Search results for "computational geometry"

Tangentes à une courbe fractale

2007

http://www.irit.fr/REFIG/index.php/refig/article/view/10; National audience; Nous nous intéressons au calcul des tangentes à une courbe fractale définie à l'aide d'un IFS. Généralement, les courbes fractales sont nulle part dérivables, mais sous certaines conditions on peut montrer qu'elles admettent, en un ensemble de points, des demi-tangentes à droite et à gauche. Nous proposons une méthode permettant de déterminer ces demi-tangentes.

Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis

2014

International audience; Computational topology has recently seen an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.

The non-degenerate Dupin cyclides in the space of spheres using Geometric Algebra

2012

International audience; Dupin cyclides are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century and \textcolor{black}{were} introduced in CAD by R. Martin in 1982. A Dupin cyclide can be defined, in two different ways, as the envelope of a one-parameter family of oriented spheres. So, it is very interesting to model the Dupin cyclides in the space of spheres, space wherein each family of spheres can be seen as a conic curve. In this paper, we model the non-degenerate Dupin cyclides and the space of spheres using Conformal Geometric Algebra. This new approach permits us to benefit from the advantages of the use of Geometric Alge…

Approche adaptative de simplification géométrique temps réel de modèles 3D distribués pour la visualisation et l'interaction à distance

2010

National audience; Deux moyens permettent aujourd'hui d'accéder visuellement à des données 3D volumineuses à distance : le premier consiste à transférer les données entre le serveur et le poste client/utilisateur, le second consiste à générer et à transférer des " photographies" de ces données 3D qui restent alors localisées sur le serveur. Le goulot d'étranglement principal dans les deux cas est la bande passante du réseau qui ne permet pas de transférer des volumes de données importants. Bien plus, la visualisation de plusieurs centaines de giga-octets d'informations nécessite de grandes capacités de stockage (disque dur ou mémoire) et des équipements de visualisation très performants (ca…

A predictive approach for a real-time remote visualization of large meshes

2012

Déjà sur HAL; Remote access to large meshes is the subject of studies since several years. We propose in this paper a contribution to the problem of remote mesh viewing. We work on triangular meshes. After a study of existing methods of remote viewing, we propose a visualization approach based on a client-server architecture, in which almost all operations are performed on the server. Our approach includes three main steps: a first step of partitioning the original mesh, generating several fragments of the original mesh that can be supported by the supposed smaller Transfer Control Protocol (TCP) window size of the network, a second step called pre-simplification of the mesh partitioned, ge…

Résolution des contraintes géométriques

1994

National audience; La modélisation par contraintes définit les objets géométriques (typiquement, en 2D, les points, droites, cercles, coniques, etc) par les contraintes qu'ils doivent vérifier (distances, angles, tangences, incidences, etc. entre paires d'objets). L'exposé tente de faire le point sur les diverses méthodes proposées à ce jour pour la résolution des contraintes, en 2D ou en 3D. Les méthodes algébriques transforment les contraintes en un système d'équations, et recourent ensuite à des méthodes numériques (relaxation, Newton-Raphson) [4] ou symboliques (bases de Grobner, méthode de Wu et Ritt) [5,3]. Les méthodes géométriques décomposent le système de contraintes en problèmes g…

Analysis of geometrical features of 3D model based on the surface curvature of a set of point cloud

2021

Modélisation géométrique de formes fractales pour la CAO

2020

International audience

Propose Semantic Formalization for 3D Reconstruction of Architectural

2010

International audience; Archi3D project is a successful practice well proved by engineering practices. In this paper, we propose to reconstruct semantics for the purpose of reconstruct 3D architecture in Archi3D fundamentally. The formalization approach starts from several hypotheses on semantics which include: there is a core mechanism of semantics which is not limited to conceptual expression level; and a complete expression of semantics necessaries the ―implicitexplicit‖ transition of human side knowledge, etc. The necessity and feasibility concerning applying the proposed method and technology to the practice of Archi3D is discussed systemically by way of semantics revelations on some …

A note on Hilbert’s weak nullstellensatz

2015

In this article, through a suitable generalization of the well-known notion of spectrum of an element of an arbitrary normed algebra of Operator Theory, it will be possible to give another simple proof of the Hilbert’s Weak Nullstellensatz.