摘 要 本論文主要討論NURBS(Non-Uniform Rational B-Spline)曲線在CNC系統裡，所遭遇到的不連續問題。傳統的CNC工具機大都以線與圓弧來逼近複雜的圖形，然而，NURBS曲線所表現的是正確的曲線，而不是近似的結果。也因此在數學的表現上沒有誤差的問題。然而，當工具機處理到圓弧接曲線，曲線接直線等等不連續的線條相接時，如果希望系統能縮短加工時間的話，除了提高工具機加工速度外，就是減少加減速時間，然而，許多由CAM軟體產生的NURBS曲線彼此之間是不連續的，因此每個NURBS曲線就得加減速一次，本篇論文即是讓不同的NURBS曲線以一個小曲線連接使得工具機能平順地開始另一條曲線。 Abstract This paper discusses the problem of the discontinuous NURBS(Non-Uniform Rational B-Spline) curves on CNC system. The traditional CNC system generally approximates the complex shape by line and circular arc. When the line meets circular arc or circular arc meets circular arc, the system has to stop at the end of every segments. If we want to speed up the machining speed, we have to increase the speed of motors or decreases the time of acceleration and deceleration. But it is usually discontinuous between NURBS curves. It has to decelerate at the end of curve and accelerate at the beginning of the next curve. This paper discusses how to insert a short curve to smooth the discontinuous curves.
