一种等距曲线生成与修正方法  

An Isometric Curve Generation and Correction Method

作　　者：曾徐佑泰 邓伟[1] 郑鹏城 崔新阳 ZENG Xu-you-tai;DENG Wei;ZHENG Peng-cheng;CUI Xin-yang(School of Science,Shanghai Maritime University,Shanghai 201306,China;School of Economics and Management,Shanghai Maritime University,Shanghai 201306,China;College of Electrical Engineering and Intelligent Control,Shanghai Maritime University,Shanghai 201306,China)

机构地区：[1]上海海事大学理学院,上海201306 [2]上海海事大学经济管理学院,上海201306 [3]上海海事大学电气工程及智能控制学院,上海201306

出　　处：《数学的实践与认识》2023年第5期271-278,共8页Mathematics in Practice and Theory

基　　金：中国高等教育学会高等教育科学研究“十三五”规划课题(2019SYSYB19)。

摘　　要：给出了一种等距曲线生成与修正方法.从离散点出发,将其经过傅里叶本轮法拟合以获得光滑简单闭曲线,同时根据等距曲线的基本定义给出初始等距曲线表达式,并由辐角原理来判断点与曲线的关系,以此给出推进的方向关于曲线所围区域内外部的判断,再指出了会导致局部曲线病态的原因,并根据曲线自交点划分子回路,由尖点及沿原初曲线主法向量指向的侧来判别该子回路是否需要去除.In this paper,an isometric curve generation and correction method is given.We start from the discrete points which are easier to obtain and fit them by Fourier principal wheel method to obtain the smooth original curve,and at the same time give the initial isometric curve expression according to the basic definition of the isometric curve,and judge the relationship between the point and the curve by the spoke angle principle,so as to give the advancing direction about the inside and outside of the area surrounded by the curve,and then point out the causes which will lead to the local curve pathology,and according to the curve self-intersection point,The sub-circuit is delineated,and the cusp point and the side along the main normal vector of the original curve are used to discern whether the sub-circuit needs to be removed.

关 键 词：等距曲线 傅里叶本轮法 辐角原理 自交点 尖点 

分 类 号：O187.1[理学—数学]