Surfaces, curves and mapping class groups 9
The Study of Curves and Surfaces
... of curves, surfaces, functions, and so on, in sufficiently small ...of curves, surfaces, functions, and so on, extended as far as ...studies surfaces on all their given span and ...
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Tzitzeica Curves and Surfaces »
... the class of affine- invariant curves and surfaces that bear his ...of curves and surfaces in three dimensions that is particularly suitable for discussion at relatively elementary ...
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Curves and Surfaces in Computer Graphics
... computer curves and surfaces. It enables to display curves and surfaces in three-dimensional space with perspective or orthogonal projection with capability of changing camera ...other ...
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Curves and Surfaces for Computer Graphics
... of Curves and Surfaces Section 2.4 discusses lofted surfaces but does not explain the reason for this unusual ...such surfaces became known as ...
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Generating Smooth Surfaces by Refinement of Curves
... smooth surfaces, but only proved to be 3D sets which retain important properties of the initial ...are surfaces, with H¨older continuous one side tangent, whenever the initial curves have a smooth ...
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The Cone of Curves of K3 Surfaces Revisited
... (1.1.2) NE(X) = ∑ R + where the sum runs over the classes of all smooth rational curves on X . Remark 1.2. To cover all cases one would also need to consider K3 surfaces with Picard number less than 3. ...
Statistical comparisons for nonlinear curves and surfaces
... NONLINEAR CURVES AND SURFACES Estimation of nonlinear curves and surfaces has long been the focus of semiparamet- ric and nonparametric ...of curves and ...
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1 Curves, Surfaces, Volumes and their integrals
... volume. Curves ~ r(t) are one dimen- sional objects so they have only one parameter t or each point on the known curve is determined by a single ...coordinate. Surfaces are two-dimensional and require two ...
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Flecnodal and LIE-curves of ruled surfaces
... ruled surfaces using a new point of view, which depends on H ESSE ’s correspondence ...ruled surfaces depending on its characteristic curve, which is an image of the flecnode curve under a so called ...
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Radical parametrization of algebraic curves and surfaces
... for curves that are of practical ...of surfaces It is possible to exploit the results outlined in the previous section for the case of ...narrow class of algebraic surfaces can be parametrized ...
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On Compact Affine Quaternionic Curves and Surfaces
... nionic curves and ...quaternionic curves are the quaternionic ...quaternionic surfaces, the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex sim- ...
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Canonical curves, scrolls and K3 surfaces
... canonical curves C ⊂ P g −1 as well as so-called relative canonical resolutions of canonical curves inside scrolls swept out by a pencil of divisors on C ...canonical curves we will show that all ...
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REGULAR HOMOTOPY OF CLOSED CURVES ON SURFACES
... closed curves in the plane up to regular homotopy sparked the investigation of winding numbers to classify regular closed curves on other ...closed curves on particular surfaces and used them ...
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Locally Defined Principal Curves and Surfaces
... Principal curves are defined as self-consistent smooth curves passing through the middle of the data, and they have been used in many applications of machine learning as a generalization, dimension- ality ...
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Curvature based sampling of curves and surfaces
... the class of surfaces generated by the Cartesian product of two or more ...) curves and surfaces are used to describe the shape of an ...
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Intersection Curves of Implicit and Parametric Surfaces in R3
... We present algorithms for computing the differential geometry properties of Frenet apparatus and higher-order derivatives of intersection curves of implicit and parametric surfaces in 3 for transversal and ...
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Tightening curves on surfaces via local moves
... Bound: Surfaces with Boundary In this section, we consider the case of surfaces with ...such surfaces is that the fundamental group of surface with boundary is free; intuitively on such surface one ...
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Billiards and Teichmüller curves on Hilbert modular surfaces
... algebraic curves iso- metrically embedded in the moduli space of Riemann surfaces of genus ...uller curves lie on Hilbert modular surfaces param- eterizing Abelian varieties with real ...
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Hilbert-Kunz Functions of Cubic Curves and Surfaces
... Combining these results with the calculation of the (generalized) Hilbert-Kunz func- tion of Cayley’s cubic surface, it follows that in each degree and over any field of positive characteristic there are curves ...
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BEZIER CURVES AND SURFACES
... Degree raising: any Bézier curve of degree n (with control points P i ) can be expressed in terms of a new basis of degree n+1.. and Lasser, D.: Fundamentals of CAGD, A.K.[r] ...
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