Search results for "algorithm"
showing 10 items of 4887 documents
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 $X$.
Facial scanning accuracy depending on the alignment algorithm and digitized surface area location: An in vitro study.
2021
To measure the accuracy (trueness and precision) of a facial scanner depending on the alignment method and the digitized surface area location.Fourteen markers were adhered on a head mannequin and digitized using an industrial scanner (GOM Atos Q 3D 12 M; Carl Zeiss Industrielle Messtechnik GmbH). A control mesh was acquired. Subsequently, the mannequin was digitized using a facial scanner (Arc4; Bellus3D) (n = 30). The control mesh was delineated into 10 areas. Based on the alignment procedures, two groups were created: reference best fit (RBF group) and landmark-based best fit (LA group). The root mean square was used to calculate the discrepancy between the control mesh and each facial s…
Approximation of Continuous Media Models for Granular Systems Using Cellular Automata
2004
In this paper a new cellular automata model suitable for granular systems simulation is presented. The proposed model is shown to be equivalent to a particularization of the well known BCRE model of granular systems and a correspondence between the parameters of the presented model and the BCRE model is also set, allowing to fit these parameters for a given system. The model has the advantage over other cellular automata models of being more realistic in the behavior of the surface of heaps and slopes. The dynamics of the CA is analyzed in order to confirm that it also has one of the most important features of these systems, 1/f noise.
An Automatic Three-Dimensional Fuzzy Edge Detector
2009
Three-dimensional object analysis is of particular interest in many research fields. In this context, the most common data representation is boundary mesh, namely, 2D surface embedded in 3D space. We will investigate the problem of 3D edge extraction, that is, salient surface regions characterized by high flexure. Our automatic edge detection method assigns a value, proportional to the local bending of the surface, to the elements of the mesh. Moreover, a proper scanning window, centered on each element, is used to discriminate between smooth zones of the surface and its edges. The algorithm does not require input parameters and returns a set of elements that represent the salient features …
Deep Gaussian Processes for Geophysical Parameter Retrieval
2018
This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well to large datasets, and improves prediction accuracy over standard full and sparse GP models. We give empirical evidence of performance for estimation of surface dew point temperature from infrared sounding data.
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…
Systematic Error Correction of a 3D Laser Scanning Measurement Device
2011
International audience; Non-contact measurement techniques using laser scanning have the advantage of fast acquiring large numbers of points. However, compared to their contact-based counterparts, these techniques are known to be less accurate. The work presented in this paper aims at improving the accuracy of these techniques through an error correction procedure based on an experimental process that concerns mechanical parts. The influence of the three parameters defining the relative position and the orientation between the sensor and the surface is studied. The process used to build an experimental global model of error is presented and applied to a typical part composed of planes or sk…
A surface hopping algorithm for nonadiabatic minimum energy path calculations
2015
The article introduces a robust algorithm for the computation of minimum energy paths transiting along regions of near-to or degeneracy of adiabatic states. The method facilitates studies of excited state reactivity involving weakly avoided crossings and conical intersections. Based on the analysis of the change in the multiconfigurational wave function the algorithm takes the decision whether the optimization should continue following the same electronic state or switch to a different state. This algorithm helps to overcome convergence difficulties near degeneracies. The implementation in the MOLCAS quantum chemistry package is discussed. To demonstrate the utility of the proposed procedur…