解析几何学

On this basis,the PDC bit's fivepoint survey theory is developed,and a series of formulas are derived,applying PDC bits' geometry and analytic space geometry.

在此基础上，运用PDC钻头几何学和空间解析几何学中的四点共面、行列式、坐标变换的知识，提出并推导出了PDC钻头的五点测绘理论及系列公式。

Comprehensively making use of the basic theory, such as Space Analytic Geometry, Gear Meshing Engagement Theory, Method of Mathematical Calculation, Theory for Error Analyzing and Data Processing, the author has established the mathematical models of the new method, which has included the analytic mathematical model for precision orientation, the mathematical model for the ball's diameter and the measuring diameter, the mathematical model about the ball's centre, the calculation model for tooth alignment diviations and the model for tooth alignment error evaluation.

本文综合应用空间解析几何学、啮合原理、计算方法、误差理论与数据处理等有关基础理论，推导建立了新方法的数学模型，包括：确定定位关系的解析法数学模型，测球直径与测量半径的数学模型，测球球心的数学模型，齿向偏差的计算模型以及齿向误差的评定数学模型等。

The analytical geometry is used to study the formulas of Moire fringes for the measurement of screen line, to analyze the geometric forms and their properties of Moire fringes , and further discusses the bases of theory for the measurement of screen line.

本文用解析几何学方法研究测量网线的莫尔条纹方程，分析莫尔条纹的几何形状与特性，并且进一步讨论网线测量的理论依据，旨在深刻地揭示测量网线的莫尔条纹原理。

Rene Descartes (1596 - 1650), the founder of analytical geometry, is also known as the father of modem philosophy.

勒内 -笛卡尔(1596-1650)，解析几何学的创始人，也称现代哲学之父。

The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.

这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。

In addition, depending on the method of numerical simulation and theoretical analyses, some kinematic and geometric features of 0° involute—enveloping worm gear drive, such as meshing surface, first—type limit, second —type limit, worm surface, the numerical representation of contact line and bearing contact, are systematically studied. These relevant conclusions provide an important basis for the design and manufacture of new type worm gear set. As we predict, the method of numerical simulation has special effect in solving the question of complex conjugate surface.

综合利用仿真方法与解析手段，对0°渐开线包络蜗杆传动的啮合面、一类界限、蜗杆齿面构成、仿真接触线及仿真接触域等运动几何学特性进行了系统研究，有关结论为此种新型蜗杆副的设计与加工提供了重要基础，并且显示出数字仿真方法在研究复杂共轭曲面问题时所具有的特殊功效。

First, this paper, in the field of intrinsic geometry, studies the geometric problems on garment design, as well as applies the frame and semi-geodesic coordinates to prove the fundamental theorem of being a developable surface.

文中首先在内在几何学的层次上，研究了服装设计所涉及的几何学问题，应用标架与半测地坐标方法证明了曲面成为可展面的基本定理，研究了可展面的分类及其性质，考虑到服装三维几何造型的需要，证明了组合式可展面各组成片相切连接条件的命题，作为构造可展面的理论依据，证明了单参数平面族的包络面必为可展面的命题，在此基础上发展出服装几何造型的"刮大白"方法以及相关的三种构造可展面的解析方法。3D→2D的变换是三维服装CAD的重要内容之一，其几何学实质是曲面的定长映射，文中总结了定长映射即可展面在平面上展开的基本准则，在这一准则的指导下，结合服装设计与相关领域的要求，讨论了可展面在平面上展开的解析方法与数字方法，上述内容确立了服装设计几何学的基本框架。

Each size structural distortions position, quality, scale, distributing and combined rule, such as drape, fault, joint, structural foliation and lineation, are found out through the base methods of the geometry, kinematics and dynamics.

以几何学、运动学和动力学全面构造解析为基本方法，查明各种规模构造变形形迹(褶皱、断裂、解理、面理、和线理等)的产状、性质、规模、分布和组合规律。

A formula for the volume of arbitrary quadrangular prism is given by using vector colculus.

本文利用空间解析几何学中的矢量方法和原理求解底为任意凸四边形的四棱柱体积、并推导出其体积公式。

In this paper, the effects of the rigid body motions and low frequency surface errors on the image quality were analyzed. Quadratic equations were used to build the mathematical model of the Wolter type I and II X-ray telescopes and reduce the computational complexity of ray tracing. With the help of a self-developed optical surface analysis code, the effects of the perturbations of the mirrors on the image quality was analyzed and the growth of the image spot formed by deformed telescopes was calculated, this is important for giving the reasonable fabrication tolerance.

在本篇文章中，详细分析了刚体运动误差和低频表面误差对成像质量的影响；使用空间解析几何学的二次曲面方程建立Wolter I、II型X射线掠入射望远镜镜片的数学模型，降低光线追踪的计算复杂度；借助自主开发的光学仿真软件分析了国内研制的X射线成像望远镜的刚体运动误差和低频表面误差对成像质量的影响，计算出像点艾里斑半径均方根值随误差变化的增长率，对工程上提出合理的制造公差的误差容限有重要的指导意义。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！