5,807 research outputs found
Computation of protein geometry and its applications: Packing and function prediction
This chapter discusses geometric models of biomolecules and geometric
constructs, including the union of ball model, the weigthed Voronoi diagram,
the weighted Delaunay triangulation, and the alpha shapes. These geometric
constructs enable fast and analytical computaton of shapes of biomoleculres
(including features such as voids and pockets) and metric properties (such as
area and volume). The algorithms of Delaunay triangulation, computation of
voids and pockets, as well volume/area computation are also described. In
addition, applications in packing analysis of protein structures and protein
function prediction are also discussed.Comment: 32 pages, 9 figure
Reconstruction of freeform surfaces for metrology
The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.EMR
Advancing In Situ Modeling of ICMEs: New Techniques for New Observations
It is generally known that multi-spacecraft observations of interplanetary
coronal mass ejections (ICMEs) more clearly reveal their three-dimensional
structure than do observations made by a single spacecraft. The launch of the
STEREO twin observatories in October 2006 has greatly increased the number of
multipoint studies of ICMEs in the literature, but this field is still in its
infancy. To date, most studies continue to use on flux rope models that rely on
single track observations through a vast, multi-faceted structure, which
oversimplifies the problem and often hinders interpretation of the large-scale
geometry, especially for cases in which one spacecraft observes a flux rope,
while another does not. In order to tackle these complex problems, new modeling
techniques are required. We describe these new techniques and analyze two ICMEs
observed at the twin STEREO spacecraft on 22-23 May 2007, when the spacecraft
were separated by ~8 degrees. We find a combination of non-force-free flux rope
multi-spacecraft modeling, together with a new non-flux rope ICME plasma flow
deflection model, better constrains the large-scale structure of these ICMEs.
We also introduce a new spatial mapping technique that allows us to put
multispacecraft observations and the new ICME model results in context with the
convecting solar wind. What is distinctly different about this analysis is that
it reveals aspects of ICME geometry and dynamics in a far more visually
intuitive way than previously accomplished. In the case of the 22-23 May ICMEs,
the analysis facilitates a more physical understanding of ICME large-scale
structure, the location and geometry of flux rope sub-structures within these
ICMEs, and their dynamic interaction with the ambient solar wind
Efficient moving point handling for incremental 3D manifold reconstruction
As incremental Structure from Motion algorithms become effective, a good
sparse point cloud representing the map of the scene becomes available
frame-by-frame. From the 3D Delaunay triangulation of these points,
state-of-the-art algorithms build a manifold rough model of the scene. These
algorithms integrate incrementally new points to the 3D reconstruction only if
their position estimate does not change. Indeed, whenever a point moves in a 3D
Delaunay triangulation, for instance because its estimation gets refined, a set
of tetrahedra have to be removed and replaced with new ones to maintain the
Delaunay property; the management of the manifold reconstruction becomes thus
complex and it entails a potentially big overhead. In this paper we investigate
different approaches and we propose an efficient policy to deal with moving
points in the manifold estimation process. We tested our approach with four
sequences of the KITTI dataset and we show the effectiveness of our proposal in
comparison with state-of-the-art approaches.Comment: Accepted in International Conference on Image Analysis and Processing
(ICIAP 2015
Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations
One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology
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
Well-Centered Triangulation
Meshes composed of well-centered simplices have nice orthogonal dual meshes
(the dual Voronoi diagram). This is useful for certain numerical algorithms
that prefer such primal-dual mesh pairs. We prove that well-centered meshes
also have optimality properties and relationships to Delaunay and minmax angle
triangulations. We present an iterative algorithm that seeks to transform a
given triangulation in two or three dimensions into a well-centered one by
minimizing a cost function and moving the interior vertices while keeping the
mesh connectivity and boundary vertices fixed. The cost function is a direct
result of a new characterization of well-centeredness in arbitrary dimensions
that we present. Ours is the first optimization-based heuristic for
well-centeredness, and the first one that applies in both two and three
dimensions. We show the results of applying our algorithm to small and large
two-dimensional meshes, some with a complex boundary, and obtain a
well-centered tetrahedralization of the cube. We also show numerical evidence
that our algorithm preserves gradation and that it improves the maximum and
minimum angles of acute triangulations created by the best known previous
method.Comment: Content has been added to experimental results section. Significant
edits in introduction and in summary of current and previous results. Minor
edits elsewher
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
- …