The outer - contained parallel hexahedron smaller then that in the now existing document is presented according to the given point series , and the definition and solution model of smallest outer - contained cylinder are introduced 摘要根据已给点列，给出了比现有文献更小的外包容平行六面体，并引进了最小外包容圆柱的定义、求解模型。
It is proved by experiments that the resulting curves in some sense have nice smoothness and inherited some properties of subdivision curves in r ^ 3 space , such as the curves might interpolate or approximate the initial points 实验证明这类曲线具有较好的光滑度，并继承了r ^ 3空间中细分曲线的一些特征，如曲线可以是插值或者逼近原始点列。
The results indicate that start and end segment of interpolation curve are changed with different boundary conditions . interpolation and approximation of arbitrary data points and ship hull surface modeling based on nurbs is implemented 研究了nurbs的曲线与曲面的正算、反算算法及其边界条件的确定方法，实现了任意点列的nurbs插值与逼近及船体曲面造型。
A mathematical model to find contain sphere of space finite points was built , the problem was discussed that minimum contain sphere was transformed to function optimization and meanwhile an optimized solution was found with genetic algorithm 摘要建立了求空间点列包容球的数学模型，将求最小包容球问题转化为函数优化问题，并用遗传算法解决了函数最优解的求解问题。
A camera calibration method with co - line points is proposed , in which distortion center is located according to cross ratio invariability , and then distortion coefficients are calculated based on a line ' s central projection is a line 摘要提出一种用共线点列标定摄像机镜头畸变参数的方法，先根据交叉比不变性确定畸变中心，再利用直线的中心投影仍为直线这一性质确定畸变系数。
This paper studies the nonparametric estimates of general weight function of the nonparametric regression function with fixed design points , when the model error is martingale sequence , and we give the optimal convergence rate under some conditions 摘要当误差为鞅差序列时，研究固定设计点列情形下非参数回归函数一般权函数的非参数估计，并在一些基本条件下给出了估计的一致最优强收敛速度。
Recently , yamashita and fukushima [ 4 ] show that the sequence produced by the levenberg - marquardt method converges quadraticlly to the solution set of the equations , if the parameter is chosen as the quadratic norm of the function and under the weaker condition than the nonsingularity that the function provides a local error bound near the solution . however , the quadratic term has some unsatisfactory properties 最近yamashita & fukushima [ 4 ]提出，在弱于非奇异性条件的局部误差界条件下，如果选取的迭代参数为当前迭代点处函数值模的平方，则levenberg - marquardt方法产生的迭代点列二阶收敛于方程组的解集。
Presents a new method for fairing of curves which has a small flexibility based on fitting the derivative of second order of curves . we fit the derivative of second order of curves by a polynomial fitting , then find an indefinite integral of this polynomial to get a approach of curves . otherwise , we discuss the analyze of the error and the optimize of fairing to this arithmetic 提出了一种针对小挠度曲线的逆向曲线光顺算法，该算法直接拟合曲线型值点列的二阶导数曲线，然后通过两次积分来反求出光顺后的曲线，并对该算法的误差分析、效果分析、光顺优化等问题进行了深入探讨。
( 4 ) the special geometric restrictions like parallelism and perpendicularity implicated in vanishing elements are deeply studied . in single - view case , the theory is presented to interpret relationship between two planar lines by applying 3d invariants of vanishing points . in two - view case , the method on extraction vanishing point of an arbitrary sp atial line is described , and moreover , the theory is presented to interpret relationship between two elements in 3d space , such as two lines , two planes , line and plane , 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。
As a result of the require of cagd in airplane , automobile shipping and electrical appliance etc , fairing of curves and surfaces has become the hot subject in all over the world . this paper presents a new method for fairing of curves based on fitting the derivative of second order of curves . several practicality examples has been given to show the advantage of this arithmetic 本文针对目前曲线光顺算法存在的问题，提出了一种采用最小二乘法来拟合曲线型值点列的二阶导数曲线，然后通过两次积分来反求光顺曲线思想的曲线光顺算法，并给出了实际的算例来说明本文算法的优越性。
