二次曲面

The available camera self-calibration is based on the image of the dual absolute quadric, but its elements have so large differences in magnitude that solutions are extremely sensitive to noise.

现有的自定标技术一般都是基于对偶绝对二次曲面像，由于对偶绝对二次曲面像元素在数量级上相差较大，在求解时必然会导致鲁棒性较差。

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。

All quadrilateral mesh automatic generation for regular quadric surfaces based on Auto CAD AME;2. Represent Quadric Surfaces Using NURBS and Calculate the Control Vertecs and Weights;3. Through study,the property is found out that planes cutting edgewise quadric curve and quadric intersections from the quadric surfaces become the harmonic division.

文中采用了射影几何的方法，证明了画法几何中关于两个二次曲面相交的著名的复切定理和蒙日定理，通过研究得出了周切线平面和交线平面成调和分割的性质，同时还得出了处于复切的二次曲面必存在相公切的二次曲面的性

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

Feature parameters are achieved by comparing the coefficient of standard representation and general representation. As for cone, parameter of general representation has no explicit geometric meaning and can not reflect design intent.

基于二次曲面的统一表示方程，采用最小二乘法进行参数拟合，通过对比其标准形式和二次曲面的统一表示方程，确定圆柱曲面特征带有明显几何意义的参数圆柱轴线法矢量、圆柱的中心和半径。

Firstly, using quadric surface to fit with given surface and calculate the error metric to identify free surface and general quadric surface.

首先用一般二次曲面方程拟合测量数据并计算曲面的拟合误差，比较拟合误差与阈值的大小来识别自由曲面和一般二次曲面。

In relation to the feature extracting, the first step is to extract the "simple" surfaces such as planes, natural quadric surfaces and tori. Planes considered as degenerated quadric surfaces, the quadric surface feature extracting should be more important in RE.

而在点云的特征提取中，首先提取的是包括平面、自然二次曲面(包括球面、圆柱面、圆锥面)和圆环面的"简单"曲面，我们认为平面是一种退化了的二次曲面，因此研究二次曲面特征的提取是其中首要的课题。

In this paper,using the classification for the point of general surface in differential geometry,a new combination that relies on the type of point on real conicoids is studied,and then can know more about the shape of conicoid.

利用微分几何中对一般曲面上点的分类来研究实二次曲面依点的类型的又一重要新组合，从而对二次曲面的形状有进一步的认识。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

Its implementation processes include:①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality;②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above;③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume.

其实现过程为：①对地震资料进行小波变换、分频重构，获得高质量的地震资料；②采用最小二乘法一次逼近，对局部二次曲面进行拟合，求取二次曲面拟合系数，并利用这些系数对网格化成图层面计算平均曲率和高斯曲率，再从两个曲率的不同线性组合，获取其他曲率；③将层面曲率推广，计算和重构曲率数据体。

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。