非球面空间

Abstract］ Objective To describe the shape of the planar space of the corneal anterior surface of children with emmetropia by using a conic section, and then to plot the changes in asphericity on 36 meridians to deduce the formulae of the three-dimensional shape of the corneal anterior surface.

目的 通过二次曲线方程来描述正视儿童角膜前表面的二维空间形态，根据各子午线非球面性的变化规律推导出其三维形态的数学表达式及非球面性变化规律表达式。

Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上，深入研究了纹理映射的基本原理与过程，根据反向纹理映射对纹理随机采样的特殊要求，提出了一种可满足存储空间和寻址时间的纹理压缩存储算法；通过对纹理映射中几何变换理论的进一步深入探讨，提出了整体参数化和面片参数化的概念，并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式；针对现有的两步映射算法所存在的中间曲面—球面的参数化问题，提出一种等积映射方法，较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射；从信号采样的角度深入分析了纹理映射中走样产生的原因，提出了改进的区域求和表算法，使图形生成的效果有所提高；还分析了一般的扫描线算法在透视变换中所存在的问题，提出了一种正确的插值算法，从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

Therefore in the teaching students should be made to actuallyfeel that spherical geometry knowledge can be used to solve or explainsome real problems in both life and production, to reach the relatedconclusions about spherical geometry by comparing it with Euclideangeometry, and to have anidea of some non-Euclidean geometry models aswell as differences between flat geomtry models and spherical geometry ones.

是为对数学有兴趣和希望进一步提高数学素养的学生而设置，重点是培养学生空间想像和几何直观能力，教学中应使学生切实地感受到利用球面上的几何知识可以解决生活或生产中的一些实际问题；让学生通过欧氏几何和球面几何的类比，得到球面上的几何的相关结论；使学生了解一些非欧几何模型，从而思考平面几何模型与球面上的几何等非欧几何模型的差异。

Development of optical manufacturing, especially aspherical manufacturing, boosted the developing of space optics. Aspheric testing for large departures from reference wavefronts becomes the bottleneck of optical manufacturing. Off-axis TMA system presented in space cameras for large field, high resolution, long focal length challenges the manufacturing and testing for aspheric components .

光学制造技术的发展，尤其是非球面加工技术的兴起，促进了空间光学的发展，大视场、高分辨率、长焦距的航天相机离轴三反系统设计的引进对非球面的加工和检测都是很大的挑战，非球面的检测技术越来越成为光学加工的瓶颈，本文从检测角度出发，提出了基于电子虚拟样板的非球面检测技术概念，建立电子虚拟样板的数学模型。

In the same time, after shortly review the Halclanes description of the quantum Hall effect on 2-sphere S2, we obtain the corresponding noncommutative algebra An and the Moyal structure of the Hilbert space.

同时在回顾了Haldane在二维球面S~2上对量子Hall效应的描述，我们构造了S~2的非对易代数及其Hilbert空间的Moyal结构。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。