曲线的假拐点及其甄别  

Discrimination on False Inflection Point of Curves

作　　者：张学山[1] 方涛[1] 王天波[1] 

机构地区：[1]上海工程技术大学基础教学学院,上海201620

出　　处：《上海工程技术大学学报》2010年第4期313-316,共4页Journal of Shanghai University of Engineering Science

基　　金：科技部创新方法工作专项项目(2009IM010400)

摘　　要：根据参数方程所确定的函数的二阶导数y″(x)在某个参数值t0的两侧邻近异号所得到的曲线上的点有可能是假拐点.究其原因,是将"y″(x)在参数t0的两侧邻近异号"等同于"y″(x)在x0的两侧邻近异号",导致误判.解决的办法是在求出可能的拐点以后,进一步利用拐点处切线的特征来识别拐点和假拐点.采用微分几何的曲率公式,可合并处理曲线弯曲程度、弯曲方向和拐点的问题.When the second derivative y″（x） of function of a curve given by parameter equation has different signs on two sides of a certain parameter value t0,the corresponding point determined may be a false inflection point.The reason why the false inflection point is erroneously claimed as an inflection point is that the different signs of y″（x） on the two sides of t0 is regarded as the different signs of y″（x） on the two sides of x0.The solution is that the characteristic of the tangent line at any inflection point can be utilized to discriminate the true or false inflection point after getting possible inflection points.By using the curvature formula in differential geometry,the curved degree,the curved direction and the inflection point of a curve can be identified together.

关 键 词：曲线 拐点 曲率 

分 类 号：O186.11[理学—数学]