共查询到20条相似文献,搜索用时 62 毫秒
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Hyeong In Choi Sung Woo Choi Chang Yong Han Tae-wan Kim Song-Hwa Kwon Hwan Pyo Moon Kyeong Hah Roh Nam-Sook Wee 《Advances in Computational Mathematics》2008,28(2):171-199
We present a mathematical theory of the two-dimensional offset curves from the viewpoint of medial axis transform. We explore
the local geometry of the offset curve in relation with the medial axis transform, culminating in the classification of points
on the offset curve. We then study the domain decomposition from the viewpoint of offsets, and in particular introduce the
concept of monotonic fundamental domain as a device for detecting the correct topology of offsets as well as for stable numerical
computation. The monotonic fundamental domains are joined by peaks or valleys of the medial axis transform, or by what we
call the critical horizonal section whose algebro-geometric properties are rigorously treated as well.
First author holds joint appointment in the Research Institute of Mathematics, Seoul National University. 相似文献
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Shiffman proved his famous first theorem, that if A R3 is a compact minimal annulus bounded by two convex Jordan curves in parallel (say horizontal) planes, then A is foliated by strictly convex horizontal Jordan curves. In this article we use Perron's method to construct minimal annuli which have a planar end and are bounded by two convex Jordan curves in horizontal planes, but the horizontal level sets of the surfaces are not all convex Jordan curves or straight lines. These surfaces show that unlike his second and third theorems, Shiffman's first theorem is not generalizable without further qualification. 相似文献
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Yufeng Tian & Maodong Pan 《计算数学(英文版)》2020,38(5):732-747
As a corner-cutting subdivision scheme, Lane-Riesefeld algorithm possesses the concise
and unified form for generating uniform B-spline curves: vertex splitting plus repeated
midpoint averaging. In this paper, we modify the second midpoint averaging step of the
Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner
cutting, and generalize the strategy to arbitrary topological surfaces of general degree.
By adjusting the free parameter, the proposed method can generate subdivision surfaces
with flexible shapes. Experimental results demonstrate that our algorithm can produce
subdivision surfaces with comparable or even better quality than the other state-of-the-art
approaches by carefully choosing the free parameters. 相似文献
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Peter Røgen 《Annals of Global Analysis and Geometry》2001,19(4):377-407
This paper deals with the problem `which knots or links in3-space bound flat (immersed) compact surfaces?' In aforthcoming paper by the author, it is proven that any simple closedspace curve can be deformed until it bounds a flat orientable compact(Seifert) surface. The main results of this paper are that there existknots that do not bound any flat compact surfaces. The lower bound oftotal curvature of a knot bounding an orientable nonnegatively curvedcompact surface can, for varying knot types, be arbitrarily much greaterthan the infimum of curvature needed for the knot to have its knot type.The number of 3-singular points (points of zero curvatureor if not then of zero torsion) on the boundary of a flat immersedcompact surface is greater than or equal to twice the absolute value ofthe Euler characteristic of the surface. A set of necessary and, in aweakened sense, sufficient conditions for a knot or link to be what wecall a generic boundary of a flat immersed compact surface withoutplanar regions is given. 相似文献
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Jonas Baltes 《Mathematische Nachrichten》2023,296(7):2701-2714
We show that on every elliptic K3 surface there are rational curves such that , that is, of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to is dense in the Zariski topology. As an application, we give a simple proof of a theorem of Kobayashi in the elliptic case, that is, there are no globally defined symmetric differential forms. 相似文献
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Ha Huy Khoai 《Proceedings of the American Mathematical Society》1997,125(12):3527-3532
We show a class of perturbations of the Fermat hypersurface such that any holomorphic curve from into is degenerate. Applying this result, we give explicit examples of hyperbolic surfaces in of arbitrary degree , and of curves of arbitrary degree in with hyperbolic complements.
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Michela Artebani 《Transactions of the American Mathematical Society》2008,360(3):1581-1599
S. Kondo used periods of surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational ``splitting curves'.
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《Applied Mathematical Modelling》2014,38(9-10):2398-2413
Generating parallel curves on parametric surfaces is an important issue in many industrial settings. Given an initial curve (called the base curve or generator) on a parametric surface, the goal is to obtain curves on the surface that are parallel to the generator. By parallel curves we mean curves that are at a given distance from the generator, where distance is measured point-wise along certain characteristic curves (on the surface) orthogonal to the generator. Except for a few particular cases, computing these parallel curves is a very difficult and challenging problem. In fact, only partial, incomplete solutions have been reported so far in the literature. In this paper we introduce a simple yet efficient method to fill this gap. In clear contrast with other existing techniques, the most important feature of our method is its generality: it can be successfully applied to any differentiable parametric surface and to any kind of characteristic curves on surfaces. To evaluate our proposal, some illustrative examples (not addressed with previous methods) for the cases of section, vector-field, and geodesic parallels are discussed. Our experimental results show the excellent performance of the method even for the complex case of NURBS surfaces. 相似文献
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Andrea Del Centina 《Annali dell'Universita di Ferrara》2008,54(1):37-59
In this note we give a historical account of the origin and the development of the concept of Weierstrass point. We also explain
how Weierstrass points have contributed to the study of compact Riemann surfaces and algebraic curves in the century from
Weierstrass’ statement of the gap theorem to the 1970s. In particular, we focus on the seminal work of Hürwitz that raised
questions which are at the center of contemporary research on this topic.
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Garikai Campbell. 《Mathematics of Computation》2004,73(248):2093-2108
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Approximate merging of B-spline curves and surfaces 总被引:1,自引:0,他引:1
Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm. 相似文献
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Ciro Ciliberto Thomas Dedieu Concettina Galati Andreas Leopold Knutsen 《Mathematische Nachrichten》2023,296(2):574-587
We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces. 相似文献
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Flaminio Flamini Andreas Leopold Knutsen Gianluca Pacienza Edoardo Sernesi 《代数通讯》2013,41(11):3955-3971
We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a δ-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p ? 2, for 2 ≤ g = p ? δ < p ≤ 11. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves ? g that associates to X the isomorphism class [C] of its normalization. 相似文献
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This article describes a practical procedure to compute, for any Fuchsian group of genus 2 acting on the unit disc, a uniformizing
function for the corresponding algebraic curve. 相似文献
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E. B. Kuznetsov 《Computational Mathematics and Mathematical Physics》2008,48(12):2162-2171
The numerical solution to a system of nonlinear algebraic or transcendental equations with several parameters is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are proved for choosing the best parameters, which provide the best condition number for the system of linear continuation equations. Such parameters have to be sought in the subspace tangent to the solution space of the system of nonlinear equations. This subspace is obtained if the original system of nonlinear equations is solved at the various parameter values from a given set. The parametric approximation of curves and surfaces is considered. 相似文献
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We study locally Cohen-Macaulay space curves lying on normal surfaces. We prove some theorems on the behaviour of the cohomology functions and initial ideals of such space curves, which give a basic distinction between those curves and curves lying on non-normal surfaces.