Search results for "Geometry"
showing 10 items of 4487 documents
Perfect Hashing Structures for Parallel Similarity Searches
2015
International audience; Seed-based heuristics have proved to be efficient for studying similarity between genetic databases with billions of base pairs. This paper focuses on algorithms and data structures for the filtering phase in seed-based heuristics, with an emphasis on efficient parallel GPU/manycores implementa- tion. We propose a 2-stage index structure which is based on neighborhood indexing and perfect hashing techniques. This structure performs a filtering phase over the neighborhood regions around the seeds in constant time and avoid as much as possible random memory accesses and branch divergences. Moreover, it fits particularly well on parallel SIMD processors, because it requ…
On the role of virtual work in Levi-Civita’s parallel transport
2015
A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics
2011
International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…
Modéliser un demi-cercle et autres questions de poids nuls
2018
National audience; Les courbes de Bézier rationnelles avec des points pondérés peinent à prendre en compte certaines situations élémentaires comme la modélisation d'un demi-cercle avec une courbe de degré 2. Dans cet article nous mon-trons comment l'utilisation de courbes de Bézier rationnelles avec des points massiques résout ce problème. Plus largement, nous montrons aussi que la formulation usuelle de Bézier rationnelles n'est pas complète.
Introduction à la modélisation de l'écriture manuscrite par des courbes Bézier Rationnelles massiques
2019
National audience; L’article est une introduction à la modélisation de l’écriture manuscrite. La représentation de l’écriture cursive in- terfère, selon l’approche hors ligne ou en ligne, sur la robustesse des algorithmes de reconnaissance des caractères manuscrits, de l’identification des auteurs et de leur signature. Les caractéristiques de base de l’écriture cursive que sont les traits et leur inclinaisons, les boucles, les pleins et déliés peuvent être modélisés par des courbes. Des méthodes existent. Elles reposent sur les B-splines et leur points de contrôle. Dans un premier temps, des traits, les auteurs proposent une modélisation, rebroussements, boucles, arrondis, pleins et déliés.…
Some remarks on Hilbert's (Weak) Nullstellensatz
2011
Certain remarks are provided related to weak nullstellensatz exploiting some problems proposed in Fulton’s book entitled “An Introduction to Algebraic Geometry” and elementary notions of Functional Analysis.
Oscillation of Second-Order Neutral Differential Equations
2013
Author's version of an article in the journal: Funkcialaj Ekvacioj. Also available from the publisher at: http://www.math.kobe-u.ac.jp/~fe/ We study oscillatory behavior of a class of second-order neutral differential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional differential inequalities. Our assumptions allow applications to differential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results reported in the literature. Two illustrative examples are provided.
Quasiconformal Jordan Domains
2020
We extend the classical Carath\'eodory extension theorem to quasiconformal Jordan domains $( Y, d_{Y} )$. We say that a metric space $( Y, d_{Y} )$ is a quasiconformal Jordan domain if the completion $\overline{Y}$ of $( Y, d_{Y} )$ has finite Hausdorff $2$-measure, the boundary $\partial Y = \overline{Y} \setminus Y$ is homeomorphic to $\mathbb{S}^{1}$, and there exists a homeomorphism $\phi \colon \mathbb{D} \rightarrow ( Y, d_{Y} )$ that is quasiconformal in the geometric sense. We show that $\phi$ has a continuous, monotone, and surjective extension $\Phi \colon \overline{ \mathbb{D} } \rightarrow \overline{ Y }$. This result is best possible in this generality. In addition, we find a n…
Lenses on very curved zones of a singular line field of ${\mathbb C}^2$ or of a singular plane field of ${\mathbb C}^3$
2020
We renormalize, using suitable lenses, small domains of a singular holomorphic line field of ${\mathbb C}^2$ or plane field of ${\mathbb C}^3$ where the curvature of a plane-field is concentrated. At a proper scale the field is almost invariant by translations. When the field is integrable, the leaves are locally almost translates of a surface that we will call {\it profile}. When the singular rays of the tangent cone (a generalization to a plane-field of the tangent cone of a singular surface is defined) are isolated, we obtain more precise results. We also generalize a result of Merle (\cite{Me}) concerning the contact order of generic polar curves with the singular level $f=0$ when $\ome…
FROM THE DESCRIPTIVE GEOMETRY TO THE INFORMATICS LANGUAGE.
2010
This study is centred in the environment of the research into solutions of the problems of graphic representation, expressing theoretical considerations which allow the carrying out of geometric-descriptive procedures decoded in informatics language, for implementing CAD commands. The solution of these problems requires a reliable command of stereometry and descriptive geometry and it can extend remarkably the level of external geometric competences. The implementation of the means of ICT has brought a higher effectiveness of graphing mapping processes. In the informatics field, the advent of software dedicated to computerized representation has increased the possibilities of investigation …