Search results for " Geometry."
showing 10 items of 2189 documents
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.
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 …
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…
Topological canal foliations
2019
Regular canal surfaces of $\mathbb{R}^3$ or $\mathbb{S}^3$ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of $\mathbb{S}^3$ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.
Introduction to Mathematical Logic, Edition 2021
2021
Textbook for students in mathematical logic. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux and resolution methods. Herbrand's theorem. Sections 1, 2, 3 represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian).
Sur la réductibilité des graphes de contraintes géométriques
2017
La modélisation géométrique par contraintes dont les applications intéressent des communautés issues de divers domaines tels l'ingénierie mécanique, la conception assistée par ordinateur, le calcul symbolique ou la chimie moléculaire est maintenant intégré dans les outils standards de modélisation. Dans cette discipline une forme géométrique est spécifiée par les relations que doivent vérifier les composants de cette forme au lieu de spécifier explicitement ces composants. Le but de la résolution est de déduire la forme répondant à toutes ces contraintes. Diverses méthodes ont été proposées pour résoudre ce problème. Nous nous intéresserons spécifiquement aux méthodes dites graphiques ou ba…