球面

Discussion is made to some properties of aspheric surface. A novel method is presented to define and calculate the best fitting sphere and the asphericity of high order aspheric surface. Thus, the asphericity calculations of the conicoid and high order aspheric surfaces are unified.

在本文中，对非球面的一些性质进行了讨论，提出一种新的高次非球面的最接近球面及最大非球面度的定义和计算方法，实现了轴对称的高次非球面和二次非球面的非球面度计算的统一。

Through finding a best fitting spherical surface, making the maximum deviation between aspheric surface and the best fitting spherical surface minimum, the maximum deviation at this time is just the maximum asphericity of aspheric surface.

寻找最接近球面，使其沿法线方向与非球面的最大偏离量最小，此时的最大偏离量即为非球面的最大非球面度。

A real-time interferometric method for testing asphere was proposed to measure aspherical surface with small asphericity without other null optics.

对非球面度较小的非球面，直接利用标准球面镜作为参考表面，通过数字干涉仪可以测得全孔径位相分布，将所得的数据剔除参考球面波相对理论非球面的偏差，并运用最小二乘拟合求得机构定位误差，消去此误差，即可获得真实的面形信息。

The said Martinez stretcher comprises concave spherical reflecting lens, plane reflecting lens and grating. The said compressor comprises plane reflecting lens, inner right angle reflecting lens and grating, which is characterized by the following: the grating fringe density of the stretcher is larger than that of the compressor.

所述的马丁内兹展宽器由凹球面反射镜、平面反射镜和光栅组成；所述的压缩器由平面反射镜、内直角形反射镜和光栅组成，其特征在于，展宽器的光栅条纹密度大于压缩器的光栅条纹密度；展宽器中的凹球面反射镜曲率半径位0.9～1.2米，光栅距凹球面反射镜的位置为凹球面反射镜曲率半径的1/3～1/2。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

For regular topology surface, intermediate surface local texture mapping are used; for irregular topology surface, subdivision surface local texture mapping are used. So different topology surface using different texture mapping methods can solve the contradiction between texture effect and processing speed when they are dealt with by single method. The three judge conditions of texture distortion in the process of mapping onto the sphere surface are discussed and the exiting algorithms of mapping are analyzed, the new algorithms of mapping onto the sphere surface are presented. In order to enhance the realistic of graphics, a new function of wood texture is presented. OpenGL is also introduced in this papers and some realization examples of texture mapping based on OpenGL under the environment of VC++ and POV-RAY are presented in some chapters.

对于简单拓扑表面，利用改进的两步纹理映射，对于复杂拓扑表面利用新的面片分割算法，初步解决了颜色纹理中速度与走样之间的矛盾；通过对球面纹理时纹理不变形的三个判断条件的研究，分析了现在各种球面纹理映射算法，并在此基础上提出了一种基于等面积的半球面纹理映射算法，明显减少了球面纹理的纹理变形；针对现有的木纹纹理中，两种表示木纹的颜色差距表现出的颜色突变问题进行研究，提出对这两种颜色进行线性插值或二次插值，使生成的木纹纹理颜色更加连续，更加逼真；在VC++环境下，通过调用Open GL的图形库及在Pov-Ray软件环境下，实现了参数化纹理、球面纹理、凹凸纹理及木纹纹理等各种算法。

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

The off-axis reflection system composed of four aspheric mirrors was designed, but the system structure was not so simple and the performance can also be improved, besides, manufacture and test for large aspheric mirrors are difficult; and then the spherical Fresnel mirror which is easier to be manufactured and tested was used to replace the aspheric mirror, the spherical Fresnel mirror has low cost of replication, but this design also can\'t be used in projection lens because it was only feasible in narrow wavebands; Furthermore, the design making use of catadioptric projection lens was accomplished, this design is greatly applied in rear projector because it has merits of both refraction and reflection. But it had difficulties in color aberration correction and had complex structure.

设计了四片非球面组成的离轴式反射系统，然而，仅采用非球面设计系统结构不够精简，性能也有待进一步提高，且非球面面形较大时加工和检测都存在一定的困难；继而提出了用球面Fresnel反射镜代替非球面的设计方法，虽然Fresnel反射镜加工和检测更为简单，且复制成本低，但对波长具有选择性；进而，应用折反系统结合的方式设计了离轴式投影镜头，该方法因兼具折射和反射的优点，在大屏幕超薄背投系统的设计中广为应用，缺点是会产生难以校正的色差，且结构复杂。

The structure shown in the figure : The governing body received direct or roller drying cylinder, as the main components of the rotation; After finishing the outside of the sphere, Bottom Cover and soak spherical carbon graphite seal ring joint seal reliable seal friction deputy, Sealing ring in the spherical shell of its annular space sliding, in addition to oil-free bearings and with the close cooperation of Shell, Rotating connector so that the free support, and therefore do not require a high level of accuracy installed; Spherical seal ring wear, Spring means of pressure at any time in advance to receive compensation, compensation for the shell slowly moved backward, accessible through the tube outside the inscription on the line to observe the seals wear; When steam, Oil flows through the media or other spherical sealing ring and oil-free bearings, the formation of thin liquid film, sealing and lubrication, thereby reducing friction and wear, extending the service life.

其结构如图所示：外管体直接接到辊子或烘筒上，为主要的旋转部件；经过精加工的外管本球面、底盖和浸泡碳石墨球面密封环共同组成密封可靠的动密封磨擦副，球面密封环在其壳体内的环形空间中滑动，加之无油轴承与壳体的密切配合，使旋转接头自由支撑，故对装机精度要求不高；球面密封环磨损后，借助于弹簧的预压力随时得到补偿，补偿时壳体缓缓向后移动，并可通过外管体上的刻线观察到密封件的磨损程度；当蒸汽、油或其它介质流经球面密封环和无油轴承时，形成一层很薄的液膜，提供密封和润滑，从而减轻了摩擦和磨损，延长了使用寿命。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。