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Topic: Paraboloid of revolution

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Parabolic reflector

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	Reflector for vehicular headlamp - Patent 5406464
		A third reflecting area consisting of an aggregation of paraboloid-of-revolution segments forms a pattern contributing to the formation of a cut line tilted a given angle with respect to the horizontal line in the distribution pattern of a passing beam.
		Further, to provide a reflecting area contributing to the formation of a cut line tapered with respect to the horizontal line to form a passing light beam, two-sheet hyperbolic paraboloid or paraboloid of revolution reflecting segments are used.
		The hyperbolic paraboloid plane 3 is parabolic in both the horizontal and vertical cross sections.
	www.freepatentsonline.com /5406464.html (3518 words)

	Parabola
		A parabola has a single axis of reflective symmetry, which passes through its focus and is perpendicular to its directrix.
		A parabola spun about this axis in three dimensions traces out a shape known as a paraboloid of revolution.
		If a mirror is constructed in the shape of a paraboloid and a light source is placed at its focus, the light will be reflected as a beam of rays parallel to the axis, and the same process works in reverse.
	www.ebroadcast.com.au /lookup/encyclopedia/pa/Parabolic.html (281 words)

	Condensing and collecting optical system using parabolic reflectors or a corresponding ellipsoid/hyperboloid pair of ...
		The collimating reflector 30 comprises a portion of a paraboloid of revolution having an optical axis 38 and a focal point 36.
		The focusing reflector 40 comprises a portion of a paraboloid of revolution having an optical axis 48 and a focal point 46.
		4, the spherical retro-reflector 50 is replaced by a secondary collimating reflector 70 comprising a paraboloid of revolution having an optical axis 78 and focal point 76 that preferably coincide with the optical axis 38 and the focal point 36, respectively, of the collimating reflector 30.
	www.freepatentsonline.com /6672740.html (6028 words)

	Volume Wave Drag
		For a paraboloid of revolution the drag coefficient based on frontal area is:
		For configurations more complicated than bodies of revolution, the drag may be computed with a panel method or other CFD solution.
		A body of revolution with the same distribution of area as that of the oblique cuts through the actual geometry is created and the drag is computed from linear theory.
	adg.stanford.edu /aa241/drag/volumedrag.html (584 words)

	U.S. Patent: 5562342 - Reflector for vehicular headlight - October 8, 1996
		By cutting the paraboloid of revolution by a plane including the vector P3.sub.-- RC and lying at right angles to the x-y plane, there is obtained a parabola 12.
		The section thereof obtained when the reflection area 3 is cut by a vertical surface including the x axis is a parabola having a focal distance f.sub.u, and the section thereof when cut by a horizontal surface including the x axis is a parabola having a focal distance f.sub.1.
		The reflection area 4 is a reflection surface having f=f.sub.u and d=0 in formula 1, that is, a paraboloid of revolution.
	www.everypatent.com /comp/pat5562342.html (4131 words)

	Calc IV Problem Set 2 (Site not responding. Last check: 2007-10-12)
		In particular, he proved that for a paraboloid of revolution the volume of the frustum is the same as the volume of the cylinder.
		Use a double integral to express the volume of a frustum of a paraboloid of revolution and show why this is true.
		Maclaurin also showed that the difference between a frustum of a right circular cone and the corresponding cylinder is one-fourth the volume of a similar cone, with the same height as the frustum and with diameter one-half the difference between the upper and lower diameters of the frustum.
	www.public.coe.edu /~jwhite/s99/Clc4ps2.htm (325 words)

	Paraboloid Info - Bored Net - Boredom (Site not responding. Last check: 2007-10-12)
		In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation:
		With a=b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.
		This also works the other way around: a parallel beam of light incident on the paraboloid is concentrated at the focal point.
	www.borednet.com /e/n/encyclopedia/p/pa/paraboloid.html (108 words)

	Abstract - PhD Dissertation of Stefanos Kozanis
		The criterion of paraboloid from revolution is given a new, x-fem, algorithm.
		In the eighth chapter, the failure criterion of the elliptic paraboloid is proposed to be used to geotechnical problems and especially to anisotropic rock-mass ones.
		Firstly, the isotropic criteria of Hoek-Brown and of paraboloid of revolution are compared and their parabolic shape is shown.
	users.ntua.gr /soulman/dissertation_abstract_en.html (696 words)

	Variable focus right angle mirror for laser beam manipulation - Patent Review 4030816
		The system includes a first mirror having the surface of a partial section of the surface of a paraboloid of revolution and mounted in a housing relative to a collimated beam such as produced by a laser, so as to reflect the beam from the direction of travel on to a second mirror.
		A mirror system for controlling a supply laser beam comprising a housing, an opening in said housing, a first mirror having the surface of a partial paraboloid of revolution, said first mirror having a reflective parabolic surface and being positioned to reflect the supply laser beam passing through said opening substantially 90.degree.
		The paraboloid mirror 28 defines a paraboloid surface 42, parabolic focus 44, and a parabolic vertex 46.
	www.wikipatents.com /4030816.html (1917 words)

	Apparatus for generating focused shockwaves having a cylindrical coil and a paraboloid of revolution reflector ...
		An apparatus for generating focused shockwaves, suitable for extracorporeal lithotripsy, has a substantially hollow-cylindrical membrane consisting of electrically conductive material and an electrical coil arrangement disposed inside the membrane which can be supplied with a high voltage pulse to rapidly repel the membrane and thereby generate a shockwave.
		The apparatus includes a concave reflector in the form of a paraboloid of revolution, which surrounds the membrane and coil, and which has a center axis substantially coincident with the center axis of the membrane.
		The shockwave generated by the cylindrical coil and membrane arrangement is reflected and focused by the paraboloid of revolution so that the shockwaves converge at a focus.
	www.delphion.com /details?pn=US05058569__ (428 words)

	Chapter 8
		The equation for the paraboloid of revolution as shown in Figure 8.4, in rectangular coordinates with the
		In spherical coordinates, the equation of a paraboloid of revolution with its vertex
		The surface area of the paraboloid may be found by integrating Equation (8.19) over the appropriate limits.
	www.powerfromthesun.net /Chapter8/Chapter8new.htm (3499 words)

	What is a Parabolic Mirror?
		Parabolic mirrors are a specific type of paraboloid, known as a paraboloid of revolution.
		This is a type of elliptical paraboloid that is rotated around its axis and may also be referred to as a circular paraboloid.
		One of the earliest uses of the parabolic mirror was in Isaac Newton's reflecting telescope of the 17th century.
	www.wisegeek.com /what-is-a-parabolic-mirror.htm (408 words)

	SBF Glossary: RL to RQC
		The filament of an R lamp is located near the focus of the paraboloid.
		Light from the focus of a paraboloid is reflected in a parallel beam.
		Hence, R lamps would radiate in a beam, except for two things: (1) Light radiated forwar from the filament is never reflected from the parabola and spreads in an approximately isotropic distribution forward of the lamp.
	www.plexoft.com /SBF/R03.html (7716 words)

	Springer Online Reference Works
		In this form, an elliptic paraboloid is situated on one side of the
		they are circles, and the surface is called a paraboloid of revolution.) The sections by planes passing through the
		The axis of symmetry of an elliptic paraboloid is called its axis and the point of intersection of the axis with the elliptic paraboloid is its vertex.
	eom.springer.de /e/e035510.htm (97 words)

	BFRL: DEPTH-SENSING INDENTATION OF POLYMERS
		The analysis of indentation load-penetration curves produced by depth-sensing indentation systems is often based on work by Oliver and Pharr.
		Their analysis was in turn based upon relationships developed by Sneddon for the penetration of a flat elastic half space by different probes with particular axisymmetric shapes (e.g., a flat-ended cylindrical punch, a paraboloid of revolution, and a cone).
		is the final unloading depth, and m is a power law exponent that is related to the geometry of the indenter; for a flat-ended cylindrical punch, m = 1, for a paraboloid of revolution, m = 1.5, and for a cone, m = 2.
	www.bfrl.nist.gov /nanoscience/DSI.htm (1324 words)

	Uniformly Valid Asymptotic Solution for Steady Viscous Flow Past a Slender Paraboloid of Revolution (Site not responding. Last check: 2007-10-12)
		An Oseen type of analytical solution for the case of paraboloid of revolution was obtained by Veldman, in terms of the Oseen model, in 1973.
		The present paper is concerned with steady viscous flow past a slender paraboloid of revolution.
		The flow is assumed to be uniform in the far field with a constant velocity U. We obtaine a uniformly valid asymptotic expansion solution for the problem in the limit of Reynolds number Re\to 0.
	flux.aps.org /meetings/YR99/DFD99/abs/S990008.html (292 words)

	Mathematical Physics Final Honours and Diploma General Relativity Some Two Dimensional Surfaces
		The surface generated by equation (3) is called a paraboloid of revolution.
		It is not known at the moment whether our universe is closed or open.
		The paraboloid of revolution also has a three dimensional version
	www.thphys.may.ie /staff/bdolan/gr-2d/gr-2d-html.html (738 words)

	Home (Site not responding. Last check: 2007-10-12)
		PRESS RELEASE -- February 10, 2004 -- Envirospace has developed an automated measuring and modeling system (AMM System) that combines state-of-the-art software and hardware for a photogrammetric point-cloud generation and a NURBS-surface creation.
		Best-fit rotational paraboloid (or rotation paraboloid, paraboloid of revolution) -- Outline of a modular software used with advantage for determination of the focal length, position, and orientation of parabolic antennas and other parabolic objects from measured 3D points.
		AMMsys -- From digital images to NURBS surfaces: Integration, with enhancements, of commercial hardware and software that produces a system for measuring physical objects and creating their digital models.
	www.envirospacesoftware.com (146 words)

	Background-Theory
		The quantitative study of dendrites began with the transport analysis of Ivantsov in 1946 [Ivantsov, 1947], and over the last fifty years a number of theories of steady-state dendritic crystal growth have been developed [Glicksman, 1993].
		Ivantsov, based his transport analysis on a suggestion made by Papapetrou [Papapetrou, 1935], who, in 1935, first described the form of a dendritic crystal as a paraboloid of revolution with fixed radius of curvature
		Ivantsov solved the diffusion equation in co-moving paraboloidal coordinates, scaled by the only length scale in the problem,
	www.rpi.edu /locker/56/000756/back-th.html (1303 words)

	Amazon.com: "general paraboloid": Key Phrase page (Site not responding. Last check: 2007-10-12)
		hyperboloid of revolution GO geometrical optics GPOR general paraboloid of revolution GTD geometric theory of...
		Our mathematical formulation refers to a general paraboloid of the form: f(x, y) = a(x-()2+b(y- r))2, where a > 0, b > 0 are constants, and (e, 7J)...
		problems here considered by treating in succession the potential problem for the paraboloid of revolution,' the parabolic cylinder' and the general paraboloid.
	www.amazon.com /phrase/general-paraboloid (583 words)

	Design - China
		Technically, FAST is not simply a copy of the existing Arecibo telescope but has a number of innovations.
		Firstly, the proposed main spherical reflector, will conform to a paraboloid of revolution in real time through actuated active control, and thus enables the realization of both wide bandwidth and full polarization capability while using a standard feed design.
		Secondly, a feed support system, which integrates optical, mechanical and electronic technologies, will effectively reduce the cost of the support structure and control system.
	www.skatelescope.org /pages/design_china.htm (194 words)

	Calc IV Problem Set 2 Hints
		Make sure you're computing the volume inside the paraboloid instead of what's underneath it.
		Note it's asking about any paraboloid of revolution, not just z = x
		The easiest way for us at this stage to think about frustums is as the difference between two paraboloids: The one up to a top height minus the one up to a bottom height.
	www.public.coe.edu /~jwhite/s99/Clc4ps2h.htm (775 words)

	Samples of 3D wave propagation (Site not responding. Last check: 2007-10-12)
		Sequence illustrating the 3D wave propagation's accuracy, between a point and square plane.
		The last image (bottom-right) shows one level set and the retrieved bisector (a paraboloid or revolution).
		Symmetries retrieved for a cylinder with open ends (left) or closed ones (right).
	www.lems.brown.edu /vision/researchAreas/Shocks3D/prop-samples.html (127 words)

	bradley newman: Paraboloid of Revolution
		In talking with Jess around the screen Tuesday night, we heard our voices intensified.
		They were being reflected off the screen (or Paraboloid of Revolution) to its focal point, just like a satellite dish or parabolic mirror.
		This dovetails nicely with the themes of communion (named my thesis, finally: Communio.
	interactive.usc.edu /members/bnewman/archives/006142.html (217 words)

	Interactive Visualizations
		These structures are the points themselves, their Voronoi diagram, Delaunay triangulation, or convex hull.
		The user can also add an abitrary paraboloid of revolution, project points onto it, add tangent planes, and verify that the paraboloid's lower hull indeed corresponds to the Voronoi diagram.
		Since this is a video tape, the viewer can't control the system, but must watch a recording of the author's interaction with the system.
	www.cs.princeton.edu /~ah/alg_anim/animation/subsection3_4_4.html (352 words)

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