在逆向工程中，复杂外形产品的曲面边界曲线的品质，是影响产品外观设计质量的关键因素。
In reverse engineering, the character of surface border curve in complex contoured product is the key factor affecting the outlook designing quality of product.
基本上，这两个公式把沿曲线的功，和被曲线包围的曲面上的旋度，联系起来了，曲面是以该曲线为边界的。
Both of these formulas basically relate work on a curve with what happens to the curl on the surface that is enclosed by this curve, that is bounded by this curve.
也可以是，自己去选择，有可能的、最简单的，以该曲线为边界的曲面。
It might be that you will be left to choose the simplest possible surface you can think of that is somehow having this curve as its boundary.
对于任意完全包含在圆环面上的曲面，这个曲线都不是它的边界。
See, this one also does not bound anything that's completely contained in the torus.
其次，在曲面片内部，曲面拟合点和边界方向导数可以从参考曲线中通过构建虚拟等参线的方法得到。
Next, in the interior of the patches, surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing virtual iso-parametric curves.
在三角形域上构造对边界曲线和跨界导数插值的三角曲面是计算机辅助几何设计和计算机图形学等领域中的基本问题。
Constructing triangle surface which interpolates the boundary curve and cross-boundary slopes on a triangle is the basic problem in computer aided geometric design, computer graphics and so on.
如果完全封闭它，那么这条曲线就不再是它的边界，因为曲面在这条曲线的两边都存在。
If I close it completely, then this curve is no longer its boundary because my surface lives on both sides of this curve.
对于三维工作空间，在按层划分得到每一层的边界曲线的基础上，采用包络原理得到空间曲面的形状和体积表达式。
The boundary surface and volume expression of 3-D workspace is addressed byenveloping boundary curves of each plane which are obtained by partitioning 3-Dspace into layers.
利用曲面网格的边界曲线直接定义3D曲面，既能保证曲面的光滑过渡，即C1连续，又可避免通过确定扭矢来达到控制曲面的复杂计算。
The 3D surface can be defined directly by the boundary curve of the patch surface. The surface will be C1 continuous if the boundary curves connecting each two patches are C1 continuous.
初始曲面拟合是利用UG的二次开发功能，将截面线与边界曲线拟合成一张初始曲面。
Original surface is formed from boundary curve and section curve using the redevelopement interface of UG.
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。
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。
It gives a relationship between a surface integral over an oriented surface and a line integral along a simple closed curve.
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