科研文章常用英语

句子
1.Stand on the shoulders of giants
2.School of Mechanical Science and Engineering, Huazhong University of Science and Technology Wuhan, Hubei 430074, P.R. China. Tel: 86-27-87543973, E-Mail: afxyang@etang.com
3.The proposed method has been successfully implemented using the visual C++ language and the ACIS geometric modeller. Finally, some illustrative examples are given.
该算法已经用visual C++语言实现。最后，给出了一些例子。
4.Rendering is one of the primary down-stream operations that requires facets.
渲染是网格化后最主要的操作之一
5.After faceting is initialized and a mesh manager specified, the application must specify some refinements. 指定
6.Increasing the efficiency of rough machining operations can produce significant productivity improvement in mould and die making because most of the metal is removed in the roughing stage.
因为大量的材料在粗加工阶段被切除，所以提高粗加工的效率可大大改进模型和冲模的加工生产效率
7.In this paper, a high-efficiency 2.5-dimensional rough milling strategy for mould core machining is presented.
本文提出了一种高效的两轴粗加工方法。
8.Rough milling is an initial machining operation used for hogging away unwanted metal from the stock so as to prepare an approximate shape for the subsequent finish milling operation.
9.I dont quite see how to generate a tool path
我不是很明白。。。
10.In this paper, the Z map is used specifically to address the difficulties involved in boundary contour generation from multi-sculptured surfaces.
在文中，特定的Z map被用来解决与多曲面轮廓边界生成有关的难题。
11.Apart from the pure construction of these curves and surfaces, the analysis of their quality is equally important in the design process.
在设计过程中，除了这些曲线曲面的构造以外，对它们质量的分析也是同等重要的。
12.We can test 1000 isophote directions, but there still can be a gap in the nest (1001st) direction.
我们可能试1000个isophotes方向，但是在第1001个方向上仍然可能存在间隙。
13.Furthermore we introduce the concept of reflection circles as a generalization of isophotes and reflection lines.
另外，我们提出反射圆的感念作为isophotes和reflection线的归纳概况（概括）。
14.Then one isophote is defined by e and a scalar value v.
于是，一个isophote通过e和一个数量值v来定义
15.Conventional algorithms for tool path generation from measured points did not use the region-by-region idea to generate adaptive tool paths since it is difficult to obtain geometric information of scattered points directly.
在传统的由测量点生成刀具路径的算法中，没有用到region-by-region的思想生成适应的刀具路径，因为直接获得离散点的几何信息是困难的。
16.Among the three phases , the second-phase RE is a roadblock to the automation of the duplication procedure.
在三个阶段中，第二个阶段RE是复制过程自动化的障碍。
17.A different approach is to transform the surface into a patchwork, consisting of triangular Bezier-patches.
另外一种不同的方法是把曲面转换为拼接曲面，由三角Bezier曲面片组成。
18.Over the past decade, high-speed machining (HSM) has provided a step change in productivity for the manufacture of moulds and dies.
在过去的十年中，高速加工大大提高了模具加工的生产率.
19.Following a survey of relevant publications, the present paper details the development of an integrated system for HSM of moulds and dies.
在对发表的相关文献研究后，本文详细介绍了一个模具高速加工集成系统的发展。
20.A terminology and classification are presented to help clarify the nature of blending
提出的术语和分类帮助阐明blending的分类。
21.This is easier to comprehend.
这更容易理解
22.Stop calling him dog 别叫他。。。。
23.The calculation of highlight lines, isophotes, and reflection lines involves solving systems of partial differential equations. In general, it is impossible to find the analytic solution, owing to the inherent complexity of the problem.
等亮度线，isophotes线和反射线的计算涉及到求解偏微分方程。通常来说，根据问题的复杂程度，不可能得到问题的解析解。
24.Economically viable cutting speeds of ~350m/min are often quote.
大约350m/min的经济可行的切削速度常常被用到。
25.In recent years, automated selection systems for machining have been in demand owing to the large variety of workpiece material ……….
最近几年中，由于工件的材料等因素，对加工自动选择系统有需要
26.Most published work, however, has focused on turning, with relatively little work on milling, possibly because of the complex nature of the latter.
然而，大量已发表的工作集中在车削加工，与铣削加工有关的相对少些，可能是由于后者比较复杂的原因。
27.Varying t within the parameter range of X(t), we obtain a curve y2(t) that describes the 2-orthotomic of X(t) with respect to P.
在X(t)的参数范围内变化参数t，可以得到关于P的描述X(t)正交曲线y2(t)
28.Figures 6 through 9 show surfaces that don’t seem to contain visual irregularities.
图6到9显示曲面………….
29.Hereinafter, this method is referred to as a point-based approach.
在下文中，称这种方法为基于点的方法。
30.Another necessary clarification is that the curve C has been assumed to be represented by a parametric form.
另一个需要澄清的是曲线C要用参数形式描述。
31.In extreme case, the distance can be approximated by discrete sampling.
极端情况下，采用离散采样的方法近似计算距离。
32.The accuracy of this triangulation is remembered in the variable bulge.
三角片的精度保存在变量bulge中。
33.The variable SurfDis keeps the shortest such distance found so far.
变量SurfDis保存目前（迄今为止）得到的最短距离。
34.Inserting these equations into the torus equation above, yields a quartic equation in t.
把这些方程代入上面的环面方程中，生成一个关于变量t的四次方程。
35.We thus do not have to conside the edge e2. Similar proofs can be made for other areas.
这样我们可以不必考虑边e2，在其他区域同样可以得到相同的证明。
36.The terms in the legend are as follows.
图例中的术语如下。
37.A chart is included for a comparison of the performance of the APT method and the subdivision method on one of the examples.
通过一个例子，用图表对APT方法和细分法进行了比较。
38.Broadly, sculptured surface machining is done in two stages.
通常，雕塑曲面加工分两个阶段。
39.While the principle is simple, the practice is significantly more complex, and a number of common pitfalls can be identified.
原理简单，实现却很复杂，并且要考虑许多共同缺陷。
40.Gouging is a particularly pernicious problem in sculptured-surface machining, and it is often encountered when the tool size is too large relative to the concave radius of curvature.
在雕塑曲面加工中，过切是非常不利的。在曲面凹区域处，曲率半径小于刀具半径时，发生过切。
41.Portions of the cutter’s leading edge sometimes extend below the designed surface, removing more material than is allowed by the designed surface profile tolerance.
部分刀具边缘切入设计曲面，切入深度超过了加工误差。
42.The detection and avoidance of tool interference is a tough problem.
检查和避免刀具干涉是个难题。
43.Many researchers have studied the interference problem, but most concentrate on interference detection and avoidance in three-axis NC machining.
许多学者对干涉问题进行了研究，但大部分研究集中在三轴干涉检查与避免。
In five-axis NC machining of sculptured surfaces, the tool interference problem is much more acute because of the complex tool movements and the irregular curvature distributions of sculptured surfaces.
在自由曲面的五轴加工中，由于刀具运动的复杂和曲面曲率分布的不规则，使刀具干涉问题更加严重。
44.They also address issues of local gouging prevention
他们同样处理干涉避免的问题。
45.Very little work has been done on tool interference detection and avoidance of filleted-end cutter. Lee et al.’s work [8] is one example.
很少有文献论及环形刀的刀具干涉检查与消除，Lee的工作就是一例。
46.In this paper, we present a systematic methodology for investigating the tool interference in five-axis NC machining of sculptured surfaces using filleted-end cutters.
在文中，我们提出一个系统的方法研究采用环形刀进行自由曲面五轴加工时的刀具干涉问题。
47.The surfaces to be machined are divided into convex and non-convex regions. For the non-convex regions, the tool interference is solved in three phases according to three scenarios.
把加工曲面分为凸区域和非凸区域。在非凸区域，根据三种情况，采用三个阶段解决刀具轨迹干涉。
48.The process continues until all the CC data are checked.
这个过程直到所有的CC点检查完毕后结束。
49.An end-mill cutter is often the choice for sculptured surface machining
常常选择端铣刀进行自由曲面加工。
50.A model of a fillet-end cutter can easily represent both the flat-end and the ball-end cutter. For this reason, this paper will consider 5-axis sculptured surface machining with a fillet-end cutter, with the flat-end cutter and the ball-end cutter as special cases.
环铣刀的描述模型很容易用来描述平底刀和球头刀。所以，本文考虑环形刀五轴加工，平底刀和球头刀只是它的特例。
51.The local coordinate system (XL-YL-ZL) is set up at the CC point.
从CC点处建立局部坐标系。
52.To avoid tool interference in machining, it is important to analyze the local surface shape.
分析局部曲面形状对于在加工中避免刀具干涉很重要。
53.At a point CC located on the torus-shaped cutter ,if the two principal curvature and of the torus can be found, the curvature along any arbitrary direction of point CC on the torus can be solved.
在环形刀的环面上的刀触点处，如果能够计算出环面的两个主曲率，那么就可以得到刀触点出沿任意方向的曲率。
54.A much larger inclination angle may extend the tool path length as well as the NC machining time, which causes low machining efficiency.
太大的倾角将延长刀具路径的长度和数控加工时间，导致加工效率降低。
55.Although NC machining as one of the key manufacturing technologies has received a lot of attention both from the technological and algorithmic point of view, the mathematical foundations of this field have seen comparatively little progress.
NC加工作为一个关键的制造技术，虽然从技术和算法的角度上得到很多关注，但是这个领域的数学基础研究进展却相当小。
56.Local millability at all points is obviously a necessary condition for global millability, but it is not sufficient in general.
所有点局部可铣削是全局可铣削的必要条件，但通常不是从要条件。
57.We will split the discussion according to the smoothness of the cutter and design surface.
我没将根据刀具和设计曲面的光滑性把讨论分为两部分。
58.the side which the positive z-axis is pointing to.
Z轴正向所指的方向。
59.Here we will need a close relation between local millability and regularity of general offset surfaces.
这里我们需要局部可铣削性和广义偏置曲面的规则之间的密切关系。
60.It is sufficient to consider this surface and we will call it the cutter henceforth. The rotation of the cutter around its axis can be neglected from now on.
今后我们把它叫做cutter，从今后，我们忽略刀具沿轴线的旋转。
61.For a three-axis milling machine, the relative motion of the cutter with respect to the workpiece is a translatory motion.
对于三轴加工，刀具相对于工件的相对运动是平动。
Note that choosing another reference point, the corresponding general offset is just a translate of the first one.
选择另一个参考点，则相应的广义偏置曲面只是第一个的一个变换。
62.With (1) this implies, that the tangent planes at corresponding points x, of the basis surface and its offset are parallel.
方程(1)暗示，在原曲面及其偏置面上的对应点x,，它们的相应切平面平行。
63.We realize that certain tools possess sharp circular edges and then the tangent planes are not uniquely determined along them.
平底刀拥有尖角，尖角处的切平面不唯一。
64.For that we exclude circular offsets and assume that the cutting part of the cutter is C2.
我们排除（不考虑）等距偏置，并且假设刀具的切削部分为C2连续。
65.This paper employs a triangular mesh for 3-axis sculptured surface machining.
本文使用三角化网格进行三轴自由曲面加工。
66.A key issue in the creation of error-free tool path for numerically controlled (NC) surface machining is gouging (over-cut) prevention.
在数控曲面加工中，产生正确的刀具轨迹的关键问题是避免过切。
67.In the case of solid-based machining, where the creation of tool paths across several surfaces in a single pass is imperative, the major sources for gouging are the tangent discontinuity (C1 discontinuity) and the surface gap (C0 discontinuity) occurred in the constituent surfaces of the part model.
在基于实体的加工中，产生的刀具轨迹在一次走刀中需要同时加工几张曲面，因此，过切的主要来源是在组成模型的曲面之间切向不连续和有间隙。
68.The local tool interference (gouging) detection is the most critical problem while generating the tool paths for sculptured surfaces. There are two possible cases of gouging.
局部干涉检查是自由曲面刀具估计生产的最关键问题。有两种干涉形式。
69.(u1, v1) and (u2, v2) are two different sets of surface parameters corresponding to the same offset point.
(u1, v1)与(u2, v2)是对应相同偏置点的不同曲面参数。
70.The solution for finding a pair of (u1,v1) and (u2,v2) is in practice an optimization problem that minimizes the function F.
求(u1, v1)与(u2, v2)的过程是一个优化过程。
71.The initial starting points are found by minimizing an optimization function. Based on the initial starting point, the interference boundary curve is traced.
初始点通过优化的方法获得。通过初始点追踪干涉边界曲线。
The modules of gouge removal are considered to be vital in any computer aided manufacturing (CAM) software.
在CAM软件中，干涉消除模块被认为是至关重要的。
72.The offset of a line segment is simply a parallel line segment at a given distance. The direction is understood to be away from the material side. A vertex can be thought of as a degenerate line segment, a constant-distance offset from which is a circular arc.
直线段的偏置是给定距离的平行线，方向为材料的外部。顶点可作为退化的线段，它的偏置为圆弧。
73.Near the transition area of two surfaces
两张曲面的过渡区域。
74.Flat and filleted endmills offer an important merit if they are used properly. Parts can always be cut by the periphery of such cutters at the maximum speed.
正确使用平底刀和环行刀将发挥它们重要的优点，刀具的边缘以最大的切削速度加工零件。
75.The proposed method of this paper employs the same idea but to extend it to the application of non-spherical cutters.
本文提出的方法使用相同的思想，并加以扩展以适应非球形刀具。
76.A part surface is first tessellated into the triangular polyhedron; cutter paths are then computed from the polyhedron surface.
零件面首先被三角剖分，然后根据多面体曲面计算刀具轨迹。
77.Part surfaces in this study are compound surfaces that include trimmed surface elements.
论文中的零件曲面指包括裁减曲面在内的复合曲面。
78.Calculating cutter paths that are based on an offset surface had already been established as early as the beginning of NC machining. However, this method had not been popular for two main reasons. First, it is difficult to obtain a precise CAD formula of an offset surface from that of the original surface because an offset surface cannot be easily expressed in a simple form (such as a formula) that is used to define an original sculptured surface. Secondly, it is difficult to remove self-interference when self-interference appears on the offset surface.
利用偏置曲面计算刀具路径在NC加工的初期就被提出，然而，有两个原因使该方法没有流行。首先，获得偏置曲面的精确描述公式很困难，因为不能用简单的形式表示自由曲面的偏置曲面。其次，当偏置曲面上有自交时，消除自交很困难。
(K. I. Kim and K. Kim. A new machine strategy for sculptured surfaces using offset surface. International Journal of Production Research, 1995, 33:6, 1683~1697)
79.
Although equation constitutes a precise parametric formulation for the offset surface, it is unsatisfactory for many purposes because the offset of a surface in a given form cannot, in general, be expressed exactly in that same form.
虽然方程构成了偏置曲面的精确参数方程，但由于它通常与原曲面的描述形式不同，所以不能满足多数应用。
80.When the offset magnitude (tool radius) exceeds one of the principal radii of curvature at some point of the original surface, self interference occurs.
当偏置的数值大于曲面上某个点处的主曲率半径时，发生自交。
81.Aomura and Uehara (1990) suggest a method to obtain the self-intersection curves of a collapsed offset surface. However, there are two main disadvantages in removing self-interference of the offset surface. First, it requires the complex and time consuming calculations. Second, the tool paths generated based on the offset surface, where self-interference was removed, result in undercut. Therefore, for a finishing cut, removing self-interference of the offset surface is not suitable.
Aomura和Uehara提出获得偏置曲面的自交曲线的方法。然而，消除偏置曲面的自交有两个主要缺点，首先，计算复杂费时。其次，基于消除自交的偏置曲面所产生的刀具轨迹会导致欠切。所以，对于精加工，消除偏置曲面的自交是不合适的。
82.For three-axis milling of parametric surfaces by ball-end cutters, detecting and removing interference in the toolpaths is equivalent to detecting the cusps and self-intersections of the offset of these surfaces.
使用球头刀进行三轴加工，干涉检查及消除与检查偏置曲面的尖点和自交等价。
83.if and only if
当且仅当
84.Generally speaking，
一般而言
85.in general
通常 （可插在句子中间，前后用逗号隔开）
86.Move from s1 towards e1 through curve C1.
沿着曲线C1，又s1移动到e1。
87.Drawn by dashed lines
用虚线表示。
88.Gouging detection and tool selection are important topics and will be discussed in depth in this paper.
干涉检查和刀具选择是重要的内容，将在论文中被深度探讨。
89.The bottleneck now exists in finding better approaches to handle these polyhedral models for machining automation.
瓶颈是如何找到好的方法处理这些多面体模型。
90.Machining of polyhedral models is becoming prevalent in recent years.
近年来，多面体模型的加工普遍使用
91.Local interference is referred to the cutting-edge protrusion into the part surface. On the other hand, global interference is referred to the shank protrusion into the part surface.
局部干涉指刀刃切入零件表面，全局干涉指刀柄干涉零件表面
92.In this paper, Gouging is interchangeable with interference.
在论文中，过切与干涉可通用（可互换）
93.Since the point-based method (Hwang) is based on the sampling of CL surfaces, Jun et.al.(CAD，2002) pointed out that it is not an easy task to avoid convex gouging in convex polyhedral surface regions [Jun 02].
因为基于点的方法是在刀位面上进行采样，所以Jun指出该方法不易避免在凸区域的线干涉（凸干涉）
94.A subset of CL points from the cutter path leading to a single traversal of the region being machined will be called a pass. The distance between two adjacent passes is called the step over, which controls the height of the cusps left between adjacent passes. The distance between consecutive CL points on a pass is called the step forward.
从刀具路径的开始到完成被加工区域的一个穿越的刀位点的集合被叫做一个pass，两个相邻pass之间的距离叫做步距（step over），步距用来控制两个pass之间的残料高度。同一条pass上的相邻两个刀位点之间大的距离叫步长（step forward）。
95.The algorithm used is a slight modification of the Inverse Offset Method (IOM) and it is assumed that a denser definition is available if required (by subdivision) to satisfy machining tolerances.
采用的算法是对反转刀具法的小小修改，并且为了满足加工精度，需要加密离散精度。
96.The Inverse Offset Method (IOM) method is robust and offers gouge free planar/non-planar cutter path.
反转刀具法稳定，并且可生成平面或非平面的无干涉刀具路径。
97.Mere data points already cannot produce precise offset surfaces, let alone efficiently solve the self-intersection problem.
仅仅数据点已经不能产生精确的偏置曲面，更不要说有效的解决自交问题了。
98.Current 5-axis CAM software, however, often requires an undesirable level of user intervention, and does not fully exploit the flexibility of 5-axis machining. In practice, 5-axis machining suffers from a number of drawbacks, most of which are related to complex tool movements and collision avoidance, whose algorithmic treatment is quite complex. Such problems are related to the two additional degrees of freedom compared to 3-axis machining. Furthermore, a detailed analysis of .at and toroidal endmills is more difficult than that of ball endmills.
可是当前的五轴CAM软件在使用时常常需要用户不同程度的交互，并且没有完全体现五轴加工的柔性。在应用中，五轴加工遇到许多困难，主要与复杂的刀具运动和复杂的碰撞检查算法有关，这些问题的出现是因为五轴比三轴多了两个自由度，此外，对圆角刀的分析要比对球头刀的分析困难许多。
99.In the polyhedron method (Duncan, Hwang) , which is one of the Cartesian-based methods, unavoidable errors always exist since the tool path is generated based on an approximated facet surface. The surfaces generated by NURBS (Non-Uniform Rational B-Spline) and approximated by a polyhedron method. Another disadvantage is that the tool path cannot be generated before converting the parametric surfaces representation into the facet surface. In other words, the tool path cannot be generated recursively unless the distinct point sets are obtained. That may cause relatively long computational time and storage problems.
多面体法生成刀具轨迹时，由于刀具轨迹是基于曲面近似三角片模型产生的，所以不可避免的存在误差。被加工曲面由NURBS表示，并用多面体近似。这种方法的另一个缺点是在曲面没被近似为多面体前，刀具轨迹是不能被生成的，换句话说，在得到离散点集之前，不能生成刀具轨迹，这将导致数据量大以及相对长的计算时间。
100.When the offset magnitude (tool radius) exceeds the principal radii of curvature at some point on the original surface, self-interference occurs. This self-interference results in overcut. Therefore, several methods for removing self-interference have been published. However, there are two main disadvantages in removing self-interference of the offset surface. Firstly, complex and time-consuming calculations are required. Secondly, the tool paths generated are based on the offset surface, where self-interference results in undercut. Therefore, removing self-interference of the offset surface is not suitable for a finishing cut. In the present research, self-interference is avoided by reducing the offset magnitude.
当偏置距离超过原曲面上某些点的主曲率半径时，会发生自交，导致过切。虽然有几种方法删除自交，可是删除自交的方法有两个缺点，第一是计算耗时，第二是由于基于偏置曲面生成刀具轨迹，在这些地方会发生欠切。所以，删除偏置曲面的方法步适合精加工。在现在的研究中，通过减小偏置量避免自交。
101.Cutter interference may occur when the sculptured surface has high curvature variation. If the local radius of curvature is less than the tool radius, then the locus of the cutter location points can produce gouging. There are two ways to avoid cutter interference. The first is to choose the appropriate cutter ( a smaller cutter ). The second method is to remove the gouging cutter path skipping the gouging segment along the cutter path. This method will leave an undercut material on the surface.
曲面上的曲率变化大时，会发生刀具干涉。当曲面局部的曲率半径小于刀具半径时，在刀位点处产生过切。有两种方法避免刀具干涉，一种是选择合适的刀具（较小刀具）；另一种是沿着刀具路径的方向跳过路径中过切段，这种方法会导致欠切。
102.They are biased against Chinese (foreigners).
他们（外国人）对中国人有偏见
103.It is a mediocre paper/research.
这是一篇普普通通的文章（研究）。
104.There are many methods of NC machining in terms of machine axis numbers and tool shape, type, and orientation.
根据机床轴数以及刀具形状、类型和方向，有许多数控加工方法。
Gouging is a common problem and has not been well resolved up to present time.
过切是普通的问题，一直到现在还没有很好的解决。
105.propose discuss suggest present solve apply use
1) Bobrow proposed two methods. One is ….. The other is …..
2) Tang Kai discussed the gouging problem in multiple-surface machining.
3) Broomhead suggested checking curvature along each pass of the path and comparing it with the tool radius to…
4) Elber and Cohen presented a method that could remove any kind of gouge.
Loney and Ozsoy presented a tool-path generation method in a parametric space.
5) George and Babu solved undercut/overcut gouging on one piece of a surface patch.
6) Choi and Jun classified two types of gouge in freeform 3-axis ball-end milling.
7) Pottmann et al. developed a so-called “millability criterion” in their work, whick can be used to obtain a locally gouge-free cutting.
8) Bobrow applied the CC method to a part CSG model created on a specific system which had an intersection function available, but limited to CSG primitives.
9) Luo an Ma used the CL method with a series of parallel planes to cut a part, which is a sculptured rather than a analytical entity as in Bobrow’s case.
106.method approach
1) Elber and Cohen presented a method that could remove any kind of gouge.
2) Two main approaches are used to generate toolpaths for surfaces, neither of which is optimal, in general.
3) In this approach, a tool path is generated as a compound curve instead of as a sequence of points.
4) The method adopted in this paper is referred to as a curve-based approach.
107.Tool path generation methods can be categorized into two types: Cartesian and parametric.
Gouging detection for parametric surfaces can be classified as two major types: Using surface model directly ans using digitized model.
刀具轨迹生成方法可分为两类：……
参数曲面的干涉检查方法可分为两种主要类型：……
108.In the past, many path-planning approaches for three-axis machining have been studied. The tool-path generation methods can be categorized into two types: Cartesian and parametric. The former is generated from cross-section planes that intersect the machined surfaces. The latter generates NC tool paths along constant u or v surface curves and the cutter location (CL) point is usually computed from the offset of the machined surface.
在过去，有许多三轴加工刀具轨迹规划的方法。刀具轨迹产生的方法可分为两种主要类型：cartesian和parametric。前者由截平面与被加工曲面相交生成刀具轨迹；后者沿着曲面的u向线或是V向线生成刀具轨迹，且刀位点常常由被加工曲面的偏置面计算获得。
109.A Zmap based approximation is one of the most popular methods.
基于Zmap的近似方法是最常用（通用）的方式之一。
110.In the past, several methods had been developed to deal with gouging problem. ……….
Recent work on the gouging problem in freeform surface machining focuses more on local gouging detection and/or the use of sophisticated 5-axis CNC machines.
以前，许多方法解决干涉问题。。。。
最近对干涉问题的研究主要集中在。。。。
111.Tool-path generation (TPG) for clean-up is one of the most challenging problems in sculpture surface machining.
清角加工的刀具轨迹规划是自由曲面加工中最困难的问题。
112.The purpose of clean-up machining is to remove uncut volumes, which are left at concave regions after finish machining, by employing ball end-mills of the same or smaller size.
清角加工的目的是取出精加工后参与在凹区域出的材料，它通常使用相同或较小尺寸的球头刀。
employ 使用 use
carry out 执行
113.A number of commercial CAD/CAM systems including CATIA, UG, and Work-NC, are capable of generating clean-up tool paths, but very few methods have been openly published.
虽然许多商业CADCAM软件可以有清角加工的功能，但是很少有方法被公开发表。
114.Conceptually, the curve-based tool path can be obtained by intersecting the offset surface (or CL-surface) with drive planes. However, it is very complicated and time-consuming to construct the offset surface of a polyhedron model exactly and completely.
概念上，基于曲线的刀具轨迹可以通过导动面与偏置曲面相交得到。但是，正确而完整地构造多面体模型的偏置曲面即复杂又耗时。（基于刀位面的刀路算法的缺点）
115.For rough machining applications, where the accuracy is not as high as in finishing, a subset of the original Zmap can also be considered to reduce the computation time for generating the rough paths.
对于粗加工应用，精度没有精加工高，所以Zmap模型可以用来减少粗加工刀具轨迹生成的计算量。
116.By the “most efficient” algorithm one normally means the fastest.
所谓最有效的算法，人们一般指最快的算法。
117.This method has a few advantage all its own.
这种方法有它的独特的优点。
118.This problem remains to be solved.
这个问题有待解决。
119.A concept of so-called “node-step” is introduced, on the basis of which all nodes in the network are organized into steps in the source-to-destination direction so as to form several sets of stepped nodes.
本文引入所谓的网络“站级”概念，并基于此概念将网络中的所有结点在源－宿方向上划分成等级，从而构成不同等级的结点集。
120.The results indicate that these two methods are consistent in essence, with the exception that they have their own specific application conditions
结果表明，这两种方法其实质是一致的，只不过各有其应用的条件。
121.Presented in this section are basic concepts and definitions that are to be used throughout the paper.
在这部分提出的全文使用的基本概念和定义
122.The CL-surface for a given surface is defined as the trajectory of the cutter’s reference-point when the cutter is slide over the entire surface.
The CL (Cutter Location) surface is a trajectory of the reference point of a cutter when the cutter slides over the designed model. It can be gathered by offsetting designed model by the amount of the cutter radius when the cutter shape is ball.
In the CL-surface approach, the first step is to compute a CL-surface defined by the Minkowski sum of the part surface and the inverse cutter. In other word, a CL-surface can be obtained by adding the swept volume of the inverse tool to the part surface.
刀位面的定义：曲面的刀位面是当刀具在整张曲面上滑动时刀具参考点的轨迹。
123.Although it is simple in concept, there are several shortcomings.
虽然概念简单，但有几个缺点。
124.The offset of CL surfaces for fillet-end mills is a more difficult problem, not to mention the more general case of APT cutters.
计算圆角刀的刀位面时很困难的问题，更不必说更加通用的APT刀具了。
125.The triangular mesh method proposed by Hwang was proven to be effective when data are undersized (less than 1000 points), and thus is able to generate a smooth cutter path. Yet in cases of larger data, its efficiency obviously plummets, mainly because the geometric calculation in gouge checking is too complicated.
Hwang提出的三角片法在数据量不够大是有效，能产生光滑的刀具轨迹。然而但数据量大时，这种方法的效率显著降低，主要因为干涉检查时的几何计算复杂。
Alan C. Lin, Hai-Terng Liu. Automatic generation of NC cutter path from massive data points. CAD, 1997,30(1)
126.In a conclusion of our careful assessment, these methods do not apply to our research.
根据前面的仔细评估，这些方法不能用于我们的研究。
127.Even though, the design surface is represented with parametric surfaces, the CL-surface may have different representation forms (triangular mesh or Z-map model), because the parametric surfaces are not invariant under the ‘Minkowski sum’ operation.
即使曲面是参数曲面，它的刀位面也可能有不同的表示形式（三角片或Z-map模型），因为经过Minkowski sum操作，参数曲面是变化的。
Sang C. Park. Tool-path generation for Z-constant contour machining. CAD, 2003, 35
128.The specified Part Geometry works in combination with the Drive Geometry (usually a boundary) to define the Cut Region.
指定的零件几何与导动几何（边界）一起确定切削区域。
129.Cut Area applies to the Area Milling Drive Method and the Flowcut Drive Method and may be defined by selecting Surface Regions, Sheet Bodies, or Faces. Unlike the Surface Area Drive Method, the cut area geometry need not be selected in an orderly grid of rows and columns.
切削区域用于区域驱动方式和清根驱动方式，且通过选择曲面，薄板或多面来定义切削区域。与曲面导动方式不同，不需要选择区域几何。




词汇
pseudo- 伪，假拟，虚 pseudo code 伪代码
die cavity n 型腔，模槽，阴模
pocket n 凹处，容器，[机]套
die-cavity pocketing 型腔加工
pocket machining 型腔加工
high resolution 高分辨率，高清晰度，高分解度 high resolution Zmap 高分解度Zmap模型
pretty much 几乎，非常接近
under control 被控制住
Since the contouring problem is pretty much under control as far as pocket machining is concerned, the 2D-curve offsetting problem has been regarded as the key issue in generating the pocketing tool-path.
至于型腔加工所涉及的问题，因为轮廓问题几乎被控制住，所以2D曲线的偏置问题被认为是生成刀具轨迹的关键问题。
Sharp turn points 急转弯点，拐点 sharp-turn points
Transition points 过渡点，转折点
Key points 关键电
PCI problem (PCI algorithms) polygonal chain intersection problem
Computational Geometry 计算几何
principal curvature 主曲率
main curvature 主曲率
mean curvature 平均曲率
lines of curvature 曲率线
curvature line 曲率线
principal curvature line 主曲率线
Lines of principal curvature 主曲率线
mean curvature lines 平均曲率线
algorithm 算法
critical region 临界区域
proposed method 提出的方法
isoparametric 等参的
converge [数]收敛；汇聚，集中
the locations T3 through T7 are。。。 从T3到T7是。。。
piecewise [数]分段的
minimum concave radius 最小曲面半径
objective function 目标函数
curvature radius 曲率半径
coefficient [数]系数，率 differential coefficient 微分系数
Room×××，Dorm East 12 东12舍×××室 或，Room×××，East 12
Derivative 导数
Directional derivative 方向导数
second Directional derivative 二阶方向导数
first partial directional derivative 一阶方向偏导数
Differential 微分
Partial derivative 偏导数，偏微分
Total differential 全微分
Higher-order partial derivatives 高价偏导数
First order derivative 一阶偏导数 first derivative
Second order derivative 二阶偏导数 second derivative
Integral [数]积分，完整，部分
Order [数]阶，级，次，度；[计]位
Euclidean 欧几里德
Trial n 试验，考验，审讯，审判
Tuple 元组，数组(在关系数据库中，标示一个实体及其属性的关系的一部分)
Abscissa 横坐标
Ordinate 纵坐标
Coordinate 坐标
Interpolation 插补，插值法，内插[推]法
Quadratic interpolation 二次插值
Cubic interpolation 三次插值
Degeneracy 退化，退步，堕落
Bivariate function 两个变量的函数
Without loss of generality 不失一般性
SSI ——surface/surface intersection
OSIC——offset surface intersection curve
Convex surface 凸面
Concave surface 凹面
Naturally parameterized curve 自然参数曲线(以弧长为参数)
Flow rate of a curve
inner product 内积（点乘） dot product 点乘
outer product 外积（叉乘） cross product 叉乘 ～of the partial derivatives with respect to u and v
Scalar product 数积，点乘，内积
Sense [数]指向，方向。 In the sense of
In a recent survey paper 在最近调查报告中
Piecewise curvature continuous 分段曲率连续
Matrix 矩阵
Determinant 行列式
Polynomial [数]多项式
Draft 拔模斜度
Crosshair (瞄准镜)十字准线，交叉线
Beginning end of the move 运动的首末端点
Shop floor 车间，工厂
Equation 方程
Algebraic equation 代数方程
Linear[simple、quadratic、cubic、simultaneous]equation 一元[一次、二次、三次、联立]方程
Differential equation 微分方程
Dynamical equation 动力学方程
Euler equation 欧拉方程
Linear equation 线性方程，一次方程
Simultaneous linear equation 联立线性方程
analytic equation 解析式 analytic technique 解析技术
analytic representation 解析表示
Moderator 斑竹，主持人，主持论坛或讨论会的人
Band 绑定
Push onto the stack 压栈
Pop off the stack 弹出栈
Rubberband 橡皮筋
Hybrid 混合的
Trap 捕捉
Modeler 造型者
Husk 壳，外壳
Fairing 光顺，整形
Run length 运转周期
Trajectory 轨线，轨道，弹道
Homeomorphous 同胚的，同拓扑的
Reliable and robust algorithm 可靠而鲁棒(健壮)的算法
GT——group technology 成组技术
CAPP——computer aided process planning 计算机辅助工艺设计
ERP——enterprise resources planning 企业资源计划
ETO——engineering to order 按订单设计
CIM——computer integrated manufacturing
MRPII——manufacturing resources planning 制造资源计划
Agile manufacturing 敏捷制造
Heterogeneous 不同种类的，异类的
Interoperability 互用性，协同工作的能力
Data redundancy 数据冗余
Architecture 体系结构
BOM——bill of material 材料清单
Exhaustive 穷举
Tool shank 刀具柄部，刀柄
Tool holder 刀架
Differential geometry 微分几何
Computational geometry 计算几何
Geometry engine 几何引擎
Connectivity 连通性
Recursive 递归
Iterative 迭代
Terminology 术语
Attachment 附件（例，email中的附件）
Constraint 约束 （例，约束求解）
Component 分量 （例，X～，X分量；Y～，Y分量；the y-component of the unit normal vector）
Servo n 伺服，伺服系统
EDM——electric discharge machining 放电加工
ECM——electro chemical machining 电化学加工
Convex hull (convex hall) 凸包
Bisector 二等分线，平分线
High-frequency chatters 高频颤动（振动）图
Cutting force（cutting resistance）切削阻力，切削力
Low-level 低水平的
Quadtree 四叉树
Octree 八叉树
Allocator 分配算符
Explicit function 显函数
Implicit function 隐函数
Real number [数]实数
Imaginary number [数]虚数
Complex number [数]复数
Synopsis 大纲
Asymptotic lines 渐进线
Anisotropic 各向异性的
curvature tensor [数]曲率张量
curvature tensor field [数]曲率张量场
umbilicus [数]脐点
proceeding 会议，学报
transaction 学报
ruled surface 直纹曲面
algebraic ruled surface 代数直纹曲面
locus 位置，地点，[数]轨迹
isoline 等值[位, 价, 高, 深, 温]线
interrogation 探寻；讯问；审问；质问
modeling [计]建模， 造型
sophisticated CAD system 成熟(复杂)的CAD系统
Critical adj. 评论的, 鉴定的, 批评的, 危急的, 临界的
Silhouette 侧面影像, 轮廓，外形
Light intensity 光强度
Isophote = equi-brightness curve=equal light intensity 等亮度曲线，等光强度线
Contour lines 等值线族
Orthogonal to contour lines 与等值线正交的正交线族
Equi-gradient lines 等梯度线族
Terminology 术语
Nature 种类，天性，本性，自然，自然界，大自然，自然状态
analytic solution （方程的）解析解
key characteristics 关键特征，主要特征
orthotomy 面正交性
affine [数]仿射（几何学）的
tool-tip point 刀尖点
chord 弦，和音，情绪 chord length 弦长
power series 幂级数
sufficient condition 充分条件
necessary condition 必要条件
necessary and sufficient condition 充要条件
bilinear interpolation 双线性插值
lemma [数]引理，辅助定理，论点，主旨，(文章论点的)标题，(词典的)词条
pointwise 逐点，点态 pointwise modification 逐点修改，pointwise convergence [数]点态收敛
variable [数]变数, 可变物, 变量 the variable A 变量A
subset [数]子集
triangle n [数]三角形，三角形的物体，三角关系
triangulation n 三角剖分，分成三角形，三角测量
point-normal representation 点法式描述 point-normal representation of the plane 平面的点法式描述
point-vector representation 点矢式描述 point-vector representation of the line 直线的点矢式描述
cylindrical surface 柱面
conical surface 圆锥面 cone 锥形物，圆锥体
spherical surface 球面
toroidal surface 圆环面 torus 环面
totoidal end mill 圆角刀，环形刀
curved surface 曲面
frustum [数]平截体，截头体，平截头体，平截面
logarithm [数]对数
high performance 高精确性，高性能
fine positioning 精确定位
level off 平整，稳定，变平
performance degradation 性能降低
built-in adj. 内置的，内嵌的，内在的，固有的，生就的
general offset surfaces 广义偏置曲面，广义等距面
generalized cutter location surfaces 广义刀位面
Generalized CL_Surfaces 广义刀位面
robust 鲁棒性 (即健壮性，指系统在错误操作下，能够保持正确运行的能力。控制专家用这个名字来表示当一个控制系统中的参数发生摄动时系统能否保持正常工作的一种特性或属性。) (什么是“程序的鲁棒性”？答：鲁棒性，是英文“Robust”的音译，指程序的健壮性。就是程序对异常情况的处理能力，例如不合理的输入、下标越界等。鲁棒性差的程序在遇到异常情况时会造出内存泄漏或是死循环等情况，而鲁棒性强的程序就能很好的处理这些异常。)
parabolic adj 抛物线的 parabolic point 抛物点
hyperbolic adj 双曲线的 hyperbolic point（saddle point）双曲点（鞍点）
tangency n 接触，[数]正切，切线
tangent n 切线, [数]正切
translatory adj [物]平移的，平动的
meridian curve 母线，子午线
modules n 模块
polyhedral adj 多面的，多面体的 polyhedral model 多面体模型
polyhedron n 多面体
concatenation n 串连
curvature indicatirx 曲率指示线，曲率曲线 curvature indicatrices (复数) 曲率指示线
inequality n 不等式
cross section 横截面 cross-section
tetrahedral adj 四面体的，有四面的
hatched area 阴影(线)区域
superscript n 上标 subscript n 下标 ～ symbol 上(下)标符号
ray tracing 光线跟踪
high performance machining 高性能加工
high speed machining 高速加工
bottleneck n 瓶颈
STL —— stereo lithography
IGES —— Initial Graphics Exchange Specifications
STEP —— STandard for Exchange of Product data
DXF —— Data eXchange File
PDES —— Product Data Exchange Specifications
ANSI —— American National Standard Institute
weighted sum 加权和 （weight sum）
parallelogram n [数]平行四边形
pyramid n 角锥、棱椎, 金字塔, 叠罗汉 v.(使)成金字塔状, (使)渐增, (使)上涨
enumerate v 枚举
generatrix n 母点，母面，母线（比如，做sweep时用的母线）
SEDE —— sweep-envelope differential equation
in terms of adv 根据，按照，用...的话，在...方面
up to 一直到，等于
radial distance 径向距离
tangent vector 切矢
normal vector 法矢
envelope n【数】包迹[线]，包络(线，面)，方框(图) upper enveloping 上包络
colinear 共线
prerequisite 先决条件






词根
soph 聪明
mor 愚蠢
ambi 两边
bene 好
scribe 写
circ=circum 环，圆
semble 脸
tribute 给与
ject 仍，投掷
med = medi 中间
se 分开


副词
therefore adv 因此，所以
further adv 此外，更进一步，更远的 （注：对事物进行更进一步的说明）
let alone 更不用提，更别说
nevertheless conj 然而，不过 adv 仍然，不过
yet conj 然而，但是
however adv 无论如何，可是，仍然，究竟； conj 不管用何种方法，然而，可是
Furthermore adv 此外，而且
thereby adv 因此，从而，在那方面，在那附近
表示程度的副词：much, far, well, greatly, considerably, appreciably, significantly, substantially, a lot, a great deal
even if 即使


科技英语写作摘抄
变化——variation，change
A随B的变化（的情况）——the variation of A with B，A against B， A vs B
强调指出——用emphasize 而不是point out emphatically，后一句用在普通英语及政治文章中
通过….——through +名词+of+～（through the study of ～）
by+动名词+～ （by studying ～）
提高速度——increase speed
提高质量——improve quality
解决方法——solution （不用 solving ways）
应注意，值得注意——deserve to be notied
最后——finally （at last, in the end 均只能表示“最终”之意，finally可以表示几项中的最后一项）
大大降低——decreased greatly （greatly 不能改为very mush）
在公式、算法、语言等词后的定语多用for短语——A simple formula for calculating…
与…相比——(as) compared with ~. 注意在“有点（advantage）”和“缺点（disadvantage）”等名词后应该使用over。例如，The advantages of this method over the scanning method have… 这种方法与扫描法相比的有点是～。
质量好——be good in quality; be of good quality; the quality of ~ is good
在…之后——in 不能用 after
有待于——remain， This problem remains to be solved. 这个问题有待解决。
表示“变化”的名词——variation；change，不用variance
几乎不能——can hardly， 不用almost not
这种材料很难加工——This material is very difficult to machine. (不能用to be machined)
把A代入B，得到——Substituting A in (into) B, we obtain (have, get)…
得多——表示比较的程度“得多”应在比较级前加上一个副词much, far, well, greatly, considerably, appreciably, significantly, substantially, a lot, a great deal. 例如，Sound travels much less fast than light (does). 声音传播的速度比光慢得多。
A乘以(除以)B——A multiplied (divided) by B.
不定式作定语时与被修饰词之间一定要存在某种逻辑关系——例如，我们已定义了度量m的质量单位：We have defined mass units with which to measure m. (用We have defined mass units to measure m 错误)
适合于——be suitable for
与…相吻合——多数英美科技工作者一般使用agree with或be in agreement with，fit into用于普通英语中。例如，所得结果与测量值相吻合，The results obtained agree with the experimental values
其实质——in essence或in nature
已知——given；knowing
降低要求——lower the requirement for 不用decrease
提出（建议）——put forward；advance；make；offer等
是取决于——depend on；is dependent on 不能用is depend on 。
是….组成的——consist of
是来自于…的——come from
成立——hold；apply
特别——especially，不能用specially，它指“专门”之意。
本文所讲的内容——不能用talk about， 可以用describe，discuss，cover，deal with， treat，present。例如，What this paper describes is～
表明——show，indicate，illustrate 不用prove（证明）。例如，模拟结果表明，The simulation results show that~
一定的（优越性）——to a certain degree (或extent). 例如，有一定的优越性，are to a certain degree superior.
计算结果——computation (computed, computational) results
模拟（仿真）结果——simulation results
实验结果——experimental results
精度高，计算量少——high accuracy and requires a small amount of computation
条件是——on condition that
限制了——set a limit to
获得，得到——obtain，一般不用get
除非…., 否则…——用unless， 不用otherwise
什么的工作原理如下——A … works as follows.
在此基础上——on the basis of which
借助于…——with the help of …
以任何形式——in any form
以任何方法——by any means
理解它的结果——appreciate its results. appreciate 理解，觉察，鉴别，正确评价 understand
广泛地用在…——be widely used in …
这种方法的另一个优点是——An added advantage of this method is
同时——also
there be——当There be句型的主语是由and连接的两个或多个时，谓语动词be的单复数形式由最靠近的主语的数决定。
在…方向上——in the … direction. 用in而不用to，on或toward
在…基础上，基于此, 根据…——一般译成定语从句，on the basis of which, 不能写成based on which。
定语从句中，先行词受到形容词最高级的修饰，后面的定语从句只能用that引导，不能用which。
为了做到所有这一切——To do all this
从而大大减少—— , thus greatly reducing …