曲面

In this paper,the B-spline curve is supposed as boundary curves,when they are in two paralled plane and two arbitrary plane,the condition about the control vertex of characteristic polygon when the ruled surface is developable are gained,solved the designing problem of degree and degree B-spline curve .Throughing (2,3) degree and (2,2) degree B-spline ,we haveproved the validity and utility of this method.

本文用两条B样条曲线作边界曲线，当它们位于两平行平面上和两任意平面上时，研究得到了由它们形成的直纹面为可展面时它们的特征多边形顶点满足的条件，解决了(n，n+1)次和次可展B样条曲面的设计问题，然后以(2，3)次和(2，2)次B样条曲面为构造实例，证明了该算法的正确性和实用性。

A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point.

仿真结果表明，该算法具有良好的收敛性、鲁棒性以及精确性。正交投影的概念最早出现在文献[1]中。所谓正交，就是在曲面上找到一点，使得该点与空间某一给定点的连线与曲面在该点处的切平面是垂直的。

In order to model complex hair styles, such as curly hairs and wavy hairs, we first construct five types of surfaces and three curves: curved cylinder, curved circular frustum, curved prism, curved edged frustum, curved revolving paraboloid, and curved cylinder helix, curved circular frustum helix and curved revolving paraboloid helix. Then we give the expressions for points and normal vectors on these surfaces, suitable to composition.

为了构造复杂发型，例如卷发发型和波浪发型，我们首先构造了五种曲面和三种曲线：弯曲圆柱面、弯曲圆台面、弯曲棱柱面、弯曲棱台面和弯曲旋转抛物面，以及弯曲圆柱螺线、弯曲圆台螺线和弯曲旋转抛物螺线，并且给出了这些曲线曲面上适合于拼接的点和向量的表示方式。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

It gives a relationship between a surface integral over an oriented surface and a line integral along a simple closed curve .

它建立了有向曲面上的曲面积分与它的边界曲线积分的关系。

In this thesis,we proposed the parametrization methods of closed surfaces for surface fitting.

本文针对曲面拟合，给出了封闭三角网格曲面的参数化方法。

And the G〓 interpolated closed surface are obtained which are pieced by triangular Bezier patches with ovder 4K+1 in most case.

因而克服了以往方法中的不足之处，使得生成的闭曲面具有所用的曲面片个数少，表示式简单统一的优点。

We shall first apply the technique ofμ-bases and local cohomology to study the minimal generators for the moving surface ideals of rational cubic space curves and rational quartic space curves,and then study the implicit equations of rational space curves under different definitions of implicit equations.

在第五章中，我们将同调代数理论与μ基理论相结合，详细分析三次及四次空间有理曲线的动曲面理想生成元，为一般空间有理曲线的动曲面理想生成元的(来源：A21B12ceC论文网www.abclunwen.com)研究开辟可能的道路。

Its main function include "arbitrary transversal analysis","complanation of the dragonfly"s wing","second curving surface fif " and "third curving surface fit.

其主要功能包括蜻蜓翅膀任意截面数据分析，蜻蜓翅膀高度数据的平面拟合、二次曲面拟合和三次曲面拟合。

For example, one of our conclusions is that a nonsingular QSIC has one affinely finite component if and only if the characteristic equation of the two quadrics has two distinct real roots and a pair of complex conjugate roots.

由于两二次曲面的特征方程实根个数及其重数可用精确的计算方法得到，本文分类结果可用于实现对任意两二次曲面的非平面交线拓扑形态的判断。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。