585 research outputs found

    Bivariate Hermite subdivision

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    A subdivision scheme for constructing smooth surfaces interpolating scattered data in R3\mathbb{R}^3 is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points {(xi,yi)}i=1N\{(x_i, y_i)\}_{i=1}^N from which none of the pairs (xi,yi)(x_i,y_i) and (xj,yj)(x_j,y_j) with i≠ji\neq j coincide, it is proved that the resulting surface (function) is C1C^1. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is C2C^2 if the data are not 'too irregular'. Finally the approximation properties of the methods are investigated

    Polynomial cubic splines with tension properties

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    In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems

    Exponential Splines and Pseudo-Splines: Generation versus reproduction of exponential polynomials

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    Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules determining successive refinements of coarse initial meshes. One important property of subdivision schemes is their capability of exactly reproducing in the limit specific types of functions from which the data is sampled. Indeed, this property is linked to the approximation order of the scheme and to its regularity. When the capability of reproducing polynomials is required, it is possible to define a family of subdivision schemes that allows to meet various demands for balancing approximation order, regularity and support size. The members of this family are known in the literature with the name of pseudo-splines. In case reproduction of exponential polynomials instead of polynomials is requested, the resulting family turns out to be the non-stationary counterpart of the one of pseudo-splines, that we here call the family of exponential pseudo-splines. The goal of this work is to derive the explicit expressions of the subdivision symbols of exponential pseudo-splines and to study their symmetry properties as well as their convergence and regularity.Comment: 25 page

    08221 Abstracts Collection -- Geometric Modeling

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    From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    Blending techniques in Curve and Surface constructions

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    Source at https://www.geofo.no/geofoN.html. <p
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