曲面

This technology not only preserves the properties of localness and affine-invariance of B-spline surface, but also has some special advantages such as adaptability to arbitrary topology which parameter surfaces dont have. These good qualities makes subdivision surface used widely in recent years.

它不仅具备B样条曲面的局部支承性、仿射不变性等良好性质，而且具有参数曲面所没有的任意拓扑适应性等特点，因而近年来得到广泛的应用。

Combined with the measurement for characterized curves of discontinuous helicoidal surfaces, a method using grey theory to detect unwanted asperities in the dynamic measurement of cutting edges is studied.

建立了具有普遍意义的仪器综合定位误差与曲面测量误差的基本关系式，并以此导出了曲面形状公差与测量仪器精度的关系式。

Hence the associated surface of minimum genus can be got by doing a sequence of exchangers on some associated surface.

通过对任一关联曲面作一系列调位，从而可得最小亏格的关联曲面，此亏格即为所求图类的最小亏格。

Numerical control lathe have following outstanding superiority than traditional lathe include:Can process out complicated parts, such as the curve coming out in traditional machine tooling, curved surface,etc;Because computer have superb operation ability is can instantaneous to calculate out each coordinate axis instantaneous amount of exercise that should move accurate, So can compound into the complicated curve or curved shttp://www.51lun-wen.cnurface ;Can realize automation that process is and flexible automation, so efficiency constant traditional lathe raises by 3-7 times;Because the computer has memory and stores ability ,Can carry out automatically according to the order that the procedure stipulates,so realize automation;Proceshttp://www.51lun-wen.cnng precision of part high, size disperse degree light, make and assemble easy, No longer need to" repair the damaged parts of a machine and supply replacements";Can realize the concentration of many processes,have many kinds of self-containment functions,such as autoalarm, controlling, automatic compensation automatically,etc;Therefore can realize that nobody guards and processes for a long time.

机床数控化改造可以加工出传统机床加工不出来的曲线、曲面等复杂的零件。数控机床比传统机床有以下突出的优越性，由于计算机可以瞬时准确地计算出每个坐标轴瞬时应该运动的运动量，因此可以复合成复杂的曲线或曲面；可以实现加工的自动化，而且是柔性自动化 http：//www.51lun-wen.cn ，从而效率可比传统机床提高3～7倍；由于计算机有记忆和存储能力，可以将输入的程序记住和存储下来，然后按程序规定的顺序自动去执行；加工零件的精度高，尺寸分散度小，使装配容易，不再需要"修配"；可实现多工序的集中，减少零件在机床间的频繁搬运；拥有自动报警、自动监控、自动补偿等多种自律功能，因而可实现长时间无人看管加工。

Numerical control lathe have following outstanding superiority than traditional lathe include:Can process out complicated parts, such as the curve coming out in traditional machine tooling, curved surface,etc;Because computer have superb operation ability is can instantaneous to calculate out each coordinate axis instantaneous amount of exercise that should move accurate, So can compound into the complicated curve or curved surface ;Can realize automation that process is and flexible automation, so efficiency constant traditional lathe raises by 3-7 times;Because the computer has memory and stores ability ,Can carry out automatically according to the order that the procedure stipulates,so realize automation;Processing precision of part high, size disperse degree light, make and assemble easy, No longer need to" repair the damaged parts of a machine and supply replacements";Can realize the concentration of many processes,have many kinds of self-containment functions,such as autoalarm, controlling, automatic compensation automatically,etc;Therefore can realize that nobody guards and processes for a long time.

机床数控化改造可以加工出传统机床加工不出来的曲线、曲面等复杂的零件。数控机床比传统机床有以下突出的优越性，由于计算机可以瞬时准确地计算出每个坐标轴瞬时应该运动的运动量，因此可以复合成复杂的曲线或曲面；可以实现加工的自动化，而且是柔性自动化，从而效率可比传统机床提高3～7倍；由于计算机有记忆和存储能力，可以将输入的程序记住和存储下来，然后按程序规定的顺序自动去执行；加工零件的精度高，尺寸分散度小，使装配容易，不再需要"修配"；可实现多工序的集中，减少零件在机床间的频繁搬运；拥有自动报警、自动监控、自动补偿等多种自律功能，因而可实现长时间无人看管加工。

Based on study of relationship between the average quadric error and the surface curvature, a variable resolution surface reconstruction algorithm was proposed.

在研究平均二次误差与曲面曲率关系的基础上，提出了变分辨率的曲面重建算法。

The paper aims at realizing automatic online measurement of free-form surface with the system of processing for the background.

本文以自由曲面的自动化加工系统为应用背景，以自由曲面的自动在线检测为研究目标。

In order to reduce the effect of imaging recognition error, the recognition location of projection is extended and refined, and the projection edge of sphere centre is implanted. So a pyramid is formed by radial line between the camera optical centre and the implanted point. A curved face is formed by the two pyramids and barbette sphere. To calculate the shape centre of the common section of the curved face, the shape centre is the coordinate of sphere centre.

为了降低图像识别误差的影响，对投影的识别位置进行拓展和细化，并对球心投影边界进行插值，摄像机光心与插值点连线射线形成了一个锥体，两摄像机的锥体分别与炮台球面相交形成曲面，计算两曲面公共部分的形心，即为球心位置。

Finally, a new method of errors analysis (midpoint and barycentric measure method )are presented to measure the errors of surface reconstruction, strong practicability shows that this error measure method is feasible to testify the validity of surface reconstruction.

最后，本文对重建曲面进行了误差分析，提出了一种新的误差度量方法，即中点、重心误差度量法；此方法运算效率高，并在一定程度上可以衡量曲面重建效果的好坏。因此有很强的实用性。

If the profile curve has been denoted by a nonuniform rational quadratic B-spline curve, it is very convenient to represent the surface of revolution as a nonuniform rational biquadratic B-spline surface.

只要轮廓曲线用非均匀有理二次B样条曲线来表示，就可相当方便地把旋转曲面表示成非均匀有理双二次B样条曲面。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。