参数方程曲线的最优逼近算法及实现

讨论了参数方程以单圆弧和双圆弧混合逼近的优点,用优化三点圆弧以允差逼近曲线和单双圆弧混合逼近的算法,使得曲线有拐点和极值点时整个逼近圆弧的光滑连接。讨论了参数方程分段点的性质,保证了分段点判断的可靠性。在曲率极值点处采用圆弧延长法,进一步减少了圆弧逼近的段数。对称图形采用对称算法,提高了图形的对称性,大大提高了程序的速度。基于Matlab采用优化的方法进行程序的编制求解节点。为CAD系统和数控加工复杂的曲线提供了参考。

Optimal Approximating Algorithm and Realization of Parameter Equation Curve

The features of single and double arc approximating,and combines the merits of two kinds of fitting are discussed. By the algorithm of approximating curve in optimizing three-point arc and mixing single and double arc in permission tolerance,smooth link of whole approximating arc with inflexion points and extreme value points is attained. The nature of segmental points of parameter equation is discussed to ensure the reliability of judging segmental points. The arc lengthening method in extreme value points of curvature is used to further decrease segments of arc approximating. Symmetrical algorithm for symmetrical graph is used to increase symmetry of the graph,thus the program runs more rapidly. The nodes are solved by programming in matlab software to provide reference for processing complex curve in numerical control and CAD system.