分析几何学

Through the analysis of geometrical features of Mesozoic-Cenzoic sedimentary basins in the Lower Yangtze area, we think them to be asymmetric tectonic sinked basins. They are bounded by a set of boundary fault system and failed conjugate fault, and they are segmented along axes.

通过对下扬子区中、新生代非对称性沉积盆地的几何学特征分析，认为这种非对称性构造沉降盆地在剖面上表现为由一组主边界断层和一组天折的共轭断层所围限，而且在走向上具有分段特征。

Formulations for analysis of geometries with closed form deviation equations are presented.

提出了以闭型偏差等式形式给出的各种几何学分析公式。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

Mathematical Notes;Descriptive Geometry;Stereonet Techniques;Stress And Strain;Analysis of Complex Structures

数学注解；画法几何学；立体图技术；应力与应变；复杂结构分析

Based on image generative model, in combination with independent component analysis model and wavelet model, the basis function representation of image information as well as its key problem are studied in this thesis.

基于基函数的图像信息表示方法研究是目前图像处理技术的前沿课题，涉及到统计学、几何学、图像处理与分析、模式识别、视觉生理学等众多学科。

Carnot wished "to free geometry from the hieroglyphics of analysis ".

Carnot希望"把几何学从分析学的画符样难懂的文字中解放出来。"

Results A view of better understanding origins of Gaussian intrinsic differential geometry is presented,and the intrinsic relation between Gauss′s thought of intrinsic differential geometry and of his non-Euclidean geometry is brought to light and discussed.

结果 总结分析了高斯建立的内蕴微分几何的思想和渊源，揭示了其与非欧几何学的内在联系。

2 ANALYSIS CONDITIONS The behavior of a tyre involves complicated non- linear problems such as geometric,material,and boundary problems.

两种分析的情况：一个轮胎的性能涉及到复杂的非线性问题，例如几何学，材料学和边界问题。

With differential geometry knowledge, the local characters of the blade surface are analyzed. Based on researching the cylindrical cutters osculating location, the methods to calculate the osculating location of the conic cutter and the torus cutter are discussed. A method of tool path planning based on the second order osculating method is preferred.

利用微分几何学知识，分析了螺旋桨桨叶曲面的局部特征，在研究圆柱刀二阶密切法规划刀位的基础上，探讨了圆锥刀和圆环刀的二阶密切刀位计算方法，采用二阶密切法规划刀位可以显著地提高加工精度。

Based on mathematical analysis, elastic geostress field is a symmetric second-order tensor, which can be expressed as symmetric matrix and studied by its eigenvalue and eigenvector.

根据对二阶张量的数学分析，通过求取二阶张量的特征值与特征向量，导出了对称张量在空间几何学中对应的二次曲面。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失