Search results for " Geometry"
showing 10 items of 2294 documents
On the Neron-Severi group of surfaces with many lines
2008
For a binary quartic form $\phi$ without multiple factors, we classify the quartic K3 surfaces $\phi(x,y)=\phi(z,t)$ whose Neron-Severi group is (rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of prime degree without multiple factors, we prove that the Neron-Severi group of the surface $\phi(x,y)=\psi(z,t)$ is rationally generated by lines.
Seifert manifolds admitting partially hyperbolic diffeomorphisms
2017
We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.
On the arithmetic of a family of degree-two K3 surfaces
2018
Let $\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\mathcal{X}$ be the generic element of the family of surfaces in $\mathbb{P}$ given by \begin{equation*} X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \end{equation*} The surface $\mathcal{X}$ is a K3 surface over the function field $\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\mathcal{X}$ and other elements of the family $X$.
Contour/Outline/Silhouette
2020
The contour is the locus at which the parts of opaque solid objects appear to form an edge because it corresponds for the viewer to the projection of the rim, namely the curve that divides the surfaces into visible and invisible parts. The rim between the visible front and the invisible rear side is projected onto the contour that is the envelope of all the curves of equal depth. Although the rim and the contour run into depth, they are distinct concepts that regard the object-centred and the viewer-centred description. The outline is the boundary of the surface delimited by the contour, which fills a spatial region. Rubin (1921) discovered the property that allows the contour and the outli…
On stability of generic subriemannian caustic in the three-space
2000
Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…
Boolean operations with implicit and parametric representation of primitives using R-functions
2005
We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition …
Multiresolution Analysis for Irregular Meshes
2003
International audience; The concept of multiresolution analysis applied to irregular meshes has become more and more important. Previous contributions proposed a variety of methods using simplification and/or subdivision algorithms to build a mesh pyramid. In this paper, we propose a multiresolution analysis framework for irregular meshes with attributes. Our framework is based on simplification and subdivision algorithms to build a mesh pyramid. We introduce a surface relaxation operator that allows to build a non-uniform subdivision for a low computational cost. Furthermore, we generalize the relaxationoperator to attributes such as color, texture, temperature, etc. The attribute analysis…
Anamorphic Projection: Analogical/Digital Algorithms
2014
The study presents the first outcomes of a wider research dealing with the theme of “anamorphosis”, a specific technique of geometric projection of a shape on a surface. Anamorphosis represents the synthesis among geometry, art and architecture and is realized in scientific and empirical research approaches. In this study we investigated how new digital techniques allow to simplify the anamorphic applications even in case of projections on complex surfaces. After a short excursus of the most famous historical and contemporary applications, we propose some possible approaches that allow you to manage the geometry of anamorphic curves both in Descriptive Geometry field (by using interactive t…
Standardization of Methods for Characterizing the Surface Geometry of Solids
2003
Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.
About Objective 3-D Analysis of Airway Geometry in Computerized Tomography
2008
The technology of multislice X-ray computed tomography (MSCT) provides volume data sets with approximately isotropic resolution, which permits a noninvasive 3-D measurement and quantification of airway geometry. In different diseases, like emphysema, chronic obstructive pulmonary disease (COPD), or cystic fribrosis, changes in lung parenchyma are associated with an increase in airway wall thickness. In this paper, we describe an objective measuring method of the airway geometry in the 3-D space. The limited spatial resolution of clinical CT scanners in comparison to thin structures like airway walls causes difficulties in the measurement of the density and the thickness of these structures.…