Search results for "Surface of revolution"

showing 4 items of 4 documents

Dupin cyclide blends between non-natural quadrics of revolution and concrete shape modeling applications

2014

Abstract In this work, we focus on the blending of two quadrics of revolution by two patches of Dupin cyclides. We propose an algorithm for the blending of non-natural quadrics of revolution by decomposing the blending operation into two complementary sub-blendings, each of which is a Dupin cyclide-based blending between one of the two quadrics and a circular cylinder, thus enabling the direct computation of the two Dupin cyclide patches and offering better flexibility for shape composition. Our approach uses rational quadric Bezier curves to model the relevant arcs of the principal circles of Dupin cyclides. It is quite general and we have successfully used it for the blending of several n…

Pure mathematicsQuadricDupin cyclideGeneral EngineeringTorusBézier curveGeometryComputer Graphics and Computer-Aided DesignHuman-Computer InteractionAlgebraic surfaceCatenarySurface of revolutionFocus (optics)MathematicsComputers & Graphics
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The Calderón problem with partial data on manifolds and applications

2013

We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flatness condition include parts of cylindrical sets, conical sets, and surfaces of revolution. We prove local uniqueness in the Calderon problem with partial data in admissible geometries, and global uniqueness under an additional concavity assumption. This work unifies two earlier approaches to this problem (\cite{KSU} and \cite{I}) and extends both. The proofs are based on impr…

Mathematics - Differential GeometryPure mathematicsGeodesiccalderón problem35J10Boundary (topology)Conformal mappartial data58J32Integral geometryMathematics - Analysis of PDEsFOS: MathematicsUniquenessMathematicsFlatness (mathematics)Numerical AnalysisCalderón problemEuclidean spaceApplied Mathematicsta11135R30Differential Geometry (math.DG)inverse problemSurface of revolutionAnalysisAnalysis of PDEs (math.AP)Analysis & PDE
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Characterization of thin plastic foils for applications in X-ray optics technology

2007

Thin plastic foils are being investigated to build shell optics for X-ray telescopes. Compared to polished glass optics, the advantage is in terms of increased collecting area, light weight and lower cost. Plastic material is also desirable to allow deformation into a complete surface of revolution. We collected plastic materials of common use for industrial applications and also specialty materials developed for the electronic industry. A comparative study was then performed to evaluate the optical quality of the selected plastic films. Surface analysis was carried out with topographic instruments to investigate the microroughness of our samples at different scan lengths. Preliminary resul…

plastic materialsMaterials sciencex-ray optics grazing incidencex-ray astronomy; x-ray optics grazing incidence; plastic materials; high-performance films; surface analysis; microroughnessbusiness.industryShell (structure)Plastic materialsX-ray opticsX-ray astronomy X-ray optics grazing incidence plastic materials high-performance films surface analysis microroughnessX-ray telescopeDeformation (meteorology)surface analysiseye diseasesx-ray astronomylaw.inventionCharacterization (materials science)Telescopehigh-performance filmsOpticsmicroroughnesslawSurface of revolutionbusiness
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Canal foliations of S 3

2012

The goal of the article is to classify foliations of S3 by regular canal surfaces, that is envelopes of one-parameter families of spheres which are immersed surfaces. We will add some extra information when the leaves are “surfaces of revolution” in a conformal sense.

foliationGeneral Mathematics53A30Foliation (geology)Conformal mapGeometryMathematics::Differential GeometrySurface of revolution53C12MathematicsComputingMethodologies_COMPUTERGRAPHICScanal surface
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