由許多個圓弧滿足在連結點有相同的切線方向(G1)連接構成之封閉曲線稱 為圓弧曲線(Arc Spline),此種曲線在數值控制切割機器的切割路徑上扮 演著重要之功能。本研究中,吾人比較由 D.S. Meek 和 D.J. Walton 提 出之二分法(Bisection)及最長弧(Longest arc)兩種以圓弧曲線逼近資 料點的演算法,另外也將 Dunham提出之以直線線段逼近資料點的演算法改 為以圓弧曲線逼近資料點來做比較,並提出一個演算法,使得在相同的誤差 範圍界定下,建構之圓弧曲線所需之雙弧數目會比二分法及最長弧法少,雖 然雙弧數比 Dunham 的演算法多,計算時間比 Dunham法少很多。吾人亦評 估二分法,最長弧, Dunham的演算法及本文提出之方法在不同的誤差範圍 下,四種演算法在處理時間長短及雙弧數目多寡之差異性。
G1 arc spline which is composed of circular arcs and straight- line segments plays an important role in paths that are used in the automatically controlled cutting machinery. In this research, one modified method is considered so that the drawbacks in fitting a G1 arc spline to a set of discrete data by Bisection and Longest arc methods proposed by D.S.Meek and D. J.Walton and Dunham's method can be overcome.The proposed method can result in less number of biarcs than the Bisection and the Longest arc and shorter time than the Dunham's method based on the same specified error distance.The comparison among these four methods are also discussed.