平面曲线的切割函数的分析性质

Analytical Properties of Tangent and Secant Function of Plane Curve

在平面区域的外形识别中,区域的边界曲线的双切圆方法占据重要的地位.平面闭曲线的切割函数在双切圆方法的研究中起着重要的作用.定义了平面曲线的拓广的切割函数,综合利用了代数和几何的方法,得到了平面曲线的拓广的切割函数分析性质,即拓广的切割函数是连续函数;光滑的曲线的拓广的切割函数是光滑的.

Bitangent circle method of boundary curve about plane region is very important to shape recognition about plane area. Tangent and secant function of plane close curve is crucial to the research of bitangent circle. With comprehensive utilization of algebra and geometry, we define extended tangent and secant function of plane curve, and obtain some analytical properties： extended tangent and secant func- tion is a continuous function~ the extended tangent and secant functions of smooth plane curves are smooth.