几何的

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。

But these methods limited by the expense of computing fundamental matrices and trifocal tensors or of the nonlinear optimization involved in computing epipolar tangencies. Through the studies of the invariants of the single axis motions, computational theories have been developed in this thesis to provide practical solutions for the problem of structure and motion from fitting the corresponding points in the whole sequence to its conic locus or conics for short.

在最近的研究中，一些研究人员利用视觉几何的方法从非定标的图象中对单轴旋转运动进行分析，提出了利用基本矩阵和三焦距张量求解单轴旋转运动中的关键参数——旋转角度的算法，但是该算法需要计算一系列相邻2图象的基本矩阵和一系列相邻3图象的三焦距张量，由于每个基本矩阵的自由度为7，每个三焦距张量的自由度为18，导致算法参数数量非常之大。

The article is divided into four chapters; The first chapter emphatically introduces the origin and the development of the Chinese geometry shape emblazonment.

全文共分为四章，第一章着重介绍了中国几何纹样的起源和发展，主要探讨了几何纹样的起源及原始社会彩陶几何纹样，原始社会到明清时期几何纹样发展的装饰特征流变，因为不同的历史时代几何纹样具有不同的形式特征，几何纹样纹样也受时代观念的影响。

After the researching about the styles, sculpting and the colors of the knitting products, the cause of the influence on the knitting from the Geometry pattern is summarized in the article. After the researching on the designing ways about Geometry patterns, the primary designing ways ang thoughts are summarized in the article. When working in the knitting factories, I tried to use what I have studied in the factories to my research. Then I added the modern technique to the geometry pattern designs. At last, the new design thoughts and the emphases of the market design for different age, jobs about the Geometry were brought forward.

本文在对毛衫上的几何图案造型、风格、色彩进行研究分析后，针对基本几何图案和组合几何图案分别总结出它们影响毛衫风格的主要因素，在对几何图案的造型手法进行深入研究分析后，归结出毛衫几何图案设计创新的主要手法和思路，同时综合在毛衫企业实习后的得到感受和经验，将几何图案结合现代毛衫工艺手法，针对不同年龄、职业、消费层次的市场提出不同的设计思路和实践操作要素。

GMODM is about the definition and calculation of geometric objects and topological relationships based on restrict plane graph. Geometric layer should be consistently maintained. This paper gives the algorithms.

它基于受限的平面图来定义几何对象和几何对象之间的拓扑关系，并给出了几何层的一致化定义以及一致化维护算法，它定义了几何对象的公共接口，使对几何对象的操作和拓扑关系的处理独立于几何对象表示。

Figure 10.1shows typical layouts of interchanges at three-legged junctions.The geometry of the interchange can be altered to favor certain movements by the provision of large turning radii and to suitable topography of the site.The trumpet interchange has been found suitable for orthogonal or skewed intersections.Figure 10.1a favors the left turn on the freeway by the provision of a semidirect connecting ramp.

数字10.1shows典型的布局交汇处，在三条腿的junctions.the几何的交汇处可以改变偏袒某些运动所提供的大转折半径和合适的地形的site.the小号交汇处已找到适合的正交或倾斜intersections.figure 10.1a ）有利于左转，就在高速公路上所提供的半连接匝道。

得 (1 2r ) A 1 + A2 = 0 由条件得 4π(1 )A1 + 2A2 = P P (1 2) A1 =, A2 = P 2π 2π由及二式的联立求解,得 42 Substitute the obtained A1 and A2 into the forgoing representations, we get (1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 43 将得出的A1及A2回代,得(1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 44 §8-4 Spherically Symmetric Problem For Space Among spatial problems, if the elasticity body's geometric shape,restraint condition and any external factors are symmetrical in a certain point (any plane which passes this point is all symmetrical one),then all stresses,strains and displacements are symmetrical in this point.

§8-4 空间球对称问题在空间问题中，如果弹性体的几何形状，约束情况以及所受的外来因素，都对称于某一点(通过这一点的任意平面都是对称面)，则所有的应力，形变和位移也对称于这一点。这种问题称为空间球对称问题。

This paper addresses the problem of real-time position and orientation estimation of networked mobile robots in two-dimensional Euclidean space with simultaneous tracking of a rigid unknown object based on exteroceptive sensory information extracted from distributed vision systems.

以知觉的数据从分配的视觉系统吸取了的 exteroceptive 为基础的硬未知的物体和同时追踪的二维欧几里得几何的空间的这一个纸住址即时位置的问题和被网络的移动机械手的定方位判断。

In order to draw a photorealistic surface, Bidirectional Texture Functions, a 6D texture function which extends Bidirectional Reflectance Distribution Function to include the self-shadowing, self-occlusion and inter-reflection effects, has been mentioned frequently in recent years. Its main drawback is its massive data size. To solve this, Spatial Bidirectional Reflectance Function techniques compress BTFs into reflectance model parameters. However, SBRDF cannot producethe self-shadowing and self-occlusion effects in real-world surface geometry. This work is aimed to this drawback. I find how self-shadowing and self-occlusion affect the surface by additional physical-based analysis. And I rely on two physical phenomena to divide self-shadowing and self-occlusion into two independent effects. First, self-shadowing is view independent. Second, self-occlusion is independent of lighting direction changes. After these analyses, I use SBRDF and additional self-shadowing and self-occlusion I found to render a photorealistic surface as non-compressed BTFs doing.

为了把物体表面呈现的更真实，六维函数BTFs ( Bidirectional Texture Functions)目前已经被使用的相当频繁，但BTFs的资料量实在太大而没办法直接使用，为了解决资料庞大的问题，传统的SBRDF以逼近光反射模型参数，来达到资料压缩的效果，但是SBRDF对於表面的凹凸所产生的阴影及遮蔽，不能达到逼真的呈现，为了改善这个问题，我们选择从物理方面，找出资料中阴影和遮蔽等属於表面几何的资料并去除，使参数更正确，同时利用两个物理现象去区分阴影及遮蔽为两个互不干涉资料，第一是阴影不会因视角不同而改变，第二是遮蔽不因光线方向不同而改变，经过这些分析，我可以利用SBRDF加上附加的阴影及遮蔽两种独立的效应，来达到彷佛跟未压缩过的BTFs一样的真实绘图。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。