Quadratic surfaces pdf

    • [PDF File]APPLICATIONS OF QUADRIC SURFACES

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      APPLICATIONS OF QUADRIC SURFACES Examples of quadric surfaces can be found in the world around us. In fact, the world itself is a good example. Although the earth is commonly modeled as a sphere, a more accurate model is an ellipsoid because the earth’s rotation has caused a flattening at the poles. (See Exercise 47.)

    • [PDF File]11.5: Quadric surfaces

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      Quadric surfaces can be classi ed into 5 categories: ellipsoids, hyperboloids, cones, paraboloids, quadric cylinders. (shown in the table, see Appendix.) The elements which characterize each of these categories: 1. Standard equation. 2. Traces (horizontal ( by planes z = k), yz-traces (by x = 0) and xz-traces (by y = 0). 3. Intercepts (in some ...

    • [PDF File]Quadric Surfaces - Purdue University

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      surfaces in standard form. All surfaces are symmetric with respect to the -axis. If a quadric surface is symmetric about a different axis, its equation changes accordingly. k z xz yz x2 4! z2 4! 1 y! 0 and y2! z2 4! 1 x! 0 x! k y! k FIGURE 9 (2, 0, 0) (0, 1, 0) x y z Surface Equation Surface Equation Ellipsoid Cone Elliptic Paraboloid ...

    • [PDF File]B-Spline and Subdivision Surfaces - Stanford University

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      • B‐Spline surfaces – NURBS surfaces • Subdivision surfaces – Theory – Zoo • Recent trends – Non linearsubdivision 2 Non linear subdivision – T‐Splines Images from: 3drender.com , sunflow.sourceforge.net , www.tsplines.com

    • [PDF File]Section 12.6: Cylinders and Quadric Surfaces

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      Quadric Surfaces: A quadric surface is the graph of a second-degree equation in three variables. They are characterized by the curves of intersection of the surface with planes of the form x = k, y = k, and z = k. These curves are called traces (or cross-sections) of the surface. Ellipsoid: The quadric surface de ned by x 2 a 2 + y b + z2 c = 1

    • [PDF File]Quadric Surfaces - Clemson University

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      Quadric Surfaces The quadrics are all surfaces that can be expressed as a second degree polynomial in x, yand z. They include important principle shapes such as those shown in Figure 13.1. The general implicit form for a 3D quadric surface can be written in homoge-neous x;y;z;wcoordinates as: ax2 +2bxy+2cxz+2dxw+ey2 +2fyz+2gyw+hz2 +2izw+jw2 = 0 ...

    • [PDF File]Quadric Surfaces - University of Washington

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      Quadric surfaces are the surfaces whose equations can be, through a series of rotations and translations, put into quadratic polynomial equations of the form ± xα a2 ± yβ b2 ± zγ c2 = k (1) which are quadratic in at least two variables. That is, α, β and γ are all either 1 or 2, and at least two are equal to 2.

    • [PDF File]3.6 Cylinders and Quadric Surfaces

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      3.6 Cylinders and Quadric Surfaces ⇤ I know the definition of a cylinder. ⇤ I can name the 6 quadric surfaces, write their equation, and sketch their graph. Objectives Let’s take stock in the types of equations we’re familiar with: • Aspherecenteredat(a,b,c)withradiusr (xa) 2+(y b)2 +(z c) = r2 • Alinethroughthepoint(p 1,p 2,p

    • [PDF File]LEAST SQUARES FITTING OF QUADRATIC CURVES AND SURFACES

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      LEAST SQUARES FITTING OF QUADRATIC CURVES AND SURFACES N. Chernov and H. Ma⁄ University of Alabama at Birmingham Birmingham, AL 35294, USA Key Words: Least squares, orthogonal regression, fitting ellipses, conics, quadrics. AMS Subject Classification: 62J. Abstract In computer vision one often fits ellipses and other conics to observed ...

    • [PDF File]Calculus III Lecture 6: Cylinders and quadric surfaces

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      CYLINDERS Definition: A cylinder is a surface that consists of all lines that are parallel to a given line and pass through a given plane curve. Example: The surface of equation z = x2 I y does not enter in the equation !let’s look at the trace of the surface z = x2 on the plane y = k I For a given y = k, a point P(x,y,z) belongs to the surface if z = x2. ...

    • [PDF File]A Quadratic surfaces - City, University of London

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      A.2 Ellipsoids Ellipsoids are quadratic surfaces parameterized by the equation x2 a2 y2 b2 z2 c2 = 1: (A.5) You can see that for a = b = c = 1 we recover the equation of a sphere centered at the origin. Therefore an ellipsoid is a \deformation" of the sphere such that the

    • [PDF File]Cylinders and quadratic surfaces (Sect. 12.6) Cylinders

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      Quadratic surfaces Definition Given constants a i, b i and c 1, with i = 1,2,3, a quadratic surface in space is the set of points (x,y,z) solutions of the equation a 1 x 2 + a 2 y 2 + a 3 z 2 + b 1 x + b 2 y + b 3 z + c 1 = 0. Remarks: I There are several types of quadratic surfaces. I We study only quadratic surfaces given by a 1 x 2 + a 2 y ...

    • [PDF File]12.6 Cylinders and Quadric Surfaces

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      Applications of Quadric Surfaces Examples of quadric surfaces can be found in the world around us. In fact, the world itself is a good example. Although the earth is commonly modeled as a sphere, a more accurate model is an ellipsoid because the earth’s rotation has caused a flattening at the poles.

    • [PDF File]Section 12.2: Quadric Surfaces

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      Section 12.2: Quadric Surfaces Goals : 1. To recognize and write equations of quadric surfaces 2. To graph quadric surfaces by hand Definitions: 1. A quadric surface is the three-dimensional graph of an equation that can (through appropriate transformations, if necessary), be written in either of the following forms:

    • [PDF File]Chapter 3 Quadratic curves, quadric surfaces

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      Chapter 3 Quadratic curves, quadric surfaces Inthischapterwebeginourstudyofcurvedsurfaces.Wefocusonthequadricsurfaces. Todothis,wealsoneedtolookatquadraticcurves ...

    • [PDF File]Exploring Quadric Surfaces with Maple

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      quadric surfaces. Unfortunately, few discuss each of the basic issues of interest to us. This paper was motivated by the desire to develop a single Maple 11 worksheet to analyze general quadric surfaces in an automatic fashion. Most of the issues discussed may be found (in one form or another) in other references.

    • [PDF File]Quadric Surfaces - UCM

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      Quadric Surfaces Example: For the elliptic paraboloid z = 4x2 + y2 : xy trace - set z = 0 →0 = 4x2 + y2 This is point (0,0) yz trace - set x = 0 →z = y2 Parabola in yz plane. xz trace - set y = 0 →y = 4x2 Parabola in xz plane. Trace z = 4 parallel to xy plane: Set z = 4 →4 = 4x2 + y2 or x2 + y2 /4 =1. This is an ellipse parallel to the ...

    • [PDF File]Math 213 - Quadric Surfaces

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      Quadratic Curves Cylinders Quadric Surfaces Summary Quadric Surfaces A quadric surface is the graph of a second-degree equation in x, y, and z taking one of the standard forms Ax2 +By2 +Cz2 J = 0, Ax2 + By2 + Iz = 0 We can graph a quadric surface by studying its traces in planes parallel to the x, y, and

    • [PDF File]HOW TO UNDERSTAND QUADRIC SURFACES De nition 1.

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      2 HOW TO UNDERSTAND QUADRIC SURFACES looks like this: z = x a 2 y b 2; where \+" yields an elliptic paraboloid and \-" yields a hyperbolic paraboloid. Probably the most di cult class is the hyperboloids, which come in three varieties: the hyperboloid of one sheet, the hyperboloid of two sheets, and the cone. For all three the

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