Optimized biarc curves with tension

The use of sets of two circular arcs (biarcs) to describe a curve, defined by a finite number of data points (knots) is considered. A previous solution to this problem is extended by the determination of the optimum pair of arcs between any two knots. Gradients at the given data points are determined by an efficient linearized approximation to a minimum strain energy solution, which is modified to include fixed end gradients and the effects of applying tension to the fitted curve and to individual panels. The use of biarcs to fit smooth curves for contour machining permits the use of the circular interpolation facility generally available on CNC machine tools.