曲面

NURBS has become a representation standard for geometric design systems since 1990.However, it is difficult to model complicated objects with only one NURBS surface patch due to its rectangular domain, and it still suffers from serious limitations in surface stitching.

九十年代以来，NURBS曲线曲面已经成为计算机辅助设计系统的表示标准，由于NURBS曲面定义在矩形域上，难以直接用一张NURBS曲面来整体表示复杂曲面，需要采用分片构造的方法才能达到目的，使得拼接边界处的光滑性也受到了严重限制。

Chapter 2 establishes a helicoid model of the 3D curved shock surface, which is a fundamental means for investigating the sweep of the 3D shock surface In chapter 3, the first step is to make definitions and detail concepts about various viewpoints of shock surface sweep. Secondly, those sweep angles of the 3D shock are calculated. After that, with the aid of the helicoid model, two general structure similarity variables are derived which are independent of any model, and their importance in shock structure investigations is discussed.

第三章首先给出激波曲面掠的各种基本概念，计算相应掠角；又借助螺面模型得到一般性的掠相似参数，并分析了它在激波结构研究中的意义，设想了激波气动掠参数的测量方法；第四章依据螺面模型探讨了前缘曲线掠与前缘激波曲面掠的关系，可能存在的均匀激波曲面、简单非均匀激波曲面和它们的运动学设计方法，其中得到一些很有用的概念。

We present two novel schemes of the interpolatory volumetric subdivision over the hexahedron lattice.

我们基于多元B形式曲面及B网表示的方法，通过对L及W曲线性质的讨论，证明了三变量的B样条曲面是多元B形式中的曲面，并进一步证明和讨论了多元B形式中的有理W曲面及其相关性质。

In the fourth section, we stress on the study of the finite type rotation hypersurfaces, and obtain the classification of two and three dimensional spherical and hyperbolic rotation surfaces of finite type. It is proved that the parabolic rotation hypersurfaces are minimal or maximal.

第四节着重对有限型旋转超曲面进行了研究，得到二维和三维球型、双曲型有限型旋转曲面的分类结果，证明了有限型抛物型旋转超曲面是极小或极大超曲面。

The hypersurface expression and the way of hypersurface obtained by support vector machine are given. The method is applied to the support of Air Force air materiel, and the result shows that more simple decision rules can be obtained.

文中提出了一种超曲面的离散化方法，给出了超曲面的表示方法，提出了基于支持向量机的超曲面寻优，并将这种方法应用于空军器材保障中，仿真结果表明，提出的超曲面方法可以获得更为简捷的决策规则。

Some properties of inversions are proved, It indicates that the inversion is conformal, the image of line of curvature is still the line of curvature of the inversion S of the hypersurface S, the principal curvature, the total curvature, and mean curvature of S are the functions...

在n-1维超曲面的反图变换中，示明反图变换为保角表示法，曲率线系的反影仍为反超曲面的曲率线系，反超曲面的主曲率，全曲率与平均曲率为原超曲面的主曲率的函数等。 3。最后导出公式(1)在四维空间与通常空间之特殊形式

The analytic expression for such kind of hypersurfaces is given. Consequently, any umbilical Lorentzian isoparametric hypersurfaces of type Ⅱ with minimal polynomial^2 of A are the parallel hypersurface of M.

并且形算子A的最小多项式为(λ0a)^2的任何Ⅱ型全脐洛伦兹等参超曲面局部地与上述超曲面的平行超曲面叠合，从而完成了S(上标 n+1 下标 1)中的Ⅱ型全脐洛伦兹等参超曲面的分类。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

We proved that the minimal surfaces were isothermal parameter surfaces and harmonic surfaces. The symmetry and the self-intersection properties of the minimal surfaces were studied.

证明了该曲面既为等温参数曲面又为调和曲面，并研究了该曲面的对称性质与自交性质。

In this paper, an iterative approach to potential field continuation from curved surface to plane is proposed. The continuation of potential field data from a curved surface to a plane can be viewed as an inverse problem of upward continuation of plane potential field data, getting a linear integral equation. Through viewing the potential field data on the curved surface as the data on the average elevation plane of the curved surface, then using the wavenumber domain generalized inverse algorithm to downward continue the data from the average elevation plane to a given plane, and a topography correction based on the change of curved surface relative to its average elevation is implemented to the downward continued data on the given plane, finally the downward continued data plane is upward continued to the curved surface.

本文提出一种位场数据曲化平的迭代方法，即通过把位场数据曲化平视为平面位场数据向上延拓的反问题，得到曲化平的线性积分方程，再把曲面上位场数据视为曲面平均高程面上的位场数据，利用向下延拓的波数域广义逆算法把平均高程面上的位场数据向下延拓到设定平面上，再根据曲面和其平均高程面的相对起伏对设定平面上的向下延拓数据进行起伏校正，最后再把所得平面上的位场数据向上延拓得到曲面上的位场数据，并进行迭代。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。