Search results for "subdivision"
showing 10 items of 52 documents
Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions
2021
Abstract Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stabilit…
A semi-empirical approach for predicting two-phase flow discharge through branches of various orientations connected to a horizontal main pipe
2010
Abstract The subdivision of two-phase flow in branching conduits consisting of a large horizontal main pipe with upward, downward, or lateral branches of reduced diameter is of great interest in various technological fields. For example, these conduits are important in light-water nuclear reactors (LWRs) in the case of a small break loss-of-coolant accident (SBLOCA) in a leg of the reactor's primary coolant loops, as well as for breaks or valve malfunctions in a large pipeline. In these kinds of circumstances, the relevant phenomenology often involves phase stratification coupled with possible liquid entrainment or gas pool-through phenomena. Therefore, these phenomena were studied in depth…
An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision
2021
Abstract Exponential polynomials are essential in subdivision for the reconstruction of specific families of curves and surfaces, such as conic sections and quadric surfaces. It is well known that if a linear subdivision scheme is able to reproduce a certain space of exponential polynomials, then it must be level-dependent, with rules depending on the frequencies (and eventual multiplicities) defining the considered space. This work discusses a general strategy that exploits annihilating operators to locally detect those frequencies directly from the given data and therefore to choose the correct subdivision rule to be applied. This is intended as a first step towards the construction of se…
Polynomial Smoothing Splines
2014
Interpolating splines is a perfect tool for approximation of a continuous-time signal \(f(t)\) in the case when samples \(x[k]=f(k),\;k\in \mathbb {Z}\) are available. However, frequently, the samples are corrupted by random noise. In such case, the so-called smoothing splines provide better approximation. In this chapter we describe periodic smoothing splines in one and two dimensions. The SHA technique provides explicit expression of such splines and enables us to derive optimal values of the regularization parameters.
A structured filter for Markovian switching systems
2014
In this work, a new methodology for the structuring of multiple model estimation schemas is developed. The proposed filter is applied to the estimation and detection of active mode in dynamic systems. The discrete-time Markovian switching systems represented by several linear models, associated with a particular operating mode, are studied. Therefore, the main idea of this work is the subdivision of the models set to some subsets in order to improve the detection and estimation performances. Each subset is associated with sub-estimators based on models of the subset. In order to compute the global estimate and subset probabilities, a global estimator is proposed. Theoretical developments ba…
Class II subdivision: Cone beam computed tomography- CBCT Analysis
2021
Background To estimate whether there is skeletal and/or dental asymmetry in class II subdivision patients, between the Class II side and the Class I side using of cone beam computed tomography (CBCT). Material and methods A sample of 30 patients, from a private clinic, retrospectively selected; with a class II subdivision diagnosis requiring treatment, who underwent wide-field CBCT that met the inclusion criteria. The data was processed with Dolphin 3D version 11.95 Premium software. The craniometric points, as well as the spatial orientation scheme of the three-dimensional model were proposed by Craig Minich, et al. (1). Results The Class II subdivision side and the Class I side of each pa…
The PCHIP subdivision scheme
2016
In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741
Annihilation Operators for Exponential Spaces in Subdivision
2022
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
Seeking for the Grasp : An Iterative Subdivision Model of Conceptualisation
2019
Concepts are fundamental collective constructs of individual items that are capable of abstracting meaningfully homogeneous groupings of phenomena. This capability is a prerequisite for communication and action and gives structure to learning and memory. Our study is aligned with the vast paradigm that assumes embodied cognition, rooted in Merleau-Ponty (Phenomenology of perception (trans: C. Smith). Routledge and Kegan Paul, London, 1962), seminally articulated by Varela et al. (Embodied mind: cognitive science and human experience. MIT Press, Cambridge, MA, 1991) and existing today in a number of variants that have been reviewed by Wilson (Six views of embodied cognition. Springer. Psycho…
Geometry control of the junction between two fractal curves
2012
International audience; The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated F…