Hermite Subdivision Schemes and Taylor Polynomials
نویسندگان
چکیده
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 C0 and H is Cd. We apply this result to two families of Hermite subdivision schemes, the first one is interpolatory, the second one is a kind of corner cutting, both of them use Obreshkov interpolation polynomial.
منابع مشابه
Hermite-interpolatory subdivision schemes
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...
متن کاملA 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 ...
متن کاملFace-based Hermite Subdivision Schemes
Interpolatory and non-interpolatory multivariate Hermite type subdivision schemes are introduced in [8, 7]. In their applications in free-form surfaces, symmetry properties play a fundamental role: one can essentially argue that a subdivision scheme without a symmetry property simply cannot be used for the purpose of modelling free-form surfaces. The symmetry properties defined in the article [...
متن کاملNoninterpolatory Hermite subdivision schemes
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...
متن کاملDual Hermite subdivision schemes of de Rham-type
Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary (I.S.) and Inherently Non-Stationary (I.N.S.) Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interp...
متن کامل