Dupin"s cyclide as a self-dual surface.
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Dupin"s cyclide as a self-dual surface.

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Published in [n.p.] .
Written in English


Book details:

The Physical Object
Pagination267-286 p.
Number of Pages286
ID Numbers
Open LibraryOL16850191M

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texts All Books All Texts latest This Just In Smithsonian Libraries FEDLINK (US) Genealogy Lincoln Collection. National Emergency Library. Top Dupin's cyclide as a self-dual surface.. by Young, Mabel Minerva, Publication date ] Topics Cyclide, Surfaces Publisher [Baltimore CollectionPages: century, the French geometer Charles Pierre Dupin discovered a nons­ pherical surface. with. circular lines of curvature. He called. it. a cyclide in his book, Applicarions de Geometrie published in Recently, cyclides have been revived for use as surface patches in computer aided geometric design (CAGD). Other applications. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link) http Author: Mabel Minerva Young. Keywords: Dupin Cyclide, inversion, Joachimsthal, Meusnier, circular line of curvature. 1 Introduction and history Maxwells construction of a Dupin cyclide During the 19th century, at the age of sixteen, the French mathematician Charles Pierre Dupin discovered a surface which is the envelope of a family of spheres tangent to threeFile Size: KB.

Introducing Dupin Cyclides. Dupin cyclides were discovered by French mathematician Charles Dupin in [1]. They received much attention including works by Arthur Cayley and James Clerk Maxwell [2, 3]. A Dupin cyclide is characterised by the property that all of its lines of curvature are (arcs/segments of) either circles or lines. Mathematicians sometimes refer to this generalisation of a. The Dupin cyclide is a quartic surface with useful properties such as circular lines of curvature, rational parametric representations and closure under offsetting. All natural quadrics (cone, cylinder, sphere) and the torus are special cases of the by: 9. 5) Fifth definition: the Dupin cyclides are the envelopes of spheres centered on a conic and perpendicular to a fixed sphere centered on the focal axis of the conic. This definition proves that the Dupin cyclides are indeed cyclides. The orthogonal sphere is the fixed sphere of the inversion that leaves the cyclide globally invariant.   Based on what you've explained, the adaptive contrast setting on your Surface Book 2 is doing its part. It's the graphics driver adjusting the screen contrast automatically based on the content that is being shown on the screen at a given time. It usually starts as an odd fade in and outs when going from dark to light screens and it might also.

of the input surface ' we obtain difierent types of Dupin cyclides (see Fig. 1). Dupin cyclides can be obtained by certain projections from supercyclides [12]. There is also a close relation between Dupin cyclides and line geometry [48] and geometric optics [34]. Dupin cyclides carry at least two one-parameter families of circles. Figure 2: View from the interiorof a singularlocus m H E3 Light Figure 3: Euclidean models in the Lorentzspace R5 1. We can see Λ4 as a sphere for the Lorentz quadratic form; as for the usual Euclidean sphere, the tangent hyperplane TσΛ4 is orthogonal to σ(seen as a vector of R5 1). It is time-like and TσΛ 4 ∩ Λ4 is a cone of dimension 3 formed of (affine) by: 1. Abstract. We develop two different new algorithms of G1-blending between planes and canal surfaces using Dupin cyclides. It is a generalization of existing algorithms that blend revolution surfaces and planes using a plane called construction by: 2. In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double particular, these latter are themselves examples of Dupin cyclides. They were discovered by (and named after) Charles Dupin in his dissertation under Gaspard Monge. [1] The key property of a Dupin cyclide is that it is a channel surface (envelope of a one.