生成正多边形和圆的新算法

摘要

针对正多边形各顶点坐标的计算,构造了新的递推公式并加以证明.以新公式为基础给出了正多边形和圆生成算法,并对算法误差进行了分析.计算正多边形每个顶点需要两次乘法和两次加法,优于目前"多边形逼近法"所采用的顶点计算方法.算法具有构造简单、执行速度较快和精度高的特点.理论分析和上机验证算法可行,完全可以满足常规的应用.%Recursion formula is generated and proved in connection with the calculation of vertex coordinates of a regular polygon. Based on the new formula, the algorithm for generating regular polygon and circle is put forward, whose error analysis is given. The calculation of every vertex of a regular polygon calls for multiplication and addition twice respectively. The new method is better than that of polygon approximation. The algorithm is of the characteristics of simple construction, fast execution speed and high accuracy.