Search results for "Geometry"

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 …

Gluing Dupin cyclides along circles, finding a cyclide given three contact conditions.

2013

Dupin cyclides form a 9-dimensional set of surfaces which are, from the viewpoint of differential geometry, the simplest after planes and spheres. We prove here that, given three oriented contact conditions, there is in general no Dupin cyclide satisfying them, but if the contact conditions belongs to a codimension one subset, then there is a one-parameter family of solutions, which are all tangent along a curve determined by the three contact conditions.

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.

Rational quasi-projective surfaces with algebraic moduli of real forms

2022

We construct real rational quasi-projective surfaces with positive dimensional algebraic moduli of mutually non-isomorphic real forms.

On the projective geometry of entanglement and contextuality

2019

$\mathbb{A}^1$-cylinders over smooth affine surfaces of negative Kodaira dimension

2019

International audience; The Zariski Cancellation problem for smooth affine surfaces asks whether two suchsurfaces whose products with the affine line are isomorphic are isomorphic themselves. Byresults of Iitaka-Fujita, the answer is positive for surfaces of non-negative Kodaira dimen-sion. By a characterization due to Miyanishi, surfaces of negative Kodaira dimension arefibered by the affine line, and by a celebrated result of Miyanishi-Sugie, the answer to theproblem is positive if one of the surfaces is the affine plane. On the other hand, exam-ples of non-isomorphicA1-fibered affine surfaces with isomorphicA1-cylinders were firstconstructed by Danielewski in 1989, and then by many other…

Stable motivic homotopy theory at infinity

2021

In this paper, we initiate a study of motivic homotopy theory at infinity. We use the six functor formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under $\ell$-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers the singular complex at in…