Convergent Vector and Hermite Subdivision Schemes
نویسندگان
چکیده
Hermite subdivision schemes have been studied by Merrien, Dyn and Levin and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level. As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision scheme which can be handled more easily. With this transformation, the study of convergence of Hermite subdivision schemes is reduced to that of vector stationary subdivision schemes. We propose a first criterion for C0 convergence for a large class of vector subdivision schemes. This gives a criterion for C1 convergence of Hermite subdivision schemes. It can be noticed that these schemes do not have to be interpolatory. We conclude by investigating spectral properties of Hermite schemes and other necessary/sufficient conditions of convergence. Math Subject Classification: 65D17, 65D10
منابع مشابه
Matrix Subdivision Schemes
Subdivision schemes with matrix masks are a natural extension of the well studied case of subdivision schemes with scalar masks. Such schemes arise in the analysis of multivariate scalar schemes, in subdivision processes corresponding to shift-invariant spaces generated by more than one function, in geometric modeling where each component of the curve/surface is designed by a diierent linear co...
متن کاملExtended Hermite subdivision schemes
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 ...
متن کاملContents Invited conferences 3
Hermite subdivision algorithms are mainly designed to interpolate functional values and associated derivatives. These schemes process non-scalar data (functional values and derivatives), and can be rewritten as non-stationary vector algorithms, although their non-stationarity is of a very specific kind. In this talk we present new families of approximating subdivision schemes derived from inter...
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