几何化

Concept of compound geometric design for at-grade intersection is presented, and in functional, economic and environmental concept's way at-grade intersection's geometric design is elaborated. Qualitative and quantitative research is provided for intersection's channelized and flared design, including detailed analyses for pocket lane, crossway and traffic island. When conventionally channelized design of signalized intersection isn't possible or these effects are poor, an unconventional geometric design for intersection is brought out and 5 kinds of modes are systematically studied. An example is illustrated to urban signalized intersection compound design's splendid future and deep importance.

对平面交叉口提出复合型几何设计理念，从功能理念、经济理念和环境理念出发研究信号交叉口的几何设计，对交叉口拓宽渠化设计中关键技术环节（专用车道、人行横道和交通岛）进行详细定性和定量分析；针对不允许进行渠化设计或渠化设计效果不佳的信号交叉口，结合交叉口的相关道路设施提出了非传统设计方法，并建立和分析了典型的5种非传统设计模式；同时结合事例说明复合型几何设计理念在城市信号交叉口设计的崭新前景和重要意义

This thesis contributes to geometry compression in the following aspects: Proposes a method of progressive spherical mesh parameterization based on local parameterization by directly projecting the deleted vertices to its neighborhood. Based on spherical mesh paramterization, an adaptive subdivision remeshing method by progressivly redistributing of sampling points is proposed, by this means, the main geometry information of the original mesh can be captured with only a small amount of samples, it can also be used in mesh simplification. By regarding attributes binded on mesh vertices as geometry signals and transferring them onto a uint sphere by means of spherical mesh parameterization, meshes with different attributes are compressed with spherical wavelet successfully with high compression rate. As a kind of lossy geometry compression technique, two mesh simplification algorthimes are also presented in this thesis.

归纳起来，本文的主要贡献有：提出了以直接投影局部参数化方法为基础的网格累进球面参数化方法；在网格球面参数化方法的基础之上，提出了一种基于累进优化布点方案的网格细分采样方法，该方法可以用很少的采样点就可以捕获到网格的主要特征，因此我们也将其用于后面的网格简化工作当中；通过将网格顶点上定义的各种属性看成几何信号，并以网格球面参数化为手段将几何信号迁移到单位球面上，从而成功地实现了用球面小波对各种几何信号的压缩；作为一种有损压缩方法，本文还提出了基于统一距离的网格简化算法和基于重采样的网格简化算法。

Based on the summarizing of the exiting algorithms of the texture mapping and antialiasing, this paper goes deeply into the basic theory and processing of texture mapping. The texture compress algorithm which can satisfy the need of the memory and time is given for the stochastic sampling in the inverse texture mapping; the geometry transformation in the texture mapping are discussed and the concepts of the unitary parametrization and the patch parametrization is proposed, some kinds of the unitary parametrization methods of parametric surfaces and the geometry transformation in the patch parametrization are also presented; in order to solve the aliasing in the parametrization of intermediate surface-sphere in two-part texture mapping, an area-preserving transformation is presented also; to improve the quality of the graph the aliasing in the texture mapping is analyzed from the aspect of signal process, and the modified summed-area tables algorithms is proposed; the distortion of the scanline conversion algorithms under perspective transformation is analyzed and the proper interpolation algorithm is presented so the aliasing problem of the polyhedral object after the unitary parametrization is efficiently solved.

本文在总结现有的纹理映射和反走样算法的基础上，深入研究了纹理映射的基本原理与过程，根据反向纹理映射对纹理随机采样的特殊要求，提出了一种可满足存储空间和寻址时间的纹理压缩存储算法；通过对纹理映射中几何变换理论的进一步深入探讨，提出了整体参数化和面片参数化的概念，并给出了参数化曲面的各种整体参数化方法和面片参数化的几何变换形式；针对现有的两步映射算法所存在的中间曲面—球面的参数化问题，提出一种等积映射方法，较好地实现了由非参数化面片拼接而成的多面体表面的纹理映射；从信号采样的角度深入分析了纹理映射中走样产生的原因，提出了改进的区域求和表算法，使图形生成的效果有所提高；还分析了一般的扫描线算法在透视变换中所存在的问题，提出了一种正确的插值算法，从而解决了整体参数化后多面体表面纹理映射的几何变形问题。

I think Haiwang regarded the land of the lotus and itself; He abandoned the details of lotus and focused on the object-oriented structure and only organic color contrast (such as the use of a lot of black); He considered only Light color with the seasons and the geometric structure of the landscape. It's different from the only source style and the natural tendency of Impressionism . It has more spirits with the traditional Chinese culture and the aesthetic value.

我想这与李海旺把荷花与生长它的大地联系起来描绘有关系；与他舍弃了荷花的细节，只注重对象的有机的结构和色彩的单纯对比有关系；也与他只考虑光色的季节和几何化的风景构造，也不同于印象派只重光源色的自然主义倾向而获得了与中国传统文化相通的审美价值。

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

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。

God eternally geometrizes.

上帝永远将一切几何化。

All formulations are completed from clarifying the specific natural phenomenon, to geometrizing a system, and finally to deducing the targeted formulas by appropriate synthesis of knowledge in physics and mathematics.

全部的方程式推导都从解释特定的自然现象开始，然后解释如何将物质系统几何化，最后再解释如何把适当且相关的物理和数学知识加以合成发展出目标参数的方程式。

At last,based on the decomposition of gauge potential and the idea ofgeometrization of Gross-Pitaevskii equation,an effective gauge dynamics forBose-Einstein condensates is proposed.

最后，基于规范势分解以及Gross-Pitaevskii方程的几何化思想，论文提出了Bose-Einstein凝聚体的有效规范动力学。

His other contributions include relativistic cosmology, capillary action, critical opalescence, classical problems of statistical mechanics and their application to quantum theory, an explanation of the Brownian movement of molecules, atomic transition probabilities, the quantum theory of a monatomic gas, thermal properties of light with low radiation density (which laid the foundation for the photon theory), a theory of radiation including stimulated emission, the conception of a unified field theory, and the geometrization of physics.

的经典问题和它们的量子理论的应用，解释了布朗分子运动，原子跃进概率，单原子气体的量子论，地辐射密度的光的热性质，包括受激发射的放射理论，统一场论的概念和物力几何化。爱因斯坦写了多于50篇的科学著作，也包括非科学的书。1999年爱因斯坦被时代杂志封为&世纪人物&，一份有卓越成就的物理学家的民意测验封他为无论何时都是最伟大的物理学家。现代文化认为&爱因斯坦&和天才是同一个意思。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐