منابع مشابه
Schlesinger Transformations for Bonnet Surfaces
Bonnet surfaces, i.e. surfaces in Euclidean 3-space, which admits a one-parameter family of isometries preserving the mean curvature function, can be described in terms of solutions of some special Painlev e equations. The goal of this work is to use the well-known Schlesinger transformations for solutions of Painlev e VI equations to create new Bonnet surfaces from a known one.
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In this work, the authors study Bonnet Problems using Cartan moving frames and associated structure equations. The Cartan structural forms are written in terms of the first and second fundamental forms, and the Lax system is consequently reinterpreted; orthonormal moving frames are obtained solutions to this Bonnet-Lax system, via numerical integration. Certain classifications of families of su...
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The envelope of a one-parameter set of spheres with radii r(t) and centers m(t) is a canal surface with m(t) as the spine curve and r(t) as the radii function. This concept is a generalization of the classical notion of an offset of a plane curve. In this paper, we firstly survey the principle geometric features of canal surfaces. In particular, a sufficient condition of canal surfaces without ...
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We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries of such canal surfaces. For Dupin cyclides in canonical form, we apply the characterization to derive an intrinsic description of their symmetries and symmetry groups, whi...
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Current CAD systems can represent curves and surfaces only in rational B-spline (NURBS) form ( .Farin, 1994; .Hoschek and Lasser, 1993). On the other hand, certain curves and surfaces that arise in practical applications such as offsets of rational curves or surfaces are in general not rational and therefore need to be approximated. This motivated .Farouki and Sakkalis (1990) to introduce the s...
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ژورنال
عنوان ژورنال: Deu Muhendislik Fakultesi Fen ve Muhendislik
سال: 2019
ISSN: 1302-9304
DOI: 10.21205/deufmd.2019216119