用计算机实现几何变换

本文探讨了用计算机实现各种几何变换的思想和方法,利用齐次坐标将射影变换、仿射变换、欧氏变换统一在高维的线性变换中,将抽象的数学思想通过计算机具体的显示出来     

关于曲面与空间曲线参数方程的参数个数

从两个方面论述了曲面的参数方程用双参数表示 ,而空间曲线的参数方程用单参数表示     

关于曲线论基本定理的一个注记

本文在曲线论基本定理的基础上,进一步给出了空间曲线如何在定解条件下的求解问题。     

曲线的参数方程与含参数的曲线方程

曲线的参数方程与含参数的曲线方程是解析几何中两类相互区别又相互联系的常见问题.当参数变化时,参数方程表示一条曲线,而含参数的方程通常表示一个曲线系.例如参数方程(x=cost y=sint)表示一个圆(圆心为原点,半径为1),而含参数的方程 x~2 y~2=t~2表示一个圆系(圆心为原点,半径为|t|).研究参数方程与含参数的方程,不仅有助于解决解析几何中的一系列问题,而且有助于理解函数思想的实质,提高对变量数学这一高中数学的主体的认识,发展数学思维.一、曲线的参数方程及其应用     

关于参数方程所表示曲线的对称性

本文讨论了参数方程所表示的曲线关于原点或关于数轴的对称性，给出了对称性的若干充分条件。     

关于齐次线性方程组的一个注记

给出了命题“齐次线性方程组Ax=0(A为方阵)有非零解的充分必要条件是|A|=0”的基于行列式理论的一个证明，并探讨了这一证明在教学中的应用。     

位似曲线与单参数曲线族

先给出了位似曲线与相似曲线的定义,然后在此基础上推导出若干结果,即:两曲线位似的充分必要条件;单参数曲线族是位似曲线族的充分必要条件;位似曲线的共有性质。     

关于参数曲线围成平面图形面积的几个计算公式

本文将参数曲线围成曲边梯表的面积公式拓广么围成封闭图形的面积的几个计算公式，并举例说明一题多个公式的解法。     

关于曲线收缩流中两个单调性公式的注记

主要研究在曲线收缩流中的两个单调性公式．在几何流的研究中,熵的单调性起着重要的作用．Gage和Hamilton首先研究了在平面曲线收缩流中的曲率玻尔兹曼熵的一阶和二阶导数,并定义了一个除非在收缩圆上否则严格递增的单调性公式,称之为W熵,它是以弧长s为参数的．另一个则是Hamilton在研究曲线收缩流的紧致的古典解分类时提出的一个单调性公式,称其为I公式．以角度θ为参数对这两个单调公式进行证明．     

五次参数插值样条曲线

给定有序的空间点列,Pi(i=0,1,…,n),构造了一类参数五次插值样条曲线,该插值曲线的每一段由四个基函数构成,曲线段之间是C^2连续的,且曲线可以局部修改。     

用Origin变换坐标精确测量RLC并联谐振电路的共振频率

介绍了用Origin变换坐标，将不对称的RLC并联电路的幅频特性曲线对称变换．从而精确求解其共振频率的方法．该方法利用Origin的LabTalk编程和坐标变换等功能．使实验的数据分析和处理过程变得快捷方便．同时又减小了实验误差．     

Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter

In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.     

Bézier curves with shape parameter

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bemstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.     

Estimation of the J-resistance curve for Cr2Ni2MoV steel using the modified load separation parameter S_（pb） method

Based on load separation theory, the load separation parameter Spb method is an effective approach for estimating the J-resistance curve from records of load versus displacement directly, using one sharp cracked specimen and an additional reference blunt cracked specimen. However, the effect of the reference blunt cracked specimen on J-resistance determination was not explicitly considered in past work. In this paper, a modified load separation parameter Spb method was developed to eliminate this effect, and then a unique estimation of instantaneous crack length for one sharp cracked specimen could be obtained. Furthermore, a forced blunting calibration method was also adopted to determine the instantaneous crack length in the load inseparable region, referring to a normalization method. Experiments on steam turbine rotator steel Cr2Ni2MoV were carried out to estimate J-resistance curves using an unloading compliance method. By removing unload and reload data from load-displacement records, the J-resistance curve for the same sharp cracked specimen was estimated using the modified separation parameter Spb method. The results indicate that the modified Spb method completely eliminates the effect of the reference blunt cracked specimen on the instantaneous crack length determination of the sharp cracked specimen. However, different J-resistance curves in a small range of crack extension are present when different blunting coefficients are used in the blunting line equation. The J-resistance curve obtained from the modified Spb method agrees well with that obtained from the compliance method.     

浅析封闭曲线上的曲线积分

本文介绍曲线积分的一种新解法,主要利用求条件极值的方法确定积分区间;利用封闭曲线的特征确定被积函数的形式;利用二次型化简曲面方程。并给出了解决此问题的一般方法。     

论几何图案在服饰上的应用

几何图案在服饰上面的应用经历了很多不同的时期并产生不同的风格,从古至今的发展让我们在服饰上得到了广泛的应用。     

热力学统计物理中的Legendre变换

试图以特性函数为起点,从Legendre变换出发,研究热力学统计物理理论的系统性.     

Mannheim曲线的性质

给出Mannheim曲线及其伴随曲线的若干条性质.     

极坐标系下使用微元法需要注意的一个问题

分析定积分微元法中微元的条件,并通过讨论极坐标情形下求平面图形面积和平面曲线弧长这两个实例说明使用微元法的关键.     

Bézier curves with shape parameter

In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface. Project supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No. G2002CB12101)