Generalized Taylor operators and polynomial chains for Hermite subdivision schemes
نویسندگان
چکیده
منابع مشابه
A generalized Taylor factorization for Hermite subdivision schemes
In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so–called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For ...
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We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...
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Subdivision schemes are efficient tools for building curves and surfaces. For vector subdivision schemes, it is not so straightforward to prove more than the Hölder regularity of the limit function. On the other hand, Hermite subdivision schemes produce function vectors that consist of derivatives of a certain function, so that the notion of convergence automatically includes regularity of the ...
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Bivariate interpolatory Hermite subdivision schemes have recently been applied to build free-form subdivision surfaces. It is well known to geometric modelling practitioners that interpolatory schemes typically lead to “unfair” surfaces—surfaces with unwanted wiggles or undulations—and noninterpolatory (a.k.a. approximating in the CAGD community) schemes are much preferred in geometric modellin...
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Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2018
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-018-0996-9