30,425 research outputs found
Linear Complexity Hexahedral Mesh Generation
We show that any polyhedron forming a topological ball with an even number of
quadrilateral sides can be partitioned into O(n) topological cubes, meeting
face to face. The result generalizes to non-simply-connected polyhedra
satisfying an additional bipartiteness condition. The same techniques can also
be used to reduce the geometric version of the hexahedral mesh generation
problem to a finite case analysis amenable to machine solution.Comment: 12 pages, 17 figures. A preliminary version of this paper appeared at
the 12th ACM Symp. on Computational Geometry. This is the final version, and
will appear in a special issue of Computational Geometry: Theory and
Applications for papers from SCG '9
3D cut-cell modelling for high-resolution atmospheric simulations
Owing to the recent, rapid development of computer technology, the resolution
of atmospheric numerical models has increased substantially. With the use of
next-generation supercomputers, atmospheric simulations using horizontal grid
intervals of O(100) m or less will gain popularity. At such high resolution
more of the steep gradients in mountainous terrain will be resolved, which may
result in large truncation errors in those models using terrain-following
coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic
atmospheric model is developed. A cut-cell representation of topography based
on finite-volume discretization is combined with a cell-merging approach, in
which small cut-cells are merged with neighboring cells either vertically or
horizontally. In addition, a block-structured mesh-refinement technique is
introduced to achieve a variable resolution on the model grid with the finest
resolution occurring close to the terrain surface. The model successfully
reproduces a flow over a 3D bell-shaped hill that shows a good agreement with
the flow predicted by the linear theory. The ability of the model to simulate
flows over steep terrain is demonstrated using a hemisphere-shaped hill where
the maximum slope angle is resolved at 71 degrees. The advantage of a locally
refined grid around a 3D hill, with cut-cells at the terrain surface, is also
demonstrated using the hemisphere-shaped hill. The model reproduces smooth
mountain waves propagating over varying grid resolution without introducing
large errors associated with the change of mesh resolution. At the same time,
the model shows a good scalability on a locally refined grid with the use of
OpenMP.Comment: 19 pages, 16 figures. Revised version, accepted for publication in
QJRM
Generating Surface Geometry in Higher Dimensions using Local Cell Tilers
In two dimensions contour elements surround two dimensional objects, in three dimensions surfaces surround three dimensional objects and in four dimensions hypersurfaces surround hyperobjects. These surfaces can be represented by a collection of connected simplices, hence, continuous n dimensional surfaces can be represented by a lattice of connected n-1 dimensional simplices. The lattice of connected simplices can be calculated over a set of adjacent n-dimensional cubes, via for example the Marching Cubes Algorithm. These algorithms are often named local cell tilers. We propose that the local-cell tiling method can be usefully-applied to four dimensions and potentially to N-dimensions. We present an algorithm for the generation of major cases (cases that are topologically invariant under standard geometrical transformations) and introduce the notion of a sub-case which simplifies their representations. Each sub-case can be easily subdivided into simplices for rendering and we describe a backtracking tetrahedronization algorithm for the four dimensional case. An implementation for surfaces from the fourth dimension is presented and we describe and discuss ambiguities inherent within this and related algorithms
The scattering from generalized Cantor fractals
We consider a fractal with a variable fractal dimension, which is a
generalization of the well known triadic Cantor set. In contrast with the usual
Cantor set, the fractal dimension is controlled using a scaling factor, and can
vary from zero to one in one dimension and from zero to three in three
dimensions. The intensity profile of small-angle scattering from the
generalized Cantor fractal in three dimensions is calculated. The system is
generated by a set of iterative rules, each iteration corresponding to a
certain fractal generation. Small-angle scattering is considered from
monodispersive sets, which are randomly oriented and placed. The scattering
intensities represent minima and maxima superimposed on a power law decay, with
the exponent equal to the fractal dimension of the scatterer, but the minima
and maxima are damped with increasing polydispersity of the fractal sets. It is
shown that for a finite generation of the fractal, the exponent changes at
sufficiently large wave vectors from the fractal dimension to four, the value
given by the usual Porod law. It is shown that the number of particles of which
the fractal is composed can be estimated from the value of the boundary between
the fractal and Porod regions. The radius of gyration of the fractal is
calculated analytically.Comment: 8 pages, 4 figures, accepted for publication in J. Appl. Crys
A novel updating modelling methodology for free-form surface modifications in the early stages of design
The paper describes the first implementation of a method in which an initial CAD model is updated from a physical model. The method is based on image-mapping in which an initial CAD model is updated from images of a soft rapid prototype model (RPM) which has been sculpted in order to carry out formal developments. The RP model is made by a 3Dimensional-colour printer, has a built-in contrasting grid composed by parallel planes in the X, Y and/or Z co-ordinates and has special consistency allowing it to be easily sculpted with hand modifications. During the sculpting process changes on the surface affect the lines on the RPM, which are the external presence of the internal grid planes and are corresponding to the initial CAD construction lines. These lines (profiles) then are visually contrasted by making use of identical perspective transformations and viewpoints for the virtual model and the RP model image. The initial CAD model is then updated by modifying the surfaceâs
construction lines to match the lines on the RP image by moving control points, such as in the Z direction
Hierarchical progressive surveys. Multi-resolution HEALPix data structures for astronomical images, catalogues, and 3-dimensional data cubes
Scientific exploitation of the ever increasing volumes of astronomical data
requires efficient and practical methods for data access, visualisation, and
analysis. Hierarchical sky tessellation techniques enable a multi-resolution
approach to organising data on angular scales from the full sky down to the
individual image pixels. Aims. We aim to show that the Hierarchical progressive
survey (HiPS) scheme for describing astronomical images, source catalogues, and
three-dimensional data cubes is a practical solution to managing large volumes
of heterogeneous data and that it enables a new level of scientific
interoperability across large collections of data of these different data
types. Methods. HiPS uses the HEALPix tessellation of the sphere to define a
hierarchical tile and pixel structure to describe and organise astronomical
data. HiPS is designed to conserve the scientific properties of the data
alongside both visualisation considerations and emphasis on the ease of
implementation. We describe the development of HiPS to manage a large number of
diverse image surveys, as well as the extension of hierarchical image systems
to cube and catalogue data. We demonstrate the interoperability of HiPS and
Multi-Order Coverage (MOC) maps and highlight the HiPS mechanism to provide
links to the original data. Results. Hierarchical progressive surveys have been
generated by various data centres and groups for ~200 data collections
including many wide area sky surveys, and archives of pointed observations.
These can be accessed and visualised in Aladin, Aladin Lite, and other
applications. HiPS provides a basis for further innovations in the use of
hierarchical data structures to facilitate the description and statistical
analysis of large astronomical data sets.Comment: 21 pages, 6 figures. Accepted for publication in Astronomy &
Astrophysic
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