曲面

Finally, the complex surfaces are developed by partition of the surfaces into small surface segment ,and approximation of the small segment with the developable surface between two Bezier curves.

最后，采用分片与近似的思想，给出了复杂曲面展开的算法，并提出由曲面面积和曲面展开面积的相对误差调节分片程度来满足精度要求。

Based on the important idea of duality between plane and point geometries,two direct explicit methods of computer-aided design for developable surface s were proposed,the developable surface s were represented using control planes with appropriate basis functions.

为了克服传统方法在可展曲面设计上的缺陷，方便地解决工程中经常遇到的可展曲面位置和形状难以调整和控制的问题，基于3D射影空间中点和平面间的对偶性这一重要思想，提出了两种直接、简单的可展曲面设计方法。

First, we extend the general finite element method from the function surface to the parameter function. Second, we bring this kind of method into the design of rational Bézier minimal surface. Third, we transform the problem of Dirichlet energy function into the problem of minimizing a discrete objective function.

首先推广了函数曲面中的有限元方法，进而研究如何针对参数曲面使用有限元方法，并把该方法引入到有理Bézier极小曲面造型的设计中，从而将连续的Dirichlet能量函数极小化问题，转化为一个离散形式的目标函数的极小化问题。

This paper de-duces the equation of scroll case surface with the enveloping theory,builds the envelope sur-face of ellipsoides with variable radius by using the the method of constructing an ellipse withseveral arcs and presents a new and simple method fOr geometry moulding of scroll case sur-face.

蜗壳是水电站的重要部件之一，本文以包络理论推导了蜗壳曲面方程；并采用分段圆弧构造椭圆的方法构造了变径椭球包络曲面，为蜗壳曲面的几何造型提出了一种新的简便方法。

And then, in this part, following the idea of Topping [51, 52], we will show an isoperimetric inequality (6.3.1) on surfaces of non-positive Gaussian curvature by means of the curve shortening flow on surfaces, this inequality can be considered as a generalization of the Banchoff-Pohl inequality in the Euclidean plane.

然后，仿照Topping[51]和[52]利用平均曲率流证明等周不等式的想法，我们利用曲面上的曲线缩短流在Gauss曲率非正的曲面上证明了一个等周不等式(6.3.1)，它可以看成欧氏平面上Banchoff-Pohl [8]不等式在曲面上的推广。

A curve or surface that is tangent to every one of a family of curves or surfaces.

包络线，包络面一条曲线或一个曲面，与一组曲线或曲面中的每一曲线或曲面保持正切

Mathematics A curve or surface that is tangent to every one of a family of curves or surfaces.

包络线，包络面：一条曲线或一个曲面，与一组曲线或曲面中的每一曲线或曲面保持正切

This limit is called the surface integral with respect to area (or the surface integral of the first type) of over and is denoted by

如果时，黎曼和的极限存在，则称此极限为在曲面上对面积的曲面积分或第一类曲面积分，记作

We prove that the two families of torsal surfaces of $T$ touch the second focal surface $S_2$ along the net of orthogonal parametric curves if and only if $S_1$ is developable.

证明了$T$的两个可展曲面族沿着第二个焦曲面$S_2$的正交曲线网相交的充要条件是$S_1$是可展曲面。

Through studying some fundamental properties of the curved surface in differential geometry , a method of linear feature extraction based on differential geometry is introduced.

通过研究微分几何理论中曲面的一些基本性质，本文介绍了一种基于微分几何的线状地物提取方法，首先在局部区域内拟合一个二次曲面函数，然后通过该函数来估算灰度曲面的梯度和曲率，设定合适的梯度和曲率阈值来检测线状地物，最后进行后处理，消除许多噪声颗粒及小块区域。

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％。