共查询到19条相似文献,搜索用时 312 毫秒
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在计算机辅助几何外型设计(CAGD)中,设计对象(主要是曲线和曲面)的形状控制是确保造型设计成功的一个重要因素.这里,形状控制包括整体形状(曲线、面的总体布局)控制和局部形状(曲线、面上每点的凸性)控制两部分.一般,前者可利用造型曲线、 相似文献
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旋转曲面的有理Bernstein—Bezier表示 总被引:1,自引:0,他引:1
王国瑾 《高校应用数学学报(A辑)》1989,4(2):157-171
本文考察了较更为一般的情况,证明了旋转曲面表为有理二次、三次Bernstein-Bézier曲面的充要条件,导出了一系列适用于计算机辅助几何设计和体素造型的算法公式,最后还给出了球面有理B-B表示的三个实例。 相似文献
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1引言经典微分几何中Gauss曲率为零的曲面称为可展曲面,它是一种特殊的直纹面.可展曲面有且只有三种,即锥面、柱面和切线面,它对于自由曲面造型具有重要的意义.例如,如果物体外壳是可展曲面,那么它可以没有形变地展开到平面上,从而可以用平板材料无形变地设计出来.这一性质对于造船业、航空业中的外形设计具有重要的意义.关于可展曲面的微分几何性质,可以在任何一本微分几何教材中找到,例如[3].可展曲面可以说是微分几何中比较简单的一类曲面,但是在计算机辅助几何设计(CAGD)和计算机图形学中至今还不存在简单有效的设计方法.在[1,2,5]以及它们的参考文献中 相似文献
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NURBS曲面的形状修改的一种方法 总被引:3,自引:0,他引:3
NURBS曲面是计算机辅助几何设计和计算机图形中最常用的参数曲面。本文采用NURBS曲面的齐次坐标表示,给出了通过控制顶点和权因子同时改变来修改NURBS曲面形状的一种方法。 相似文献
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在计算机辅助几何设计中, B\''ezier曲面是一类重要的参数曲面.在微分几何中,坐标曲线网也是重要的研究内容.本文中,我们对具有特殊坐标曲线网(如正交曲线网、曲率曲线网、共轭曲线网等)的B\''ezier曲面进行研究.此外,我们还构造了满足能量约束的特殊B\''ezier曲面,给出了基于控制结构的充分条件并给出具体实例. 相似文献
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曲线几何连续性及其应用 总被引:1,自引:0,他引:1
曲线、曲面的几何连续性问题在计算几何、计算机辅助几何设计及图形学中愈来愈引起人们的注意,见.由于几何连续性是曲线、曲面的内在几何性质,它的研究标志着人们对自由曲线、曲面的研究提高到一个新的阶段.另一方面.由于几何连续性比参数连续性具有更多的自由度,因而在几何连续性基础上的曲线、曲面造型具有更大的灵活性,便于构造更复杂的曲线、曲面并对自由曲线、曲面进行设计、修改和处理.因此、几何连续性问题正在成为计算机辅助几何设计的一个重要课题. 相似文献
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Bézier曲面片光滑连接的几何条件 总被引:9,自引:0,他引:9
曲面造型是计算几何领域中一个重要的研究方向,它在汽车、造船、航空、模具等行业的外形设计和制造中有着广泛的应用,目前还在发展之中.Bézier 曲面和 B 样条曲面是当前曲面造型的两大主要方法,各有长处,互相补充.B 样条曲面具有连续性高,整体配置顶点的优点.Bézier 曲面则有装配灵活、适应性强的优点.我们将矩形域和三角域两种 Bézier 曲面片混合造型,几乎可以构造出任意形状的曲面,而这对 B 样条曲面说来则 相似文献
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Least-Squares Fitting of Algebraic Spline Surfaces 总被引:11,自引:0,他引:11
We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation. 相似文献
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Efficient Global Optimization of Expensive Black-Box Functions 总被引:41,自引:0,他引:41
Donald R. Jones Matthias Schonlau William J. Welch 《Journal of Global Optimization》1998,13(4):455-492
In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome. 相似文献
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We solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating minimal, including unstable, surfaces. In this paper we introduce the general framework and some preliminary estimates, develop the algorithm, and give the numerical results. In a subsequent paper we prove the convergence estimate. The algorithmic procedure is to find stationary points for the Dirichlet energy within the class of discrete harmonic maps from the discrete unit disc such that the boundary nodes are constrained to lie on a prescribed boundary curve. An integral normalisation condition is imposed, corresponding to the usual three point condition. Optimal convergence results are demonstrated numerically and theoretically for nondegenerate minimal surfaces, and the necessity for nondegeneracy is shown numerically.
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Robert W. Neel 《Journal of Functional Analysis》2009,256(8):2440-2472
We provide a probabilistic approach to studying minimal surfaces in R3. After a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way of coupling Brownian motions on two minimal surfaces. This coupling is then used to study two classes of results in minimal surface theory, maximum principle-type results, such as weak and strong halfspace theorems and the maximum principle at infinity, and Liouville theorems. 相似文献
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We introduce the notion of harmonic nodal maps from the stratified Riemann surfaces into any compact Riemannian manifolds
and prove that the space of the energy minimizing nodal maps is sequentially compact. We also give an existence result for
the energy minimizing nodal maps. As an application, we obtain a general existence theorem for minimal surfaces with arbitrary
genus in any compact Riemannian manifolds.
Received: 1 April 1997; revised: 15 April 1998. 相似文献
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Minimal Surfaces in the Heisenberg Group 总被引:9,自引:0,他引:9
Scott D. Pauls 《Geometriae Dedicata》2004,104(1):201-231
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot–Carathéodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces and Riemannian constant mean curvature surfaces in H equipped with different Riemannian metrics approximating the Carnot–Carathéodory metric. We generate a large library of examples of minimal surfaces and use these to show that the solution to the Dirichlet problem need not be unique. Moreover, we show that the minimal surfaces we construct are in fact X-minimal surfaces in the sense of Garofalo and Nhieu. 相似文献
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In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case. 相似文献
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An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is constructed as follows. Firstly, we elevate the degree of the approximated rational triangular Bézier surface, then a polynomial triangular Bézier surface is produced, which has the same order and new control points of the degree-elevated rational surface. The approximation method has theoretical significance and application value: it solves two shortcomings-fussy expression and uninsured convergence of the approximation-of Hybrid algorithms for rational polynomial curves and surfaces approximation. 相似文献
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Haizhong Li 《Annals of Global Analysis and Geometry》2002,21(2):203-213
A surface x>
: M S
n
is called a Willmore surface if it is a critical surface of the Willmore functional. It is well known that any minimal surface is a Willmore surface and that many nonminimal Willmore surfaces exists. In this paper, we establish an integral inequality for compact Willmore surfaces in S
n
and obtain a new characterization of the Veronese surface in S
4 as a Willmore surface. Our result reduces to a well-known result in the case of minimal surfaces. 相似文献