Non-conjugate osculating quadrics of a curve on a surface ...
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Non-conjugate osculating quadrics of a curve on a surface ... by Roberts Cozart Bullock

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Published in [New York .
Written in English


  • Quadrics.,
  • Curves on surfaces.

Book details:

Edition Notes

Statementby Roberts Cozart Bullock ...
LC ClassificationsQA561 .B8 1932
The Physical Object
Pagination[1], 518-531 p., 1 l.
Number of Pages531
ID Numbers
Open LibraryOL6300169M
LC Control Number34000840

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A "quadric surface" is an algebraic surface, defined by a quadratic polynomial. Non-degenerate quadrics in $\mathbb{R}^3$ (familiar 3-dimensional Euclidean space) are categorised as either ellipsoids, paraboloids, or hyperboloids. Our collection contains most of the different types of quadric, including degenerate cases. Quadric Surfaces In 3-dimensional space, we may consider quadratic equations in three variables x, y, and z: ax2 +by2 +cz2 +dxy +exz +fyz +gx +hy +iz +j = 0 Such an equation defines a surface in 3D. Quadric surfaces are the surfaces whose equations can be, through a series of rotations and translations, put into quadratic polynomial equations File Size: KB. OSCULATING BEHAVIOR OF KUMMER SURFACE IN P5 3 One defines the sth osculating (vector) space T(s) x Xto be the span of all partial derivatives of ˚of order sat (0;;0). The expected dimension of T x (s)Xis n+s s 1, but in general dimT(s) x X n+s s 1; if strict inequality holds for all smooth points of X, and dimT(s) x X= n+s s 1 for general x, then Xis said. Bézier Curves and Surface Patches on Quadrics Josef Hoschek Abstract. Bézier curves, Bézier spline curves, Bézier tensor product patches and triangular patches on quadrics (sphere, hyperboloid of one or two sheets, paraboloid) are constructed with the help of quadratic maps {.Cited by: 8.

to the classical quartic Kummer surface. In Hudson’s book, the Weddle surface is constructed as image of a Kummer quartic K by the rational map associated to the linear system of sextic curves passing through ten nodes ([H], pag –). A table states a dictionary between nodes and particular curves on the two surfaces. the shape of the surface in consideration [9, pp,91]. Two extensions are usually ignored: (a) The osculating paraboloid has a planar counterpart, the osculating parabola to a curve in R2. This fact is mentioned only in passing as an exercise [5, p] [4, p], if at all. (b) The fact that the osculating paraboloid may be used to produce con-File Size: KB.   The proposed quadratic curve and surface fitting algorithm combines direct fitting with a noise cancellation step, producing consistent estimates close to maximum likelihood but without iterations. REFERENCES [1] Andrew W. Fitzgibbon, Maurizio Pilu and Robert B. Fisher, "Direct Least Squares Fitting of Ellipses", IEEE Trans. P Reviews: Absolute Surface Area Up: Description of Three Dimensional Previous: Relative Boundary Orientation Surface Curvature. By the surface shape segmentation assumptions (Chapter 3), each surface region can be assumed to have constant curvature signs and approximately constant curvature magnitude. Using the orientation information, the average orientation change per image distance is estimated and.

If two curves passing through a point P on a surface S have the same osculating plane at P, and their common direction at P is not an asymptotic direction, they have the same curvature at P. This theorem says, in particular, that the curvature at point P of a given curve C on a surface S is equal to the curvature at P of the plane curve in. Based on Lloyd iteration, we present a variational method for extracting general quadric surfaces from a 3D mesh surface. This work extends the previous variational methods that extract only planes or special types of quadrics, i.e., spheres and circular by: It follows that the radius of the osculating circle of a surface curve is given by ρ = ρ 0 cos δ, where δ denotes the angle between the surface normal and the osculating plane and ρ 0 is the radius of Meusnier' sphere. The inverse κ 0 = 1/ρ 0 is called the normal curvature of the surface at pin direction of t.   8. Diameters and Diametral Planes of a Quadric Surface 9. Axes of Symmetry for a Curve. Planes of Symmetry for a Surface Exercises to Chapter VII Part Two. Differential Geometry Chapter VIII. Tangent and Osculating Planes of Curve 1. Concept of Curve 2. Regular Curve 3. Singular Points of a Curve 4.