1,721,593 research outputs found
From approximating subdivision schemes for exponential splines to high-performance interpolating algorithms
No full textAbstractIn this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension.In particular, throughout this paper we will focus on the derivation of 6-point interpolating schemes that turn out to be unique in combining vital ingredients like C2-continuity, simplicity of definition, ease of implementation, user independency, tension control and ability to reproduce salient trigonometric and transcendental curves
A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control
No full textWe present a tension-controlled 2-point Hermite interpolatory subdivision scheme that is capable of reproducing circles starting from a sequence of sample points with any arbitrary spacing and appropriately chosen first and second derivatives.
Whenever the tension parameter is set equal to 1, the limit curve coincides with the rational quintic Hermite interpolant to the given data and has guaranteed C2 continuity, while for other positive tension values, continuity of curvature is conjectured and empirically shown by a wide range of experiments
A Chaikin-based variant of Lane-Riesenfeld algorithm and its non-tensor product extension
Full text linkIn this work we present a parameter-dependent Refine-and-Smooth (RS) subdivision algorithm where the refine stage R consists in the application of a perturbation of Chaikin's/Doo-Sabin's vertex split, while each smoothing stage S performs averages of adjacent vertices like in the Lane-Riesenfeld algorithm (Lane and Riesenfeld, 1980). This constructive approach provides a unifying framework for univariate/bivariate primal and dual subdivision schemes with tension parameter and allows us to show that several existing subdivision algorithms, proposed in the literature via isolated constructions, can be obtained as specific instances of the proposed strategy. Moreover, this novel approach provides an intuitive theoretical tool for the derivation of new non-tensor product subdivision schemes that in the regular regions satisfy the property of reproducing bivariate cubic polynomials, thus resulting the natural extension of the univariate family presented in Hormann and Sabin (2008)
On the refinement matrix mask of interpolating Hermite splines
No full textWe propose a new computational approach for constructing the refinement matrix mask of interpolating Hermite splines of any order and with general dilation factor. Our strategy exploits the refinability properties of cardinal B-splines with simple knots and simplifies the constructive procedures proposed so far
A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines
No full textThis paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The proposed approach is based on the analysis of certain polynomial identities in two variables and leads to interesting new interpolatory bivariate subdivision schemes
A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling
No full textUnivariate subdivision schemes are efficient iterative methods to generate smooth limit curves starting from a sequence of arbitrary points. Aim of this paper is to present and investigate a new family of 6-point interpolatory non-stationary subdivision schemes capable of reproducing important curves of great interest in geometric modeling and engineering applications, if starting from uniformly spaced initial samples. This new family can reproduce conic sections since it is obtained by a parameter depending affine combination of the cubic exponential B-spline symbol generating functions in the space V_4,\gamma=1,x,e^tx,e^−tx with t in 0,s,is|s>0. Moreover, the free parameter can be chosen to reproduce also other interesting analytic curves by imposing the algebraic conditions for the reproduction of an additional pair of exponential polynomials giving rise to different extensions of the space V_4,\gamma
Dual univariate m-ary subdivision schemes of de Rham-type
No full textIn this paper, we present an algebraic perspective of the de Rham transform of a binary subdivision scheme and propose an elegant strategy for constructing dual mm-ary approximating subdivision schemes of de Rham-type, starting from two primal schemes of arity mm and 2, respectively. On the one hand, this new strategy allows us to show that several existing dual corner-cutting subdivision schemes fit into a unified framework. On the other hand, the proposed strategy provides a straightforward algorithm for constructing new dual subdivision schemes having higher smoothness and higher polynomial reproduction capabilities with respect to the two given primal schemes
Solar-Driven Hydrogen Generation by Metal Halide Perovskites: Materials, Approaches, and Mechanistic View
No full textSolar-driven photocatalysis by metal halide perovskites (MHPs) is emerging as an exciting and promising field to promote several relevant catalytic reactions taking advantage of the superior optical properties of MHPs. Their electronic structure is suitable to run reduction reactions (H2 generation, CO2 reduction) and even oxidation reactions, in particualr for perovskites with higher band gap values, and further extends their possible use in the field of photochemical organic syntheses. This Mini-Review focuses on the application of MHPs in the solar-driven hydrogen generation with particular emphasis on the materials' design and mechanistic features involved in the catalytic reactions
Building blocks for designing arbitrarily smooth subdivision schemes with conic precision
No full textSince subdivision schemes featured by high smoothness and conic precision are strongly required in many application contexts, in this work we define the building blocks to obtain new families of non-stationary subdivision schemes enjoying such properties. To this purpose, we firstly derive a non-stationary extension of the Lane-Riesenfeld algorithm, and we exploit the resulting class of schemes to design a non-stationary family of alternating primal/dual subdivision schemes, all featured by reproduction of 1, x, e^tx, e^-tx, t in [0, π) ∪ iR+. Then, we focus our attention on interpolatory subdivision schemes with conic precision, that can be obtained as a byproduct of the above classes. In particular, we present a novel construction of a family of non-stationary interpolatory 2n-point schemes which generalizes the well-known Dubuc-Deslauriers family in such a way the nth (n ≥ 2) family member reproduces Π_2n-3 ∪ e^tx, e^-tx, t in [0, π) ∪ iR+, and keeps the original smoothness of its stationary counterpart unchanged
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