查询词典 spherical geometry

There are convex spherical roller bearing ring raceway is spherical-shaped, with concave spherical roller bearing axle ring raceway is spherical-shaped.

有凸球面滚子的轴承座圈的滚道为球面形，有凹球面滚子轴承的轴圈滚道为球面形。

In this study, a commercial CAD/CAM Software is used to plan and generate the multi-axis tool path, and a table rotating/tilting type five-axis machining center is used to perform the experimental machining operation. The material of the die studied is NAK 80 die tool steel, and the geometries are modeled as concave and convex spherical surfaces. Milling parameters considered are spindle speed, feed rate, and different types of cutting tool path. The experimental results show that the surface roughness for concave spherical surface is about 0.247 μm and roundness is about 0.0283 mm and the surface roughness for convex spherical surface is about 0.250 μm and spherical roundness is about 0.0551 mm under the cutting conditions mentioned in this study.

本研究的实验方法与步骤包括利用商用CAD/CAM系统针对实验对象规划三轴/五轴同动加工路径，并经后处理程式转换，在本实验室之平台倾斜/旋转型之五轴加工机上进行实验，实验对象为NAK80模具钢材料之凹与凸球形曲面之加工，此外考虑的切削条件有主轴转速、进给速度、加工路径等，在本研究所设定之最佳切削条件下，凹球形曲面之真圆度约为0.0283 mm，粗糙度为0.247 μm，而在相同切削条件下，凸球形曲面之真圆度为0.0551 mm，粗糙度为0.250 μm。

Spherical trigonometry is a part of spherical geometry, mainly in the processing, discovery and interpretation of polygons on the spherical surface contact angle and the edge and relevance.

球面三角学是球面几何学的一部分，主要在处理、发现和解释多边形在球面上的角与边的联系和关联。

Ah specifically, the angle of the sphere and the relationship side of spherical geometry, spherical trigonometry is a part, mainly in the processing, discovery and interpretation of polygons on the spherical surface contact angle and the edge and relevance.

具体一点啊研究球面上的角与边的关系球面三角学是球面几何学的一部分，主要在处理、发现和解释多边形在球面上的角与边的联系和关联。

It thinks that Complete Principle of Measurement inherited the Writing Style of Elements. Secondly, it is taken out five key parts——plane geometry, solid geometry, conic, spherical trigonometry and spherical astronomy part——to comprehend. The main contents of mathematics and astronomy involved in Complete Principle of Measurement have been set up respectively in accordance with the characteristics of their subject.

其次，又按照学科分布从中抽出平面几何、立体几何、圆锥曲线、球面三角和球面天文等五部分内容进行重点解读，认为《测量全义》中所涉及到的主要数学和天文学内容已经按照学科特点分别形成和建立起来，为后来西学的进一步传播做出了贡献。

Based on the features of spherical geometry, the writer thinks thatit is an effective way for students to learn spherical geometry wellby "practising mathematics" themselves.

鉴于球面上的几何内容的特点，笔者认为使学生切身体会"做数学"是学好球面上的几何的有效途径。

Spherical geometry;; spherical triangle;; non-Euclidean geometry;; Euler formula;; cognition;; SOLO taxonomy theory

论文导师张红，论文学位硕士，论文专业学科教学论文单位四川师范大学，点击次数 8，论文页数 73页File Size3160K

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

Based on projective geometry,the research works about 3D invariances extraction and application have been done in this thesis as following:(1) The basic theories and concepts in projective geometry are systematically summarized. It includes:the camera models of perspective imaging,projective collineation,cross ratio,a simple compare about invariance among some geometry transformations,fundamental matrix,epipolar and epipolar line in epipolar geometry,and so on.

基于射影几何理论，论文围绕3D不变特征的提取和应用进行了如下的研究工作：(1)系统总结了射影几何中的若干基础概念，包括：透视成像的相机模型、射影对应、交比不变量、基于不同几何变换下的不变量的简单对比、对极几何中的基础矩阵、对极点、对极线等。

Green function defined inphase space differs from one in coordinate space by its struc-ture which exhibits nonlocatity in coordinates and oscillatorybehavior with respect to momenta.

在相空间中定义的Green函数不同于通常坐标空间的Green函数，在结构上显示出对坐标的高度非局域性，而对动量则显示出振荡行为。

The upper front part of a saddle;a saddlebow.

前鞍桥马鞍前面的上部分；前鞍桥