偏心圆以及最小二乘圆理论的研究

应用科学学报 ›› 1992, Vol. 10 ›› Issue (3): 259-264.

偏心圆以及最小二乘圆理论的研究

朱训生, 薛秉源

上海交通大学

收稿日期:1990-10-12 修回日期:1991-07-15 出版日期:1992-09-30 发布日期:1992-09-30
基金资助:
国家自然科学基金;上海市自然科学基金课题

STUDY ON THEORY FOR ECCENTRIC CIRCLE AND LEAST SQUARE CIRCLE

ZHU XUNSHENG, XUE BINYUAN

Shanghai Jiao Tong University

Received:1990-10-12 Revised:1991-07-15 Online:1992-09-30 Published:1992-09-30

摘要/Abstract

摘要： 给出了偏心圆的严格等式,xc利用这一等式得到了与传统公式类似的最小二乘圆圆心坐标表达式及较传统公式更精确的最小二乘圆半径的表达式.并给出了最小二乘统计意义下的圆度值公式,论证了它与曲线的直流分量及一次谐波无关.

关键词: 偏心圆, 拟合圆, 半径公式, 圆度

Abstract: A strict equation of eccentric circle is offered in this thesis. Using this equation we get the expression of the coordinates of the least square circle center which is similar to the conventional formula, and the expression of the least square circle radius which is more precise than the conventional formula. Furthermore a formula of the value of roundness is offered in the sense of least square statistics and it is verified that it has nothing to do with the D. 0 component and the primary harmonic wave of the curve.

Key words: fitting circle, radius formula, roundness, eccentric circle

朱训生, 薛秉源. 偏心圆以及最小二乘圆理论的研究[J]. 应用科学学报, 1992, 10(3): 259-264.

ZHU XUNSHENG, XUE BINYUAN. STUDY ON THEORY FOR ECCENTRIC CIRCLE AND LEAST SQUARE CIRCLE[J]. Journal of Applied Sciences, 1992, 10(3): 259-264.

[1]	毛友根. 最小条件圆度误差的唯一性及其精确解[J]. 应用科学学报, 1992, 10(1): 38-42.
[2]	朱训生, 薛秉源, 贝季瑶. 求最小二乘参考圆心与圆度值的采样法则[J]. 应用科学学报, 1992, 10(1): 31-37.