Dupin cyclides osculating surfaces
نویسندگان
چکیده
منابع مشابه
Symmetries of canal surfaces and Dupin cyclides
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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Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives...
متن کاملBlending of Surfaces of Revolution and Planes by Dupin cyclides
This paper focuses on the blending of a plane with surfaces of revolution relying on Dupin cyclides, which are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century. A general algorithm is presented for the construction of two kinds of blends: pillar and recipient. This algorithm uses Rational Quadric Bézier Curves (RQBCs) to model ...
متن کاملArrangements on Surfaces of Genus One: Tori and Dupin Cyclides
An algorithm is presented to compute the exact arrangement induced by arbitrary algebraic surfaces on a parametrized ring Dupin cyclide, including the special case of the torus. The intersection of an algebraic surface of degree n with a reference cyclide is represented as a real algebraic curve of bi-degree (2n, 2n) in the cyclide’s two-dimensional parameter space. We use Eigenwillig and Kerbe...
متن کاملOrtho-Circles of Dupin Cyclides
We study the set of circles which intersect a Dupin cyclide in at least two different points orthogonally. Dupin cyclides can be obtained by inverting a cylinder, or cone of revolution, or by inverting a torus. Since orthogonal intersection is invariant under Möbius transformations we first study the ortho-circles of cylinders/cones of revolution and tori and transfer the results afterwards.
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ژورنال
عنوان ژورنال: Bulletin of the Brazilian Mathematical Society, New Series
سال: 2014
ISSN: 1678-7544,1678-7714
DOI: 10.1007/s00574-014-0045-y