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Topic: Quadric

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	Quadric - Wikipedia, the free encyclopedia
		In mathematics a quadric, or quadric surface, is any D-dimensional hypersurface defined as the locus of zeros of a quadratic polynomial.
		In general, the locus of zeros of a set of polynomials is known as an algebraic variety, and is studied in the branch of algebraic geometry.
		A quadric is thus an example of an algebraic variety.
	en.wikipedia.org /wiki/Quadric (282 words)

	Quadric fitting
		Quadric fitting is usually formulated as a nonlinear least squares problem, which is solved either using iterative methods for minimizing a nonlinear function or casting it as an eigenvalue problem which is solved directly and no approximate values for the parameters are needed.
		31], the reconstruction of objects having quadric patches is improved by incorporating geometric constraints that fix feature relationships between the patches.
		7], the parameters of a quadric are estimated from two quadratic curves fitted to the measured image coordinates of two stripes projected onto the object surface.
	foto.hut.fi /~ojokinen/vtyo/node16.html (502 words)

	Online Encyclopedia and Dictionary - Quadric (Site not responding. Last check: 2007-11-06)
		In mathematics a quadric, or quadric surface, is any D-dimensional hypersurface represented by a second-order equation in spatial variables (coordinates).
		for a specific choice of Q, P and R. The normalized equation for a three-dimensional (D=3) quadric centred at the origin (0,0,0) is:
		http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node61.html, Quadrics in Geometry Formulas and Facts by Silvio Levy, excerpted from 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press).
	fact-archive.com /encyclopedia/Quadric (152 words)

	Talk:Quadric - Wikipedia, the free encyclopedia
		A quadric in n-dimensional space has dimension n-1 as it is determined by one equation.
		You can either start a new section in this article, or you can create new articles such as projective quadric or quadric over a general field or something like that.
		Another possibility might be to rename this article to affine quadric, and start from scratch here.
	en.wikipedia.org /wiki/Talk:Quadric (399 words)

	Surface Simplification using Quadric Error Metrics
		Quadric error metrics provide a useful characterization of local surface shape, and they have modest computational and storage requirements.
		Combining quadric error metrics with iterative vertex pair contraction results in a fast algorithm for producing high-quality approximations of polygonal surfaces.
		While analyzing the properties of the quadric error metric, we discovered that (under suitable assumptions) minimizing the quadric error will (in the limit) produce triangles of optimal aspect ratio.
	graphics.cs.uiuc.edu /~garland/research/quadrics.html (642 words)

	Interactive Gallery of Quadric Surfaces (Site not responding. Last check: 2007-11-06)
		Quadric surfaces are important objects in Multivariable Calculus and Vector Analysis classes.
		We like them because they are natural 3D-extensions of the so-called conics (ellipses, parabolas, and hyperbolas), and they provide examples of fairly nice surfaces to use as examples for the rest of your class.
		The basic quadric surfaces are described by the following equations, where A, B, and C are constants.
	www.math.umn.edu /~rogness/quadrics (666 words)

	HKUST Institutional Repository: Item 1783.1/1967
		In this thesis, the revolute quadric (RQ) decomposition is proposed for solving the intersection problem of surfaces of revolution and canal surfaces.
		Instead of quadrilateral/triangular decompositions, a surface of revolution is subdivided into a group of G0 truncated cones or G1 bounded revolute quadrics, and a canal surface is subdivided into a set of G1 bounded revolute quadrics and joint spheres (RQ-Spheres).
		The revolute quadric decomposition reduces the complex and difficult intersection problem on surfaces of revolution and canal surfaces to the simpler one on revolute quadrics or truncated cones.
	hdl.handle.net /1783.1/1967 (381 words)

	Quadric
		Quadric has partnered with global suppliers to further expand its business breadth and depth.
		Quadric provides its clients with an unequalled range of services, with the primary focus of enhancing the spaces in which people work.
		With a joinery workshop of over 8000m2, Quadric is equipped with the necessary staff and machinery to produce quality, custom built furniture, as well as supporting onsite fitout requirements.
	www.spec-net.com.au /company/quadric.htm (409 words)

	16 Quadrics
		Spheres, circular cylinders, and circular cones are quadrics.
		A surface with equation (5) can be regarded as a cone (Section 13.3) over a conic C (any ellipse, parabola or hyperbola can be taken as the directrix; there is a two-parameter family of essentially distinct cones over it, determined by the position of the vertex with respect to C).
		The surfaces with equations (1) --(6) are central quadrics; in the form given, the center is at the origin.
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node61.html (363 words)

	My Humble Graphics Page: The Quadrics (Site not responding. Last check: 2007-11-06)
		The Quadric Surfaces: three squares yield 6 curves
		This page describes the Quadric Surfaces, there are 6.
		Since we're on the topic of the Quadric Surfaces, we may wish to recall our old friend the Quadradic Equation.
	www.frontiernet.net /~imaging/quads.html (255 words)

	Quadric (Site not responding. Last check: 2007-11-06)
		Quadric specializes in helping companies achieve strategic differentiation, accelerating integration and growth.
		We would be happy to discuss your situation and suggest possible ways forward.
		Quadric works with international companies that want to move beyond the competitive advantages they have achieved using rational approaches (e.g.
	www.quadric.dk (97 words)

	Mesh Simplification and Multiresolution Data Structures
		There are also a lot of other uses for mesh simplification and multiresolution data structures, like collision detection at a different resolution than the one use for rendering, editing a model not in its highest resolution, but at an arbitrary level of detail, automatically applying the changes to the entire multiresolution structure, and so on.
		"Surface Simplification Using Quadric Error Metrics", introduced at SIGGRAPH 1997 by Michael Garland and Paul S. Heckbert [Gar97] uses a remarkable error metric that can be used for efficient generation of multiple levels of detail for a given triangle mesh of arbitrary topology.
		A quadric (represented by a symmetric, positive semi-definite matrix Q) is associated with each vertex, subsuming the sum of the squared distances of the vertex to all its incident planes:
	www.cg.tuwien.ac.at /studentwork/VisFoSe98/msh (1248 words)

	POV-Ray 3.1g Documentation - Quadric (Site not responding. Last check: 2007-11-06)
		A quadric is a 2nd order polynomial while a quartic is 4th order.
		Quadrics render much faster and are less error-prone but produce less complex objects.
		It contains several pre-defined quadrics and you can transform these pre-defined shapes (using translate, rotate and scale) into the ones you want.
	www.cacr.caltech.edu /~slombey/asci/povray/pov260.htm (249 words)

	About "The Quadric Surfaces" (Site not responding. Last check: 2007-11-06)
		There are 6 quadric surfaces: sphere, cone, hyperbolid of one sheet, hyperboloid of two sheets, paraboloid, and hyperboloic paraboloid.
		The cylinder, related but not a quadric, is also included.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/view/5360.html (44 words)

	Ray / Quadric Intersection
		The class of quadrics (surfaces that can be defined by a quadratic equation) include cylinders, cones, ellipsoids, paraboloids, etc. Note that spheres and planes are a special subclass but have faster routines as special cases.
		To define a quadric surface with location and geometrical properties other than that given above we can perform the following steps, usiing an ellipsoid as an example.
		Rearrange the equation to put it into the format of the general quadric surface equation as given above.
	www.bmsc.washington.edu /people/merritt/graphics/quadrics.html (500 words)

	Quadric at opensource encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates).
		\sum_{i,j=1}^D Q_{i,j} x_i x_j + \sum_{i=1}^D P_i x_i + R = 0 for a specific choice of Q, P and R. The normalized equation for a three-dimensional (D=3) quadric centred at the origin (0,0,0) is:
		http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node61.html, 16 Quadrics in Geometry Formulas and Facts by Silvio Levy, excerpted from 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press).
	www.wiki.tatet.com /Quadric.html (298 words)

	Quadric Splines (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: this paper is to derive their quadric splines solely geometrically in projective space.
		It provides a geometric meaning for certain parameters chosen to be the same constant by Dahmen and Guo.
		Furthermore, it facilitates the classification of the quadrics, avoids the global dependencies of Dahmen's and Guo's transversal system, and renders the Powell-Sabin interpolant as a special case.
	citeseer.ist.psu.edu /278476.html (220 words)

	Publications of the SPACES team
		We are interested in efficiently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coefficients.
		Combining results from the theory of quadratic forms, a projective formalism and new theorems characterizing the intersection of two quadratic surfaces, we show how to obtain parametric representations that are both ``simple'' (the size of the coefficients is small) and ``as rational as possible''.
		It is shown that any intersection of two quadrics may be pamareterized with at most two square roots by components (except when the intersection consists in 4 colinear lines), and we provide an algorithm for computing which is always optimal in the number of square roots which are involved.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Quadric Surfaces - Eduseek (Site not responding. Last check: 2007-11-06)
		Quadric Surfaces - Defines Quadratic surfaces, and provides information on unit spheres, and normal vectors.
		Quadric Surfaces Gallery - A picture collection of Quadric Surfaces.
		Identifying Quadric Surfaces - Provides information on the identification of quadric surfaces.
	www.eduseek.com /navigate.php?ID=8144 (85 words)

	Code Documentation (Site not responding. Last check: 2007-11-06)
		Quadric (const double and, const double and, const double and)
		This function computes the range of values taken by a quadric over a given interval.
		Computes the derivative of a quadric, which is actually a linear expression, although returned as a quadric.
	www710.univ-lyon1.fr /~abarbier/Doc/Math/a00020.html (294 words)

	Citebase - Topology of Quadric Bundles
		This paper begins with a description of cohomological invariants of non-degenerate quadric bundles, in terms of the cohomology rings of the classifying spaces of the general orthogonal groups.
		Following this, the Main Theorem of the paper determines the behavior of these invariants under the Gysin boundary map, when a quadric bundle degenerates over a divisor.
		The above equalities are used only in the explicit computations of the Gysin boundary images of the quadric invariants (see Section 8).
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0008104 (402 words)

	Commercial Interiors (Site not responding. Last check: 2007-11-06)
		We consider the fit-out of the interiors is paramount to your success (and ours).
		At Quadric we have the capacity, experience and manpower to meet the market's conditions, completing contracted work within budget, and with feasible programming to ensure a precise and quality fit-out.
		of multi-level buildings, to the minor refurbishment of a reception area, quality custom joinery, or service and maintenance to the workplace - Quadric is the specialist in the industry.
	www.quadricptyltd.com.au (134 words)

	Quadric - Building the Environment (Site not responding. Last check: 2007-11-06)
		Aerial photographs of the £16m hotel at the East Sussex National Golf Course during week 43 of this 78 week contract.
		Quadric Awarded the prestigious ISO9001:2000 by Lloyds Register for our quality control and management systems.
		West Quay Phase 2, Newhaven, £13m New build scheme to construct 105 apartments and a retail shopping area in four blocks surrounding the marina.
	www.quadric.co.uk (160 words)

	Quadric - DmWiki
		n : a curve or surface whose equation (in Cartesian coordinates) is of the second degree [syn: quadric surface]
		Spheres, spheroids, ellipsoids, paraboloids, hyperboloids, also cones and cylinders with circular bases, are quadrics.
		This page was last modified 05:01, 1 Nov 2005.
	www.devmaster.net /wiki/Quadric (73 words)

	Diamond Theory References (Site not responding. Last check: 2007-11-06)
		Part I gives a survey of finite fields and an outline of the fundamental properties of projective spaces and their automorphisms; it includes the properties of algebraic varieties and curves used throughout the book and in the companion volumes.
		Part II covers, in an arbitrary dimension, the properties of subspaces, of partitions into both subspaces and subgeometries, and of quadrics and Hermitian varieties, as well as polarities.
		Part III is a detailed account of the line and plane; with little reference to the generalities from Parts I and II, the author revisits fundamental properties of the plane and then describes the structure of arcs and their relation to curves.
	www.m759.freeservers.com /refs.html (4893 words)

	Algebraic Surfaces
		One for quadric, cubic and quartic surfaces which are commonly used.
		To specify a quadric surface, use quadric {}:
		where these ten values are coefficients of a quadric polynomial as follows:
	www.cs.mtu.edu /~shene/COURSES/cs3621/LAB/povray/alg-surface.html (470 words)

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