共查询到20条相似文献,搜索用时 31 毫秒
1.
Zane Kun Li 《Journal of Pure and Applied Algebra》2010,214(11):2078-2086
The intersection curve between two surfaces in three-dimensional real projective space RP3 is important in the study of computer graphics and solid modelling. However, much of the past work has been directed towards the intersection of two quadric surfaces. In this paper we study the intersection curve between a quadric and a cubic surface and its projection onto the plane at infinity. Formulas for the plane and space curves are given for the intersection of a quadric and a cubic surface. A family of cubic surfaces that give the same space curve when we intersect them with a quadric surface is found. By generalizing the methods in Wang et al. (2002) [6] that are used to parametrize the space curve between two quadric surfaces, we give a parametrization for the intersection curve between a quadric and a cubic surface when the intersection has a singularity of order 3. 相似文献
2.
Tor Dokken 《PAMM》2007,7(1):1022203-1022204
Most published work on intersection algorithms for Computer Aided Design (CAD) systems addresses transversal intersections [1], situations where the surface normals of the surfaces intersected are well separated along all intersection curves. For transversal intersections the divide and conquer strategy of recursive subdivision, Sinha's theorem [2] and the convex hull property of NonUniform Rational B-Spline surfaces (NURBS) efficiently identify all intersection branches. However, in singular or near singular intersections, situations where the surfaces are parallel or near parallel in an intersection region, along an intersection curve or in an intersection point, even deep levels of subdivision will frequently not sort out the intersection topology. The paper will focus on the novel approach of Approximate Implicitization to address these challenges. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
We present the construction of a kind of convex core for the product of two actions of a group on R-trees. This geometric construction allows one to generalize and unify the intersection number of two curves or of two measured foliations on a surface, Scott's intersection number of two splittings, and the appearance of surfaces in Fujiwara-Papasoglu's construction of the JSJ splitting. In particular, this construction allows a topological interpretation of the intersection number analogous to the definition for curves in surfaces. As an application of this construction, we prove that an irreducible automorphism of the free group whose stable and unstable trees are geometric, is actually induced by a pseudo-Anosov homeomorphism of a surface. 相似文献
4.
Alan P. Wang 《Applied mathematics and computation》1975,1(3):263-277
A technique is developed here to estimate an unknown curve joining two points in a three dimensional Euclidean space. A special application presented here is a computer procedure to determine the intersection of two arbitrary given smooth surfaces. The method used is to assume that y is a function of x and the set (x,y(x)) lies on the projection of the intersection of two surfaces. The function y is determined by least square curve fitting on a Latin square of experimental values. The procedure is written in APL (A Programming Language). A set of preliminary results is presented. The results indicate that this is a successful procedure for some simple surfaces, including some conic surfaces. 相似文献
5.
6.
The multivariate splines as piecewise polynomials have become useful tools for dealing with Computational Geometry, Computer Graphics, Computer Aided Geometrical Design and Image Processing. It is well known that the classical algebraic variety in algebraic geometry is to study geometrical properties of the common intersection of surfaces represented by multivariate polynomials. Recently the surfaces are mainly represented by multivariate piecewise polynomials (i.e. multivariate splines), so the piecewise algebraic variety defined as the common intersection of surfaces represented by multivariate splines is a new topic in algebraic geometry. Moreover, the piecewise algebraic variety will be also important in computational geometry, computer graphics, computer aided geometrical design and image processing. The purpose of this paper is to introduce some recent researches on multivariate spline, piecewise algebraic variety (curve), and their applications. 相似文献
7.
Johan Björklund 《Arkiv f?r Matematik》2013,51(2):251-267
We construct an invariant of parametrized generic real algebraic surfaces in ?P 3 which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using self-intersections, which are real algebraic curves with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. In Kirby and Melvin (Local surgery formulas for quantum invariants and the Arf invariant, in Proceedings of the Casson Fest, Geom. Topol. Monogr. 7, pp. 213–233, Geom. Topol. Publ., Coventry, 2004) the Brown invariant was expressed through a self-linking number of the self-intersection. We extend the definition of this self-linking number to the case of parametrized generic real algebraic surfaces. 相似文献
8.
Izuru Mori 《Journal of Pure and Applied Algebra》2007,211(1):25-41
In this paper, we will extend several results on intersection theory over commutative ruled surfaces to quantum ruled surfaces. Typically, we define the fiber of a closed point, the quasi-section, and the quasi-canonical divisor on a quantum rules surface, and study how these “curves” on a quantum ruled surface intersect with each other. 相似文献
9.
We give a Poincaré formula for any real surfaces in the complex projective plane which states that the mean value of the intersection numbers of two real surfaces is equal to the integral of some terms of their Kähler angles. 相似文献
10.
《Finite Fields and Their Applications》2007,13(4):727-737
In this paper we construct some algebraic geometric error-correcting codes on surfaces whose Néron–Severi group has low rank. If the Néron–Severi group is generated by an effective divisor, the intersection of this surface with an irreducible surface of lower degree will be an irreducible curve, and this makes possible the construction of codes with good parameters. Such surfaces are not easy to find, but we are able to find surfaces with low rank, and those will give us good codes too. 相似文献
11.
Annelies Jaspers 《Comptes Rendus Mathematique》2017,355(2):200-204
Inspired by the motivic monodromy conjecture, Halle and Nicaise defined the global monodromy property for Calabi–Yau varieties over a discretely valued field. In this note, we discuss this property for K3 surfaces allowing a strict normal crossings model where no three components in the special fiber have a common intersection. The main result is that the global monodromy property holds for a K3 surface with a so-called flowerpot degeneration. It also holds for K3 surfaces with a chain degeneration under certain conditions. 相似文献
12.
We study the connection between characteristics of moduli spaces of Riemann surfaces with marked points and matrix models. The Kontsevich matrix model describes intersection indices on continuous moduli spaces, and the Kontsevich–Penner matrix model describes intersection indices on discretized moduli spaces. Analyzing the constraint algebras satisfied by various generalized Kontsevich matrix models, we derive time transformations that establish exact relations between different models appearing in mathematical physics. We solve the Hermitian one-matrix model using the moment technique in the genus expansion and construct a recursive procedure for solving this model in the double scaling limit. 相似文献
13.
Xuan Hien Nguyen 《偏微分方程通讯》2013,38(3):257-280
In this paper, we describe the construction of new examples of self-translating surfaces under the mean curvature flow. We find the new surfaces by desingularizing the intersection of a grim reaper and a plane to obtain approximate solutions, then we solve a perturbation problem to find the exact solutions. Our work is inspired from Kapoulea' construction of minimal surfaces but differs from it by our more abstract and direct study of the linear operator, via Fredholm operators. 相似文献
14.
Christopher B. Croke 《Proceedings of the American Mathematical Society》2008,136(3):1083-1086
We show that round hemispheres are the only compact two-dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once and only once. We prove this by establishing a sharp isoperimetric inequality for surfaces with boundary such that every pair of geodesics has at most one interior intersection point.
15.
本文研究了R3中相交子流形的不变量.利用活动标架法,得出了一个类似的欧拉公式. 即两曲面交线的挠率可以用两曲面的测地挠率、法曲率及两曲面的夹角表示. 相似文献
16.
This paper presents a simple method for computing the intersection curve of a ruled surface and a free-form surface. The basic
idea is to reduce the problem of surface intersection to the one of projecting an appropriate curve such as a directrix of
the ruled surface, along its indicatrix curve (direction vector field of its generating lines), onto the free-form surface;
the projection curve is just the intersection curve. With techniques in classical differential geometry, we derive the differential
equations of the intersection curve in the cases of parametrically and implicitly defined free-form surfaces. The intersection
curve naturally inherits the parameter of the chosen directrix. Moreover, it is independent of the base surface geometry and
its parameterization, and is obtained by numerically solving the initial-value problem for a system of first-order ordinary
differential equations in the parametric domain associated to the surface representation for parametric case or in 3D space
for implicit case. Some experimental examples are also given to demonstrate that the presented method is effective and potentially
useful in computer aided design and computer graphics.
An erratum to this article can be found at 相似文献
17.
Alberto Dolcetti 《Annali dell'Universita di Ferrara》2001,47(1):231-241
In this note we classify subcanonical, Gorenstein and complete intersection smooth connected curves lying on del Pezzo surfaces,
by showing their classes in Picard groups of the surfaces.
To Mario Fiorentini 相似文献
Sunto In questa nota si classificano le curve liscie connesse, che sono sottocanoniche, Gorenstein o intersezioni complete, tracciate sulle superfici di del Pezzo, esibendone le classi nei gruppi di Picard delle superfici stesse.
To Mario Fiorentini 相似文献
18.
Ahmed Abbes 《Compositio Mathematica》2000,122(1):23-111
We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic. 相似文献
19.
We give examples of complete normal surfaces that are not embeddable into simplicial toric prevarieties nor toric prevarieties of affine intersection.
20.
Fabien Pazuki 《Comptes Rendus Mathematique》2010,348(9-10):483-486
We give in this Note some squares of Abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points. 相似文献