1,721,031 research outputs found
Non-uniform interpolatory subdivision schemes with improved smoothness
No full textSubdivision schemes are used to generate smooth curves or surfaces by iteratively refining an initial control polygon or mesh. We focus on univariate, linear, binary subdivision schemes, where the vertices of the refined polygon are computed as linear combinations of the current neighbouring vertices. In the classical stationary setting, there are just two such subdivision rules, which are used throughout all subdivision steps to construct the new vertices with even and odd indices, respectively. These schemes are well understood and many tools have been developed for deriving their properties, including the smoothness of the limit curves. For non-stationary schemes, the subdivision rules are not fixed and can be different in each subdivision step. Non-uniform schemes are even more general, as they allow the subdivision rules to be different for every new vertex that is generated by the scheme. The properties of non-stationary and non-uniform schemes are usually derived by relating the scheme to a corresponding stationary scheme and then exploiting the fact that the properties of the stationary scheme carry over under certain proximity conditions. In particular, this approach can be used to show that the limit curves of a non-stationary or non-uniform scheme are as smooth as those of a corresponding stationary scheme. In this paper we show that non-uniform subdivision schemes have the potential to generate limit curves that are smoother than those of stationary schemes with the same support size of the subdivision rule. For that, we derive interpolatory 2-point and 4-point schemes that generate C-1 and C-2 limit curves, respectively. These values of smoothness exceed the smoothness of classical interpolating schemes with the same support size by one. (C) 2022 The Author(s). Published by Elsevier B.V
Interpolatory blending net subdivision schemes of Dubuc–Deslauriers type
No full textNet subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc-Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interpolants to nets of univariate functions, and on a particular class of blending functions with properties related to the Dubuc-Deslauriers schemes. The general analysis tools for net subdivision schemes, developed in a previous paper by the authors, together with the properties of the blending functions, lead to the proof of the convergence of these schemes to limit functions having the same integer smoothness as the limits of the corresponding Dubuc-Deslauriers schemes. These results are proved for net subdivision schemes corresponding to the first 84 members of the Dubuc-Deslauriers family, and conjectured for the rest. A concrete example of a family of piecewise polynomial blending functions is considered, together with the corresponding family of net subdivision schemes. The performance of the first two net subdivision schemes in this family is demonstrated by two examples
Convergence of univariate non-stationary subdivision schemes via asymptotic similarity
No full textA new equivalence notion between non-stationary subdivision schemes, termed asymptotic similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is known that asymptotic equivalence between a non-stationary subdivision scheme and a convergent stationary scheme guarantees the convergence of the non-stationary scheme. We show that for non-stationary schemes reproducing constants, the condition of asymptotic equivalence can be relaxed to asymptotic similarity. This result applies to a wide class of non-stationary schemes. (C) 2015 Elsevier B.V. All rights reserved
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A survey on L2-approximation orders from shift-invariant spaces
No full textThis chapter aims at providing a self-contained introduction to notions and results connected with the L2-approximation order of finitely generated shift-invariant (FSI) spaces SΦ ⊂ L2(Rd). Here, the approximation order is with respect to a scaling parameter and to the usual scaling of the L2-projector onto SΦ, where Φ = {φ1, …, φn} ⊂ L2(Rd) is a given set of functions, the so-called generators of SΦ. Special attention is given to the principal shift-invariant (PSI) case, where the shift-invariant space is generated from the multi-integer translates of just one generator. This case is interesting in itself because of its possible applications in wavelet methods. The general FSI case is considered subject to a stability condition being satisfied, and the recent results on so-called superfunctions are developed. For the case of a refinable system of generators the sum rules for the matrix mask and the zero condition for the mask symbol, as well as invariance properties of the associated subdivision and transfer operator are discussed. References to the literature and further notes are extensively given at the end of each section. In addition, the list of references has been enlarged in order to provide a rather comprehensive overview of the existing literature in the field
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Uniform subdivision algorithms for curves and surfaces
No full textA convergence analysis for studying the continuity and differentiability of limit curves generated by uniform subdivision algorithms is presented. The analysis is based on the study of corresponding difference and divided difference algorithms. The alternative process of "integrating" the algorithms is considered. A specific example of a 4-point interpolatory curve algorithm is described and its generalization to a surface algorithm defined over a subdivision of a regular triangular partition is illustrated
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