OPTIMAL BIARC-CURVE FITTING

被引:39
作者
PARKINSON, DB
MORETON, DN
机构
[1] Department of Mechanical Engineering, University of Liverpool, Liverpool, L69 3BX
关键词
CNC MACHINING; SPLINES; BIARCS; CURVE FITTING; INTERPOLATION METHODS;
D O I
10.1016/0010-4485(91)90009-L
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
The determination of the optimum biarc curve through a given set of points with given end gradients is considered. The method adopted is that of finding the optimum gradients at all the given points such that the integral of the square of the local curvature along the curve is a minimum. It is shown that this is equivalent to the simultaneous solution of the same problem for a set of 2-panel (3-point) curves, and such solutions are then investigated. A linearized method of solution for the required gradients is proposed that results in a set of linear equations that can be inverted directly, and that should be capable of solution on a CNC machine control unit, following the direct input of the coordinates of the given points and relevant end slopes. Initial results are compared with those obtained from a rigorous numerical optimization procedure for the biarc curve and with a cubic-spline function. It is shown that instabilities may be avoided, and a smoother curve obtained, by the effective decoupling of segments of the whole curve by the specification of gradients at additional, intermediate, points.
引用
收藏
页码:411 / 419
页数:9
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