微分几何学

基于微分几何学的钢丝绳结构CAD

CAD of wire rope structure based on the differential geometry

自从1945年MacLane与Eilenberg提出范畴的概念和理论以来，它在数学的许多分支，例如代数几何学、拓扑学、微分几何学以及函数理论中均已有所应用。

In 1945 MacLane and Eilenberg introduced the concept and theories of categories , which have played a role in many branches of mathematics such as algebraic geometry , topology , differential geometry and functional theories .

给出一种重力作用下静止液体自由面的数值解方法。根据流体力学Young-Laplace公式和微分几何学主曲率方程，并利用液体自由面的对称性质，导出重力作用下静止液体自由面母线的常微分控制方程。

The differential equation governing the curvature of free surface of static liquid is deduced based on the Young-Laplace formula , the principal curvature function and the symmetry of the surface configuration simultaneously are employed .

微分几何学在地质构造定量研究中的应用

Applications of differential geometry to quantitative analysis of structural geology

本文应用现代微分几何学的方法，对机器人机构操作性能评价指标和轨迹规划问题进行了研究。

Some problems about robot manipulability are researched based on modern differential geometry .

他亲身参加实际的物理测量，激起了他对微分几何学的兴趣。

His participation in actual physical surveys stimulated his interest in differential geometry .

光学中的微分几何学简介

A brief introducting to differential geometry in optics

论文提出利用物体表面微分几何学特性的方法，这种方法通过两组数据的对比消除歧义。

We developed a method for using the differential-geometrical property of the object surface .

一般空间微分几何学

Differential geometries of generalized spaces

本文以拓扑学、微分几何学为理论基础，根据栅格数据栅格点的几何特征值，运用解析几何的方法，实施栅格数据到矢量数据的转换。

This paper presents a method for converting raster data into vector data based upon topology and differential geometry .

以微分几何学和矢量分析为工具，提出了复杂曲面加工路径规划的新方法。

Using differential geometry and vector analysis , a new tool-path generation method for freeform surface machining is presented .

为解决工程实际中的曲面展开问题，以微分几何学中可展面展开的基本原则等相关理论为基础，提出锥面和切线曲面展开的理论方法。

This paper discusses the method of development for developable surface in order to solve the development problem in engineering .

利用微分几何学的知识建立了一种登机模型，模型主要研究一般关系的时空。

We established an airplane boarding model with differential geometry , which is used to lime the space-time of general relativity .

由微分几何学原理得到计算主曲率的一般公式，克服了由薄板小扰度弯曲理论得到的主曲率计算公式的局限性。

The general equations of principal curvature derived from differential geometry overcame the limitations of previous equations derived from the theory of elastic thin plate with small deflection .

并根据微分几何学中局部椭圆对于光滑表面是最好的线性逼近的性质，提出可采用椭球基函数作为函数基进行曲面重建。

Based on the differential geometry theorem , which local ellipse is the best linear approximation for smooth surface , an ellipsoidal basis function surface reconstruction method is given .

阐述了在构造地质学定量研究中引入微分几何学的必要性，并讨论了在地质构造定量研究中的具体应用及相关的数值计算方法。

This paper elucidates the necessity of introducing differential geometry in the quantitative study of structural geology and discusses its applications in the quantitative study of structural geology and relevant numerical calculation method .

论文从微分几何学中白川德曲线的概念入手，提出广义白川德曲线，从工程实践的经验中抽象出白川德曲面，研究了它们的几何性质与内在联系。

Starting with Bertrand curve in differential geometry , Bertrand curve with broad sense is put forward , and Bertrand surface is refined from the practice experience . Their geometry nature and inner relationship are studied .

利用经典微分几何学的理论对曲面在空间中的弯曲状态进行了分析，定义了曲面弯曲的概念，指出了可展曲面的基本特征。

The bending status of curved surfaces is analyzed with differential geometrical theory and the concept curve of a surface is defined . As a result , the essential features of a developable surface are presented .

用圆柱形砂轮刃磨球头立铣刀端刃后刀面时，运用微分几何学中的测地曲率算法建立了砂轮与S型刃的曲率干涉校核数学模型。

Based on the geodesic curvature calculating method in differential geometry , a mathematical model for checking curvature interference between the major cutting edge and the cylindrical grinding wheel during grinding clearance face of a ball nose end milling cutter with S shaped major cutting edge is developed .

其次，以现代微分几何学为工具，采用选择性局部细分插值的方式对犁铧和犁胸曲面拼接处进行光顺，构造相对光顺的插值曲面，极大地改善了曲面的光顺效果。

Secondly , the fairing of surface to the joint of plough share and plough breast surface was made through adopting the selective partial subdivision interpolation way with the modern differential geometry , which can construct the relative smooth interpolating surface and improve the fairing effect of surface .