系统将从曲面边界衍生所有其它刀具向量。
The system will derive all other tool vectors from the surface boundary.
研究曲面边界建模过程中的曲面求交问题。
This paper focuses on the surface-surface intersection problem in surface border modeling.
介绍离散形式下的曲面边界检测问题及研究进展。
In this chapter the problem and recent developments about boundary detection for surfaces in discrete forms is summarized.
充分利用曲面边界信息查找两曲面公共边界上的网格；
The surface boundary information was used to seek surface mesh on the common boundary;
相切是由曲面边界的最初两个控制点控制的（假设这些点在一条线上）。
Tangency is controlled by the first two control points from a surface boundary, assuming that these points lie in one line.
另外，对路径偏移中出现的缝隙给出了填补方法，并使偏移后的路径轨迹延伸至曲面边界。
Furthermore, a method is presented to fill the gaps between paths and extend the endpoints of path trajectory to the surface boundary.
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.
该算法将边缘检测应用于区域生长规则中，充分发挥了边缘方法和区域生长方法两者的优点，实现了三维曲面边界的精确定位。
In this way, this proposed algorithm takes merits of the combination of edge detection and region growth to realize the accurate boundary location of 3d curved surface.
利用三维边界拟合坐标变换技术，可将具有任意曲面边界的三维物理区域变成长方体计算区域，在该区域中形成单位立方体差分网格。
By means of BFCT, a three-dimensional physical space with arbitrary configuration can be transformed into standard cube, forming the unit cubic grid.
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.
如果存在一些区域空间,边界为曲面,定义n为指向区域R外的法向量。
So if you have some region of space S and you call its boundary surface S and you let n be the normal vector that goes out of the region R.
定理说，What，Stokes’，theorem，says，is，that,可以选择最喜欢的曲面，只要边界是这个圆就可以了。
Stokes I can choose my favorite surface whose boundary is this circle.
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.
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.
研究了模型边界处理方法及复杂曲面局部特征设计方法。
A design methodology dealing with boundary and local features on the surface model is researched mainly.
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.
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.
第二章：离散曲面的边界检测。
针对空间网格曲面，提出空间三角网格曲面的边界提取方法。
As for space mesh surface, the method of getting the contour from space mesh surface is achieved.
提出了二重八面体变几何桁架机器人工作空间的边界曲面分析方法。
Boundary surface analysis method for workspace of double-octahedron variable geometry truss robotic manipulators(VGTRM) is proposed in this paper.
并根据各种曲面的特点，进行边界环处理。
Finally, it deals with the boundary loop according to the characteristic of all surfaces.
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.
本文在总结曲面重建主流算法的基础上，对点云的边界检测问题进行了研究，提出了一种基于空间正规分割的边界检测新算法。
In this thesis we summarize the main approaches for surface reconstruction, study the problem of boundary detection for point clouds, and propose a new algorithm based on regular space subdivision.
摈弃了目前国际上通常采用的周期边界条件，以及以平板代替曲面的做法。
The common calculating methods, i. e. using periodic boundary condition and curved surface replaced by flat plane, were discarded.
实践表明，该算法既能准确提取边界形状的特征关键点，又保证了重构后曲面的光滑规整。
It is proved this algorithm can not only extract the key points which can represent border shape, but also guarantee the reconstructed model have smooth surfaces.
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.
数学上，最小曲面指的是（在给定边界条件下的）面积最小曲面。
Mathematic minimal surface is a surface of minimal area under prescribed boundary condition.
本文计算了沿不同曲面流动的湍流边界层。
Turbulent boundary layers along two surface of curvature were investigated with computation.
本文计算了沿不同曲面流动的湍流边界层。
Turbulent boundary layers along two surface of curvature were investigated with computation.
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