曲面

Generally the surface of objects such as mechanical parts is mainly composed of quadric surface, free-form surface and blending surface, which are defined as features in this paper.

实物产品尤其是机械零件的表面通常是由一些可以称为特征的几何曲面组成，这些几何特征曲面主要包括二次曲面、自由曲面和过渡曲面等。

The surface of conventional engineering part is composed of simple analytical surfaces and four-boundary ruled surface primarily. Therefore a point cloud segmentation method based on those feature surfaces is proposed. Several algorithms to identify the simple analytical surface feature are investigated and discussed. The theory of fitting scattered point to B－Spline and Bézier surfaces is introduced and a fitting method based on four boundary and point set is also discussed. Moreover, anew method to recover the fix-radius rolling ball blend is proposed and discussed in detail.

常规工程零件的外表面中包含了大量的特征曲面，如简单解析曲面和四边直纹面，因此，本文提出基于特征曲面的的点云分割方法，研究几种识别简单解析曲面的算法；研究由点云拟合B－Spline和Bézier曲线的理论基础，总结曲面拟合的几种方法，提出一种反求定半径滚球圆角的方法。

It seems natural to use this idea into the parameterization of the blending surfaces of three pipe surfaces, however, the blending surface of three pipe surfaces is very complicated and the inappropriate choice of parameters can lead to singular blending surface.

将这一思想应用于三管拼接曲面的参数化是自然的，但是由于三向管道曲面的拼接曲面是是复杂的，并且由于参数选取不当可能出现三个管道曲面分别拼接于混合拼接曲面的不同分支等奇异情况，从而这一思想的实现具有现实难度。

In chapter 4, basing theories and methods of scientific visualization, and artificial neural network BP algorithm, we integrate the Visual C++, OpenGL graphics library and Excel VBA technique to develop the program of artificial neural network and to make the BP algorithm visually, this program works can be divided into four parts: Using C language to develop program about BP algorithm; Using Visual C++, develop the GUI Interface, make input parameter visually; Using OpenGL graphic technique to display the training sample point in three dimension; at last using Excel DDE technique display the error graphic tables in Excel system In chapter 5, on the view of engineering application, we establish new method of surface reconstruction basing artificial neural network, develop interface program between module and commercial CAD/CAM system, meantime deeply discuss some key problems, for example, setting up the base plane, using the API technique, cutting and editing surface boundary, and also discuss the more compliant problem: how to intersect surface, at end we finish the work of translation from our surface reconstruction module to commercial CAD/CAM system, then make reverse engineering system basing artificial neural network more useful.

第四章基于科学计算可视化理论，依据人工神经网络BP算法理论模型，综合Visual C++，OpenGL图形库以及Excel VBA等多项软件开发技术，编制了人工神经网络程序，实现了BP算法的可视化映射。具体工作分为四部分：利用C语言实现人工神经网络BP算法；利用VisualC++的GUI技术开发图形用户界面，实现参数设置可视化；利用OpenGL图形技术进行三维映射，显示学习样本及训练样本点；利用微软电子表格DDE动态数据交换技术，在Excel上动态显示学习误差曲线图。第五章从工程应用的角度出发，提出了一种新的基于人工神经网络算法的曲面裁剪重构方法，完成了曲面重建模块与通用CAD/CAM系统的接口设计工作，对其中的若干关键问题进行了深入讨论，例如基平面设定、API技术的应用、边界裁剪等问题，同时，对曲面计算中较为困难的曲面相交问题也进行的专门探讨，最终完成了曲面重建模块向CAD/CAM系统的数据传输工作，使人工神经网络逆向工程系统趋向实用。

In feature-based reverse engineering, with the research of surface feature handling done wieldy and deeply, a methodology of surface-feature based re-modeling has come into being, with which the quadric surface, simple free-form surface and blend surface feature can be directly extracted from point cloud conveniently.

目前，在基于特征的反求工程中，有关曲面特征处理的研究已经比较深入，可以方便的直接从点云数据中提取二次曲面特征、简单自由曲面特征和过渡曲面特征，基本形成了一种基于曲面特征的反求工程CAD建模方法。

This paper put forward the optimized methods include reconstructing the characteristic curve by reasonable use of the adjust tools and analyse tools of the modeling software, admeasuring the automotive model surface correctly, simulating the breaking surface and creating the surface in the right turns which is good for modeling a smooth and exactitude surface.

本文通过合理利用反求软件中的造型工具和分析工具，正确划分反求模型的造型区域，使用正确的曲面造型方法，对反求曲面的特征网格线进行二次优化，并对突变曲面进行拟合再生成处理及建立合理的曲面生成顺序等方法，最终获得了仿型度和光顺度都很高的反求曲面。

Surface quality analysis is the indispensable step in car body development process . Accurate surface quality analysis needs high quality surface tessellation .

曲面品质分析是车身开发过程中必不可少的一步，准确的曲面品质分析需要高质量的曲面离散网格，提出了一种新的面向曲面品质分析的裁剪参数曲面离散技术。

This article mainly introduced the theory,the classification of COONS surfuce and the analysis of the surface ,in view of each type of COONS surface's insufficiency, KongSi etc took the improvement of its methods and in accordance with the different requirements of continuity of surface, COONS surface will be divided into three Categories.

本文主要介绍了COONS曲面的理论、分类及曲面分析，针对每类COONS曲面的不足，孔斯等人采取一定的方法对其进行改进，并按照曲面连续性的不同要求，将COONS曲面分为了三大类。

The invention comprises a free-form surface prism with three optical surfaces, and a micro-image display; the free-form surface prism is made of plastic glass materials with the refractive index greater than 1; the three free-form optical surfaces are concave surfaces, which meet one of the three surface-type equations, and the location relationship of each surface meets three condition equations; the incident angle formed between the widest-field upper edge rays emitted by an LCD and the second free-form surface meets the total reflection conditions; and an image source element is an LCD of 0.61 or 0.59 inches.

本发明包含一个具有三个光学表面的自由曲面棱镜和一个微型图像显示器，自由曲面棱镜采用折射率大于1的塑料玻璃材料，自由曲面棱镜的三个自由曲面光学表面均为凹形面，它们应满足三个面型方程之一，并且各表面的位置关系应满足三个条件方程，由LCD发出的最大视场上边缘光线在第二自由曲面上的入射角应满足全反射条件，像源元件为0.61或0.59英寸的LCD。

On the geometric modeling, flat surface and curved surface are used to mesh and describe the model;on the electromagnetic modeling. Different basis functions( flat surface roof-top basis function, flat surface RWG basis function, curved surface roof-top basis function, curved surface RWG basis function) and different test functions (line-matching, Galerkin method) are applied to different cells(plat rectangle facet, triangular patch, Bezier patch, parametric surface, curved triangular patch etc.).

在几何建模方面，分别采用平面元和曲面元对模型进行了剖分和拟合；在电磁建模方面，针对不同的单元(平面元、平面三角元，、Bezier元、参数曲面、曲面三角元等)采用不同的基函数(平面roof-top基，平面RWG基，曲面roof-top基，曲面RWG基)和不同的检验函数进行处理。

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％。