4,149 research outputs found
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
High-Performance and Tunable Stereo Reconstruction
Traditional stereo algorithms have focused their efforts on reconstruction
quality and have largely avoided prioritizing for run time performance. Robots,
on the other hand, require quick maneuverability and effective computation to
observe its immediate environment and perform tasks within it. In this work, we
propose a high-performance and tunable stereo disparity estimation method, with
a peak frame-rate of 120Hz (VGA resolution, on a single CPU-thread), that can
potentially enable robots to quickly reconstruct their immediate surroundings
and maneuver at high-speeds. Our key contribution is a disparity estimation
algorithm that iteratively approximates the scene depth via a piece-wise planar
mesh from stereo imagery, with a fast depth validation step for semi-dense
reconstruction. The mesh is initially seeded with sparsely matched keypoints,
and is recursively tessellated and refined as needed (via a resampling stage),
to provide the desired stereo disparity accuracy. The inherent simplicity and
speed of our approach, with the ability to tune it to a desired reconstruction
quality and runtime performance makes it a compelling solution for applications
in high-speed vehicles.Comment: Accepted to International Conference on Robotics and Automation
(ICRA) 2016; 8 pages, 5 figure
Dense point sets have sparse Delaunay triangulations
The spread of a finite set of points is the ratio between the longest and
shortest pairwise distances. We prove that the Delaunay triangulation of any
set of n points in R^3 with spread D has complexity O(D^3). This bound is tight
in the worst case for all D = O(sqrt{n}). In particular, the Delaunay
triangulation of any dense point set has linear complexity. We also generalize
this upper bound to regular triangulations of k-ply systems of balls, unions of
several dense point sets, and uniform samples of smooth surfaces. On the other
hand, for any n and D=O(n), we construct a regular triangulation of complexity
Omega(nD) whose n vertices have spread D.Comment: 31 pages, 11 figures. Full version of SODA 2002 paper. Also available
at http://www.cs.uiuc.edu/~jeffe/pubs/screw.htm
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
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
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