查询词典 foundation of geometry

This paper presents a fast approach to estimate the pose of human face from a monocular image, combining with the Chinese's appearance morphologic characteristic discovered by human appearance morphologic statistics, and cooperating with the theoretical foundation of projective geometry.

主要研究内容包括： 1。计算机辅助的面貌形态测量模型的建立。在人类学和形态学知识的基础上，分析了姿态估计技术需要使用的面貌形态特征，确定了测量涉及到的人脸特征点，形成可计算模型。

The foundation of geometry topology relation between points each other and being many redundancy data are two great difficulties in the process of reconstruction of scattered data.

散乱数据重建存在点与点之间几何拓扑关系建立困难和存在大量冗余数据两大难点。

This article also points out that"existence of squares","Out-In Complementary Principle","the principle of limit","Liu-Zu cross -section princeple","the area formula for rectangle and the volume formula for cuboid" determine the nature and lay the foundation of geometry in ancient China.

提出了我国古代论证几何所依据的原始命题，指出"存在正方形"连同"出入相补原理"、"极限原理"、"刘－祖截面原理"以及长方形面积公式和长方体体积公式确定了我国古代几何的性质，奠定了我国古代几何的基础。

In the fourth chapter, I analyze and contrast many architectural cases in history and modern times which ellipse were applied to, and explore the ellipse"s development in historic sense. The fifth chapter investigates the dynamic relationship between geometry and architecture based on ellipse"s geometric character, and analyzes ellipse architecture"s characters in symbolism, dualism, diversity and unity these four facets. In the sixthchapter, taking ellipse architecture as examples, I try to explore the relationship between the more general geometry"s purity and architecture"s complexity, and build the foundation for future exploration of geometry"s purity.

第四章从历史和现代两个方面展开了大量对椭圆形式在建筑中应用的个案和实例的研究与对比，探讨了椭圆形式在历史上意义的变迁；第五章以椭圆的几何特性为立足点，研究了椭圆几何--建筑之间的动态关系，从标志性，二元对立，多样和统一四个方面分析了椭圆建筑的特点；第六章以椭圆建筑为例，尝试探讨了更一般的几何的纯粹性与建筑的复杂性的关系，对几何纯粹性意义的挖掘为进一步的研究提供基础；第七章采用了类型对比的研究方法，分析了安藤忠雄和库哈斯两位设计哲学截然不同的建筑师对椭圆形式的使用；另外，以位置关系为线索，将椭圆和其他的几何形式结合起来，总结了一般情况下几何的纯粹性对建筑复杂性的作用。

In chapter 4, some vector mathematical definitions are first given to position tolerance zones; second, the principle of variation geometry is introduced, and the mathematical foundation of automatic generation of a approximate linear equation of tolerance design function by variation geometry is first proven; tangent method and two-point slope method based variation geometry are main studied.

第四章首先对一些位置公差带给出了矢量化的数学定义；然后介绍了变动几何的原理，首次论证了变动几何能产生近似线性公差设计函数的数学依据，并着重研究了基于变动几何的切线法和二点斜率法。

Nan; You are absolutely right, I have studied in pure abstract image and geometry mountain stone image for a dozen of years, they are the foundation of other images.

南溪：您说得很对，纯抽象的图像，几何山石图像，我研究十几年，这类作品实际是形成今天其它图像的基础。

Supported by the National Science Foundation of China, this thesis concentrates on the image sparse representation theories, methods and the image processing applications based on sparse representation. We make deeply study for the applications based on multiscale geometry analysis, theories of overcomplete sparse image representation and its applications, theories of sparse image representation via combined transforms and its applications.

本文在国家自然科学基金项目&联合基图像稀疏表示理论研究及其应用&的资助下，针对图像稀疏表示理论、方法以及基于稀疏表示的图像处理应用问题，重点围绕多尺度几何分析在图像处理中的应用、基于冗余字典的超完备图像稀疏表示理论及应用、组合变换图像稀疏表示理论及应用等内容进行了探索性的研究。

The foundation of arch dam usually is layer rock base, and the depths of the layer are small, it is common that several layer rock base contact with one layer element grid. According to the geometry relation and the property of shape function, a new element kind that includes 24 nodes has been proposed to dissect the dam and foundation effectively, whose shape function are independent. In fact the element can be looked as a hexahedron divided into five small hexahedrons. It can be simulate all kind of the condition of the base and the dam.

拱坝的地基一般是层状岩石地基，有的层厚度很小，这样就有多个岩层和坝体某层单元接触，本文根据岩基与坝体接触的几何关系，利用形函数的性质，提出24节点六面体层单元，这种单元实际上是将一个厚的六面体单元分成5个更薄的六面体单元而形成的，其形函数采用可以拆分的形式表达，因此可以方便地解决坝体单元的一、二、三、四个面与错动带接触的情况，可以模拟一、二、三、四个棱边与错动带接触的情况，还可以退化为12节点的四边形面单元，以及五面体层单元。

As a foundation of measuring the dynamic stress intensity factor, the influences of geometry and size of the caustics due to the crack propagation velocity are analyzed in detail.

特别分析了裂纹扩展速度对焦散斑和初始曲线的形状、大小的影响，为测量扩展裂纹尖端的动态应力强度因子K_1~d提供了依据，并通过拟合得到了以裂纹扩展速度为参量的修正因子表达式。

The foundation of these work is the analysis on the boundaries of domains, namely, CR geometry and analysis.

这些工作的基础是域的边界上的分析理论，即CR几何和分析。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。