Search results for "Geometric"
showing 10 items of 652 documents
Visual Perception and Graphic Analysis. The Pattern of Inlays in the Cathedral of Palermo
2017
The Cathedral of Palermo is one of the monuments belonging to the Arab-Norman Itinerary, declared a UNESCO World Heritage site in 2015. This text uses geometric analysis to describe some of the inlaid circular designs from the eastern façade, the corner towers and the apses. The cataloguing of the two-tone geometric motifs also reveals aspects that can be linked back to the laws of visual perception. Hence, the text investigates these aspects based on a new reading. In fact, decomposing these elements based on the experience of their perception also facilitates the recognition of elementary figures. The attempt made in this brief text intends to induce a new perceptive awareness resulting f…
Off-axis focal shift for rotationally nonsymmetric screens
2009
We report on an analytical formulation for evaluating the amplitude distribution along any line directed toward the geometrical focus of a spherical wave front that passes through a rotationally nonsymmetric diffracting screen. Our formula consists of two factors. The first factor involves the one-dimensional Fourier transform of the projection of the screen function onto the off-axis line. The second factor depends on the inverse distance to the screen and permits us to recognize the existence of focal shift along off-axis lines.
THE SCUOLA OFFICINA MECCANICA IN VILLAGGIO MONTE DEGLI ULIVI IN RIESI. READING AND ANALYSIS THROUGH SURVEYING.
2017
This research analyses in depth the project of one of the most representative work of the Modern Architectural Movement in Sicily – the Scuola Officina Meccanica, located in Villaggio Monte degli Ulivi, in Riesi (CL), designed by the architect Leonardo Ricci between 1962 and 1968. The main objective is to contribute to the conservation of the architectural work through its analysis and study for a careful and conscious restoration. The research methodology aimed to retrace the compositional and geometric principles that defined the design process and its unique configuration.
Extending CSG with projections: Towards formally certified geometric modeling
2015
We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…
Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems
2011
International audience; This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems. Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number …
Building Anosov flows on $3$–manifolds
2014
We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic trans- verse tori.
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.
Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d
2016
International audience; We consider simple random walks on random graphs embedded in R-d and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we show an annealed invariance principle for these random walks. These results hold for a large variety of point processes including Poisson point processes, Matern cluster and Matern hardcore processes which have respectively clustering and repulsiveness properties. The proof relies on the use the process of the environment seen from the particle. It allows to reconstruct the original process as an additive functional of a Markovian process und…
Arrangements de cercles sur une sphère: Algorithmes et Applications aux modèles moléculaires representés par une union de boules
2008
Since the early work of Richard et al., geometric constructions havebeen paramount for the description of macromolecules and macro-molecularassemblies. In particular, Voronoï and related constructions have beenused to describe the packing properties of atoms, to compute molecularsurfaces, to find cavities. This thesis falls in this realm, andafter a brief introduction to protein structure, makes fourcontributions.First, using the sweep line paradigm of Bentley and Ottmann, wepresent the first effective algorithm able to construct the exactarrangement of circles on a sphere. Moreover, assuming the circlesstem from the intersection between spheres, we present a strategy to reportthe covering …
The tennis racket effect in a three-dimensional rigid body
2017
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Differen…