摘要
对空间圆线精确拟合算法进行研究.线性和非线性最小二乘法是拟合规则曲线和曲面方程的常见方法.空间圆线作为规则的二次曲线,由于没有特定的曲线方程无法直接使用线性和非线性最小二乘法来进行求解.由于空间圆线可以被看作平面和球面相交形成,圆线特征值可以通过平面和球面特征值求解.提出了基于投影二阶段拟合算法完成空间圆线拟合的方法.对空间圆线拟合原理进行了介绍,通过数据验证了算法的正确性、可行性和精确程度.使用程序进行了算法实现.与贝塞尔和B样条曲线算法精度进行了比较,表明该算法在精度方面具有优势,可用于逆向工程中提高空间拟合算法的精确度.
Research on accurately fitting method of spatial circle is carried out. Linear and nonlinear least square fitting are common methods for fitting regular curve and surface. As a regular quadric curve, spatial circle has no specific curve formula and therefore linear and nonlinear least square methods cannot be directly applied to it. Due to the fact that spatial circle can be regarded as the intersection line of a plane and a spherical surface, spatial circle eigenvalue can be solved by eigenvalues of the plane and the spherical surface. The two-step spatial circle fitting method based on projection is proposed. The spatial circle fitting principle is presented, and the correctness, feasibility and accuracy are validated. The method is implemented by programming. The method has superiority in accuracy comparing with Beziert and B-spline curves fitting methods, and it can improve spatial circle fitting accuracy in reverse engineering.
出处
《工程设计学报》
CSCD
北大核心
2009年第2期117-121,共5页
Chinese Journal of Engineering Design
基金
国家自然科学基金资助项目(50875076)
河南省高校杰出科研人才创新工程资助项目(2004KYCX006)
关键词
空间圆线
最小二乘法
拟合
投影
spatial circle
least square
fitting
projection
