Romans 1 : 27 and in the same way also the men abandoned the natural function of the woman and burned in their desire toward one another , men with men committing indecent acts and receiving in their own persons the due penalty of their error 罗马书1 : 27男人也是如此、弃了女人顺性的用处、欲火攻心、彼此贪恋、男和男行可羞耻的事、就在自己身上受这妄为当得的报应。
This results in enormous and redundant data . two adaptive subdivision schemes , which can satisfy engineering requirements , are proposed in this thesis . one is based on shape precision control , another on surface fairness criterion 本文提出了两种符合要求的自适应细分模式：一是基于形状精度控制的自适应细分模式；二是基于表面光顺性要求的自适应细分模式。
( 3 ) the thesis proposes an improved algorithm for fairing of bi - cubic b - spline surface which detects the location of non - fairing automatically and adjusts the relative control points . in addition , a new highlight - line method used for surface interrogation is presented 另外,对曲面光顺性检查的高光线方法进行了改进,用光片模型取代光柱模型,解决了现有高光线方法存在的检查结果与基准光线相关的问题。
3 ) b - spline surface fitting to contour data is studied . a fitting method of using uniform knot vector is given . using this method , the resulted b - spline s urface not only satisfy the requirements of precision , but also possess fewer c ontrol vertices and good fairness , the computation speed is greatly improved t oo 3 )研究了逐层扫描数据的曲面拟合问题，给出了一种是利用统一的节点矢量进行拟合的算法，用该法得到的b样条曲面不仅可以满足精度要求，而且具有较少的控制顶点和较好的光顺性，计算速度也有较大的提高。
The quality of reconstructed surfaces is related to many factors , such as quality of original data and surface fitting strategy , surface post - processing , and so on . in this thesis , the relative techniques of high quality surface reconstruction and surface interrogation based on triangular mesh are studied in depth . the main contents are as follows : ( 1 ) typical mesh smoothing schemes are analyzed 本文对基于三角网格模型的高质量工程曲面重建及曲面光顺性分析的相关问题进行了研究,主要内容包括: ( 1 )在对现有几种常用的三角网格模型光顺算法进行分析比较的基础上,结合图像处理中的kuwahara滤波以及双边滤波思想,提出了基于法矢修正的三角网格模型光顺算法。
The typical optimizing criterion of triangulation is max - min angle criteria , but it has some restriction when applying in three dimensions . we proposed some amelioration by taking into consider the relationship of points and their neighbors . that can make the triangulation ' s space variation more even , and can reach the surface fairness request 对三角剖分中的典型优化准则?最小内角最大准则应用于三维空间中时的局限性问题提出了改进方法，充分考虑数据点与近邻点的空间关系，使三角剖分的空间形状变化尽量均匀，保证了三角剖分网格的光顺性要求。
Curve ' s curvature monotony condition which is related to the curve ' s fairness , is the important content in cad and computer graphics . the study of curvature monotony is useful to know the curve ' s essence , hence we can found the theory base for fairness method with " curvature monotony of segment " 曲线的曲率单调性是指其曲率单调增大或单调减少的性质，与曲线的光顺性密切相关，它是计算机辅助设计与图形学中的重要内容，开展曲率单调性方面的研究，有利于我们进一步认识曲线的性质，并为‘分段曲率单调’光顺方法奠定理论基础。
The author also studied ugii , interface statements and internal functions , after a development by using visual c + + 、 ug / open api , inherit functions of ugii , the functions of curve smooth , surface smooth and surfaces combination . after the tests in motorcycle reverse engineering , 1 ) the bad points can be deleted by using curve smoothing function , so the curve become more smooth 二次开发的功能在某摩托车型的反求过程中的应用，取得了良好的效果： 1 )曲线中的坏点可以通过调用曲线光顺的模块而得到修改，曲线的光顺性大大改观。
The paper concludes the 12 types of zhou yi thinking mode : the comprehensive empiric mode , the organic set mode , the original natural pattern mode , the mode of the combination of human being and the nature , the confucian orthodoxy mode , the mode of neutralization of yin and yang , the teleological mode of causation , the mode of induction and deduction , the sequential resultant mode , the opposite and complementary mode , the life subjective mode , and the mode of promoting disposition and virtue 是其“周易思维” ，它是通过一整套基本的“周易思维”模式体现出来影响后人，具体可概括为“十二型” ：经验综合型思维模式，有机整体型思维模式，天源物本型思维模式，天人合一型思维模式，三才道统型思维模式，阴阳中和型思维模式，因果目的型思维模式，归纳演绎型思维模式，有序生成型思维模式，相反相成型思维模式，生命主体型思维模式，顺性修德型思维模式。
Several key techniques of carving and milling machine cnc system are deeply studied they include : the transformation , data rebuild and interface design of huge volume nc program produced by cam ; the algorithm of cubic parametric spline pre _ interpolation and high speed real time interpolation in the cnc system , which . will gain a much higher surface precision and cutting speed ; methodology and algorithm of movement velocity acceleration control on a real time forecast _ and _ prejudge basis is designed . therefore , a smooth movement is insured . the shake and noise problem caused by non _ uniform pules for driving stepping or servo motor is solved by an improving algorithm to generate uniform pules 同时，本文对基于统一的pc平台的雕铣机数控系统中的几项关键技术进行了深入的研究，包括： cam生成加工程序的传送、接收、读取及其加工链表的生成和实时重构；对cam生成的离散数据进行三次参数样条插值和基于累加弦长的三次参数样条插补控制，保证加工工件表面的精度和光顺性；设计具有“前瞻”功能的自动升降速控制方法，保证加工过程的平稳性；通过脉冲均匀化，有效地解决加工过程中因为脉冲不均匀而引起的震动问题。
