几何基础

Based on the spherical and plane triangular relationships of the spacecraft, the center of the earth, the projected-cloud and the true-cloud, several error analyses were done for the computing of parallax with different intersection angle of crafts, and incorrect images match.

利用卫星、真云、投影云和球心的平面球面几何关系，在几何反演方法的基础上，对卫星间隔和图像错误匹配带来的反演误差进行了分析。

Based on the spherical and plane triangular relationships of the spacecraft, the center of the earth, the projected-cloud and the true-cloud, several error analyses were done when one pixel was incorrectly matched with different intersection angle of crafts and the same cloud height.

利用卫星、真云、投影云和球心的平面球面几何关系，在几何反演方法的基础上，分析了在固定云高、不同卫星间隔和固定卫星间隔、不同云高这两种情况下，错误对比1个像素导致的可能的反演误差。

A new and efficient geometrical correction algorithm is proposed for MODIS IB data, and possesses of the merits of forward mapping and inverse mapping algorithms; 3. Algorithms to remove stripe noise in MODIS IB data are developed, including Fourier Transform, Wavelet Transform and interpolation method; 4. MODIS data composite algorithm is developed, and a 16-day composite map covering entire China and its outward is produced.

本文介绍了开发MODIS数据基础处理软件的基本算法和成果，主要包括：(1)用C++语言开发和实现了MODIS数据基础处理软件；(2)研究和发展了一个普适的、全新的、兼有前向映射和后向映射优点的MODIS 1B数据几何纠正算法；(3)研究和实现了MODIS条带噪声消除算法，包括傅立叶变换、小波变换和插值三种算法，并对其进行了比较；(4)研究和实现了MODIS影像合成算法，并在此基础上完成了中国及周围地区16天MODIS彩色影像和植被指数的合成。

First, this paper, in the field of intrinsic geometry, studies the geometric problems on garment design, as well as applies the frame and semi-geodesic coordinates to prove the fundamental theorem of being a developable surface.

文中首先在内在几何学的层次上，研究了服装设计所涉及的几何学问题，应用标架与半测地坐标方法证明了曲面成为可展面的基本定理，研究了可展面的分类及其性质，考虑到服装三维几何造型的需要，证明了组合式可展面各组成片相切连接条件的命题，作为构造可展面的理论依据，证明了单参数平面族的包络面必为可展面的命题，在此基础上发展出服装几何造型的"刮大白"方法以及相关的三种构造可展面的解析方法。3D→2D的变换是三维服装CAD的重要内容之一，其几何学实质是曲面的定长映射，文中总结了定长映射即可展面在平面上展开的基本准则，在这一准则的指导下，结合服装设计与相关领域的要求，讨论了可展面在平面上展开的解析方法与数字方法，上述内容确立了服装设计几何学的基本框架。

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。

Parametrization is a crucial problem in computer graphics,computer aided geometric design and digital geometric processing.

三角网格的参数化是对三角网格的几何和拓扑信息作进一步处理的基础，它在计算机图形学、计算机辅助几何设计和数字几何处理等领域有着广泛的应用。

The special geometric restrictions like parallelism andperpendicularity implicated in vanishing elements are deeply studied. In single-view case,the theory is presented to interpret relationship between two planar lines by applying 3Dinvariants of vanishing points. In two-view case, the method on extraction vanishing pointof an arbitrary spatial line is described, and moreover, the theory is presented to interpretrelationship between two elements in 3D space, such as two lines, two planes, line andplane, and so on.

4详细论述了消失元素(消失点、消失直线、消失平面等)所体现的垂直、平行等特殊几何约束关系；对单视图，提出了一种利用消失点列的3D不变量解释平面直线关系的方法；对双视图，提出了利用自共轭三角形和对极几何约束，提取任意直线的消失点的算法，并在此基础了提出了一种利用消失元素的3D不变量解释直线间、直线与平面间、平面间等多种空间几何关系的方法。

A new 3D human face model is put forward in this paper after some characters of the human face and the muscle tissues on the face are researched and some actions of the facial expression are analyzed. In this model we divide the whole face into some parts according to its structure. To each part, we apply the principle of elastomer metamorphosing to our face model, so a specific face model can be easily gotten by modifying a common face model.

本文在分析和总结了前人工作的基础上，深入研究了人脸的生理特征、面部肌肉组织结构，分析了人脸面部表情的基本动作，提出了将人脸整体分解为若干个小块的三维人脸几何模型，并根据力学中的弹性体形变原理，将弹性体的形变应用于上述基于面分块的三维人脸几何模型，使特定人脸几何模型的建立变得简单、效率高。

Basic symbols;Coatings;Definition;Definitions;Dimensions;Drawing specifications;Drawings;Engineering drawings;Finishes;Geometric;Geometrical product specification;GPS;Graphic representation;Graphic symbols;Inscriptions in a drawing;Letterings;Machining;Machining tolerances;Marks;Product specifications;Production processes;Products documentation;Ratings;Reference length;Reference lines;Representation of characters;Roughness;Roughness value;Specification;Statement;Surface properties;Surface roughness;Surface texture;Surface treatment;Surface-roughness measurement;Surfaces;Symbols;Technical drawing;Treatment;Wear-quantity

中文标题产品几何量技术规范。技术产品文件中表面结构的表示方式中文主题词图形表示；参考长度；尺寸；加工公差；表面性质；产品规范；覆层；制图规范；精整；表面粗糙度；粗糙度；表面粗糙度测定；表面结构；磨损量；图纸标题；表面处理；技术制图；几何的；基准线；图形符号；符号；标记；加工工艺；文字书写；产品文件；定义；表面；粗糙度值；工程图；额定值；产品几何量技术规范；GPS；叙述；处理；图纸；机械加工；字符表示；基础符号；规范验收

Based on the framework of wheat morphology visualization, the 3D geometric modeling technologies of wheat organs were investigated, and the organ geometrical models were developed with characteristic architecture parameters. The model included three submodels: leaf geometry, stem geometry and wheat spike geometry submodels.

本研究以小麦作物为对象，在提出小麦形态可视化技术框架的基础上，首先研究了小麦不同器官的三维几何建模技术，构建了基于器官形态特征参数的几何模型，包括叶、茎秆和麦穗几何模型。

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。