查询词典 projective conic

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

In the first part, depending on three or more images, the main research work are listed as follows:(1) using SVD decomposition to realize projective reconstruction;(2) realizing camera self-calibration by solving Kruppa's equation;(3) recovering Euclidean reconstruction from projective reconstruction. Depending on only two images, the main researches are:(1) making out infinite plane homography matrix by using scene structure information, then recovering affine reconstruction from projective reconstruction;(2) making out the absolute conic images by using scene structure information, and then recovering Euclidean reconstruction from projective reconstruction.

在第一部分中，针对三幅及三幅以上的图像，主要研究：①利用矩阵奇异值分解实现射影重构，②通过求解Kruppa方程实现摄像机自标定，③由射影重构恢复欧氏重构；针对只有两幅图像的情况，主要研究：①利用场景结构信息求解无穷远平面的单应矩阵，由射影重构恢复仿射重构，②利用场景结构信息求解绝对二次曲线的像，由仿射重构恢复欧氏重构。

An image conic can be the projection of either a planar conic or silhouette of a conicoid. We show that at least three images, taken from the same position with different camera orientations, of two planar conics, or two conicoids, or one conic and one conicoid, are needed for the calibration, and a closed-form solution can be obtained. Our new conic based calibration technique requires no knowledge of camera's orientations, and relies solely on image correspondences.

在不同的方位拍摄三幅或三幅以上图像，每幅图像至少包含两个空间平面二次曲线、或两个二次曲面、或一个平面二次曲线与一个二次曲面的投影，利用图像之间的二次曲线对应关系，可以确定摄像机的内参数矩阵，同时可以获得摄像机不同方位之间的旋转矩阵。

Chapter Five shows the case study of the beauty of math in high school teaching. Conic section is taken as an example to unearth the beauty of mathematics in from the following three aspects: 1. the language beauty of conic section reveals the external formal beauty; 2. the methodological beauty and the logical beauty of conic section reflect the internal rational beauty; 3. the beauty of mathematics in conic section reveals the new value in internal knowledge structure of textbooks. Moreover, the application of the beauty of mathematics in high school math teaching is also discussed from the following four points of view: the pursuit of conciseness, the construction of symmetry, the utilization of unity and the discovery of uniqueness.

首先，以圆锥曲线教学为案例来挖掘中学数学教学中的数学美，具体从三个层次探讨①圆锥曲线语言之美，是数学美的外在形式美具体展现；②圆锥曲线方法美、逻辑美，是深层次数学美的内在理性美的反映；③在圆锥曲线的教学过程中，利用其数学美处理教材，揭示内在知识结构的新价值；其次，提出数学美在中学数学学习中的具体案例运用，并具体从追求简洁性、构造对称性、利用统一性和发现奇异性四个方面来举例探讨。

The paper puts forth that the numerical model of actual forming part is reconstructed by RE and the surface is regarded as actual trimmed surface, then grids and nodes mapping relationship between design model and actual forming part is acquired through compelling deformation simulation, and the design trimming line is dispersed into points according to a certain precision and the projective points and the coordinate values of the intersection points of projective line on the grids formed by discrete points are calculated along trimming direction, the new coordinate values of projective points and intersection points of projective line after deformation are calculated based on the mapping relationship of grids and nodes, the deformed trimming line can be acquired through fitting the points into curve.

本文提出通过逆向工程技术重构出实际冲压件的型面并以此型面为修边后实际冲压件的型面，然后采用强制变形仿真的方法建立设计模型和实际冲压件重构模型的网格和节点映射关系。将设计修边线按一定精度离散成点，然后根据修边方向计算出各点在网格上形成的投影点和投影线交点，根据之前计算出来的网格和节点映射关系就可以计算出投影点和投影线交点在变形后的新坐标，将其拟合成曲线就可以得到变形后修边线的形状。

We give three constraints of absolute conic images and use these constraints to evaluate absolute conic images and then to recover Euclidean reconstruction from projective reconstruction.

总结了三种关于绝对二次曲线的像的约束，并利用这些约束求解绝对二次曲线的像，进而实现从仿射重构恢复欧氏重构。

According to the fUndamental theorem of coniC In projective geometry any five points can decide one conic section .

在射影几何中，二次曲线定理告诉我们任意五点可以决定一条二次曲线。

Based on these theories, it develops a GIS map projection software using Visual C++ as a platform. The software consists of two parts: analytical ordinal transformation and analytical athwart transformation. Analytical athwart transformation implements map projective transformation with coefficients obtained through numerical method, which is also the main idea of this paper. Map projective transformation process is illustrated with the examples of Mercator projection and conic projection.

地图投影建立了平面上的点(用平面直角坐标或者极坐标表示)和地球表面上的点之间的函数关系，而地理信息系统以平面直角坐标形式通过计算机图形学的方法表示2维或3维地理空间信息，因此，地图投影起到了地球空间与地理信息系统之间的坐标转换的桥梁作用[1]。

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。

Based on projective geometry, the research works about 3D invariance's extractionand application have been done in this thesis as following:(1) The basic theories andconcepts in projective geometry are systematically summarized. It includes: the cameramodels of perspective imaging, projective collineation, cross ratio, a simple compare aboutinvariance among some geometry transformations, fundamental matrix, epipolarand 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。

You have to walk your own alk in this life.

次生中你必须走自己的路。

To start with, the thesis analyses ***ism in terms of the generic masculine words, word order and semantic derogation of women in greater detail.

论文首先从阳性词泛指，词序，词义的贬降等方面对英语中的性别歧视现象进行了详细的分析。