracy and
speed limit is realistic during forest operations
A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs
We present a new algorithm that produces a well-spaced superset of points
conforming to a given input set in any dimension with guaranteed optimal output
size. We also provide an approximate Delaunay graph on the output points. Our
algorithm runs in expected time , where is the
input size, is the output point set size, and is the ambient dimension.
The constants only depend on the desired element quality bounds.
To gain this new efficiency, the algorithm approximately maintains the
Voronoi diagram of the current set of points by storing a superset of the
Delaunay neighbors of each point. By retaining quality of the Voronoi diagram
and avoiding the storage of the full Voronoi diagram, a simple exponential
dependence on is obtained in the running time. Thus, if one only wants the
approximate neighbors structure of a refined Delaunay mesh conforming to a set
of input points, the algorithm will return a size graph in
expected time. If is superlinear in , then we
can produce a hierarchically well-spaced superset of size in
expected time.Comment: Full versio
On Deletion in Delaunay Triangulation
This paper presents how the space of spheres and shelling may be used to
delete a point from a -dimensional triangulation efficiently. In dimension
two, if k is the degree of the deleted vertex, the complexity is O(k log k),
but we notice that this number only applies to low cost operations, while time
consuming computations are only done a linear number of times.
This algorithm may be viewed as a variation of Heller's algorithm, which is
popular in the geographic information system community. Unfortunately, Heller
algorithm is false, as explained in this paper.Comment: 15 pages 5 figures. in Proc. 15th Annu. ACM Sympos. Comput. Geom.,
181--188, 199
One machine, one minute, three billion tetrahedra
This paper presents a new scalable parallelization scheme to generate the 3D
Delaunay triangulation of a given set of points. Our first contribution is an
efficient serial implementation of the incremental Delaunay insertion
algorithm. A simple dedicated data structure, an efficient sorting of the
points and the optimization of the insertion algorithm have permitted to
accelerate reference implementations by a factor three. Our second contribution
is a multi-threaded version of the Delaunay kernel that is able to concurrently
insert vertices. Moore curve coordinates are used to partition the point set,
avoiding heavy synchronization overheads. Conflicts are managed by modifying
the partitions with a simple rescaling of the space-filling curve. The
performances of our implementation have been measured on three different
processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we
have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds
to a generation rate of over 55 million tetrahedra per second. We finally show
how this very efficient parallel Delaunay triangulation can be integrated in a
Delaunay refinement mesh generator which takes as input the triangulated
surface boundary of the volume to mesh
Optimal randomized incremental construction for guaranteed logarithmic planar point location
Given a planar map of segments in which we wish to efficiently locate
points, we present the first randomized incremental construction of the
well-known trapezoidal-map search-structure that only requires expected preprocessing time while deterministically guaranteeing worst-case
linear storage space and worst-case logarithmic query time. This settles a long
standing open problem; the best previously known construction time of such a
structure, which is based on a directed acyclic graph, so-called the history
DAG, and with the above worst-case space and query-time guarantees, was
expected . The result is based on a deeper understanding of the
structure of the history DAG, its depth in relation to the length of its
longest search path, as well as its correspondence to the trapezoidal search
tree. Our results immediately extend to planar maps induced by finite
collections of pairwise interior disjoint well-behaved curves.Comment: The article significantly extends the theoretical aspects of the work
presented in http://arxiv.org/abs/1205.543
Improved Implementation of Point Location in General Two-Dimensional Subdivisions
We present a major revamp of the point-location data structure for general
two-dimensional subdivisions via randomized incremental construction,
implemented in CGAL, the Computational Geometry Algorithms Library. We can now
guarantee that the constructed directed acyclic graph G is of linear size and
provides logarithmic query time. Via the construction of the Voronoi diagram
for a given point set S of size n, this also enables nearest-neighbor queries
in guaranteed O(log n) time. Another major innovation is the support of general
unbounded subdivisions as well as subdivisions of two-dimensional parametric
surfaces such as spheres, tori, cylinders. The implementation is exact,
complete, and general, i.e., it can also handle non-linear subdivisions. Like
the previous version, the data structure supports modifications of the
subdivision, such as insertions and deletions of edges, after the initial
preprocessing. A major challenge is to retain the expected O(n log n)
preprocessing time while providing the above (deterministic) space and
query-time guarantees. We describe an efficient preprocessing algorithm, which
explicitly verifies the length L of the longest query path in O(n log n) time.
However, instead of using L, our implementation is based on the depth D of G.
Although we prove that the worst case ratio of D and L is Theta(n/log n), we
conjecture, based on our experimental results, that this solution achieves
expected O(n log n) preprocessing time.Comment: 21 page
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