求解最大内切圆的一种新方法

提出了一种求解最大内切圆的新方法,给出了最大内切圆圆心坐标值的计算公式,该方法的基本思路是:首先在被测轮廓上选取初始三点,并保证这三点构成一个锐角三角形;接下来通过给出的公式计算出这三点所在圆的圆心坐标值,被测轮廓各点到该圆心的距离序列;最后判断该圆半径是否等于上述距离序列中的最小值,如果条件不满足,用最短距离所对应的被测轮廓点代替上述三点之一,并保证新的三点仍然形成一个锐角三角形,然后重复上述计算和判断过程,直至条件满足。最后一次计算所得到的圆心恰好是被测轮廓的最大内切圆圆心,该方法的优点在于不存在原理误差,速度快,一般二、三次计算即可,给出了程序流程图。

Novel method for solving maximum inscribed circle

A novel method has been proposed according to the minimum criterion for solving maximum inscribed circle. Two mathematical formulae have been developed for the establishment of the center of the maximum inscribed circle for the profile measured in such a way that a circle is decided by putting the coordinate values of the three points selected from the profile measured into the formulae developed. These three points form an acute triangle. The formulae can be used two or three times. Another point selected from the profile replaces one of the former three points each time. According with the minimum criterion, the final circle is just the maximum inscribed circle, of the profile measured when the whole profile measured is outside the circle. A flow chart of program and two examples are given in the paper. There is no principle error or method error in the results calculated by the formulae.