NURBS提供了豐富的彈性，可以讓使用者自行設計想要的曲線，但受限於其複雜的數學形式，以及龐大的計算量，使得傳統的NURBS插補器是使用簡化的數值方法計算出下一時刻的路徑參數，使得插補精度無法提昇。
FAST NURBS插補法以預處理的方式建立出路徑長反函數，在即時的插補環境中，根據速度規劃所設定的進給量，利用路徑長反函式可以做到快速且高精度的插補效果，建立路徑長反函數最重要的部份為路徑總長的計算，在FAST NURBS插補法中，使用整段路徑以辛普森面積法進行數值積分的計算，但是在曲線路徑參數分佈極不均勻的情形之下，路徑總長的計算會發生錯誤，進而導致錯誤的路徑長反函數以及錯誤的插補路徑，本論文提出以節點向量為分割點，分段計算路徑總長的FAST ROBUST NURBS插補法，成功的消除了FAST NURBS在曲線節點參數分佈極不均勻時錯誤的發生。
刀具半徑補正是相當複雜的CNC智慧型功能之一，本論文所提出的刀具半徑補正針對直線線段進行處理，根據不同的轉接夾角選擇出適當的轉接路徑，可以做到確保斜率連續，部份的角度範圍中，更可以確保轉接路徑曲率連續，避免驅動馬達有劇烈的加速度變化，減輕機台的振動以提高加工及表面精度。在本論文中也實現刀具半徑補正預視功能，可以判斷封閉曲線，正確的修改進刀及退刀路徑，並可以偵測出補正路徑是否與工件發生過切，進行迴避或是路徑的修正。

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