Search results for "Geometric"
showing 10 items of 652 documents
Environmental and ontogenetic constraints on developmental stability in the spatangoid sea urchin Echinocardium (Echinoidea).
2006
13 pages; International audience; Spatangoid irregular sea urchins are detritivorous benthic organisms particularly prone to variations of environment, and their mode of growth and plate morphology make them an appropriate model to assess the effects of environmental variations. Two populations of Echinocardium flavescens were sampled in two sites of the Norwegian coast characterized by contrasted environmental conditions. Different morphological descriptors (plate areas, interlandmarks distances, overall size, and shape of the posterior ambulacra) were used to appraise interindividual variations, and fluctuating asymmetry. The comparisons were carried out using classical fluctuating asymme…
Geometrical super resolved lensless imaging
2011
In the field of super resolution researchers are trying to overcome both the diffraction as well as the geometrical bounds of an imaging system. In this paper we present a recently developed approach that aims to overcome the geometrical bounds while using a unified spatial light modulator (SLM) based lensless configuration.
Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes
2007
We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.
Effective Fresnel-number concept for evaluating the relative focal shift in focused beams
1998
We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.
ETP/GDOP Behavior Study for N-Sensors Arrays ina Multilateration Radar System
2009
In this paper, we evaluated the ETP (Expected Theoretical Precision) and GDOP (Geometric Dilution Of Precision) enhancement related to the number of sensors in a Multilateration radar system. An introduction about the principles of the Multilateration radar system basis operation is described, then, the formulation for evaluation the ETP/GDOP of the 3D positioning is shown. We observed that the ETP and GDOP enhance with the increase of the number of sensors. A substantial improvement was obtained until nine sensors but, for more sensors that improvement is reduced. Results for a 75km×75km area are shown, including LAM (Local Area Multilateration) and WAM (Wide Area Multilateration) settings…
Potential approach in marginalizing Gibbs models
1999
Abstract Given an undirected graph G or hypergraph potential H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph G A or hypergraph H A associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to G A or H A , respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works.
Exact, efficient, and complete arrangement computation for cubic curves
2006
AbstractThe Bentley–Ottmann sweep-line method can compute the arrangement of planar curves, provided a number of geometric primitives operating on the curves are available. We discuss the reduction of the primitives to the analysis of curves and curve pairs, and describe efficient realizations of these analyses for planar algebraic curves of degree three or less. We obtain a complete, exact, and efficient algorithm for computing arrangements of cubic curves. Special cases of cubic curves are conics as well as implicitized cubic splines and Bézier curves.The algorithm is complete in that it handles all possible degeneracies such as tangential intersections and singularities. It is exact in t…
An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
2005
We present the first exact, complete and efficient implementation that computes for a given set P=p1,...,pn of quadric surfaces the planar map induced by all intersection curves p1∩ pi, 2 ≤ i ≤ n, running on the surface of p1. The vertices in this graph are the singular and x-extreme points of the curves as well as all intersection points of pairs of curves. Two vertices are connected by an edge if the underlying points are connected by a branch of one of the curves. Our work is based on and extends ideas developed in [20] and [9].Our implementation is complete in the sense that it can handle all kind of inputs including all degenerate ones where intersection curves have singularities or pa…
Witness computation for solving geometric constraint systems
2014
International audience; In geometric constraint solving, the constraints are represented with an equation system F(U, X) = 0, where X denotes the unknowns and U denotes a set of parameters. The target solution for X is noted XT. A witness is a couple (U_W, X_W) such that F(U_W, X_W) = 0. The witness is not the target solution, but they share the same combinatorial features, even when the witness and the target lie on two distinct connected components of the solution set of F(U, X) = 0. Thus a witness enables the qualitative study of the system: the detection of over- and under-constrained systems, the decomposition into irreducible subsystems, the computation of subsystems boundaries. This …
Complete, exact, and efficient computations with cubic curves
2004
The Bentley-Ottmann sweep-line method can be used to compute thearrangement of planar curves provided a number of geometricprimitives operating on the curves are available. We discuss themathematics of the primitives for planar algebraic curves of degreethree or less and derive efficient realizations. As a result, weobtain a complete, exact, and efficient algorithm for computingarrangements of cubic curves. Conics and cubic splines are specialcases of cubic curves. The algorithm is complete in that it handles all possibledegeneracies including singularities. It is exact in that itprovides the mathematically correct result. It is efficient in thatit can handle hundreds of curves with a quart…