12,102 research outputs found
Query processing of geometric objects with free form boundarie sin spatial databases
The increasing demand for the use of database systems as an integrating
factor in CAD/CAM applications has necessitated the development of database
systems with appropriate modelling and retrieval capabilities. One essential
problem is the treatment of geometric data which has led to the development of
spatial databases. Unfortunately, most proposals only deal with simple geometric
objects like multidimensional points and rectangles. On the other hand, there has
been a rapid development in the field of representing geometric objects with free
form curves or surfaces, initiated by engineering applications such as mechanical
engineering, aviation or astronautics. Therefore, we propose a concept for the realization
of spatial retrieval operations on geometric objects with free form
boundaries, such as B-spline or Bezier curves, which can easily be integrated in
a database management system. The key concept is the encapsulation of geometric
operations in a so-called query processor. First, this enables the definition of
an interface allowing the integration into the data model and the definition of the
query language of a database system for complex objects. Second, the approach
allows the use of an arbitrary representation of the geometric objects. After a
short description of the query processor, we propose some representations for free
form objects determined by B-spline or Bezier curves. The goal of efficient query
processing in a database environment is achieved using a combination of decomposition
techniques and spatial access methods. Finally, we present some experimental
results indicating that the performance of decomposition techniques is
clearly superior to traditional query processing strategies for geometric objects
with free form boundaries
Focusing: coming to the point in metamaterials
The point of the paper is to show some limitations of geometrical optics in
the analysis of subwavelength focusing. We analyze the resolution of the image
of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab
lens. The former optical medium is deduced from the stereographic projection of
a virtual sphere and displays a heterogeneous refractive index n(r) which is
proportional to the inverse of 1+r^2. The latter is described by a homogeneous,
but negative, refractive index. It has been suggested that the fisheye makes a
perfect lens without negative refraction [Leonhardt, Philbin
arxiv:0805.4778v2]. However, we point out that the definition of
super-resolution in such a heterogeneous medium should be computed with respect
to the wavelength in a homogenized medium, and it is perhaps more adequate to
talk about a conjugate image rather than a perfect image (the former does not
necessarily contains the evanescent components of the source). We numerically
find that both the Maxwell fisheye and a thick silver slab lens lead to a
resolution close to lambda/3 in transverse magnetic polarization (electric
field pointing orthogonal to the plane). We note a shift of the image plane in
the latter lens. We also observe that two sources lead to multiple secondary
images in the former lens, as confirmed from light rays travelling along
geodesics of the virtual sphere. We further observe resolutions ranging from
lambda/2 to nearly lambda/4 for magnetic dipoles of varying orientations of
dipole moments within the fisheye in transverse electric polarization (magnetic
field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for
which the source and its image are either located within a unit disc of air, or
within a corona 1<r<2 with refractive index . In both cases,
the image resolution is about lambda/2.Comment: Version 2: 22 pages, 11 figures. More figures added, additional cases
discussed. Misprints corrected. Keywords: Maxwell fisheye, Eaton lens;
Non-Euclidean geometry; Stereographic projection; Transformation optics;
Metamaterials; Perfect lens. The last version appears at J. Modern Opt. 57
(2010), no. 7, 511-52
Modelling potential movement in constrained travel environments using rough space-time prisms
The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space-time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space-time points in obstacle-constrained travel environments
Difference of Normals as a Multi-Scale Operator in Unorganized Point Clouds
A novel multi-scale operator for unorganized 3D point clouds is introduced.
The Difference of Normals (DoN) provides a computationally efficient,
multi-scale approach to processing large unorganized 3D point clouds. The
application of DoN in the multi-scale filtering of two different real-world
outdoor urban LIDAR scene datasets is quantitatively and qualitatively
demonstrated. In both datasets the DoN operator is shown to segment large 3D
point clouds into scale-salient clusters, such as cars, people, and lamp posts
towards applications in semi-automatic annotation, and as a pre-processing step
in automatic object recognition. The application of the operator to
segmentation is evaluated on a large public dataset of outdoor LIDAR scenes
with ground truth annotations.Comment: To be published in proceedings of 3DIMPVT 201
The Inhuman Overhang: On Differential Heterogenesis and Multi-Scalar Modeling
As a philosophical paradigm, differential heterogenesis offers us a novel descriptive vantage with which to inscribe Deleuze’s virtuality within the terrain of “differential becoming,” conjugating “pure saliences” so as to parse economies, microhistories, insurgencies, and epistemological evolutionary processes that can be conceived of independently from their representational form. Unlike Gestalt theory’s oppositional constructions, the advantage of this aperture is that it posits a dynamic context to both media and its analysis, rendering them functionally tractable and set in relation to other objects, rather than as sedentary identities. Surveying the genealogy of differential heterogenesis with particular interest in the legacy of Lautman’s dialectic, I make the case for a reading of the Deleuzean virtual that departs from an event-oriented approach, galvanizing Sarti and Citti’s dynamic a priori vis-à-vis Deleuze’s philosophy of difference. Specifically, I posit differential heterogenesis as frame with which to examine our contemporaneous epistemic shift as it relates to multi-scalar computational modeling while paying particular attention to neuro-inferential modes of inductive learning and homologous cognitive architecture. Carving a bricolage between Mark Wilson’s work on the “greediness of scales” and Deleuze’s “scales of reality”, this project threads between static ecologies and active externalism vis-à-vis endocentric frames of reference and syntactical scaffolding
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle
highly packed situations. The model we propose rests on two principles: We
first define a spontaneous velocity which corresponds to the velocity each
individual would like to have in the absence of other people; The actual
velocity is then computed as the projection of the spontaneous velocity onto
the set of admissible velocities (i.e. velocities which do not violate the
non-overlapping constraint). We describe here the underlying mathematical
framework, and we explain how recent results by J.F. Edmond and L. Thibault on
the sweeping process by uniformly prox-regular sets can be adapted to handle
this situation in terms of well-posedness. We propose a numerical scheme for
this contact dynamics model, based on a prediction-correction algorithm.
Numerical illustrations are finally presented and discussed.Comment: 22 page
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