臺灣博碩士論文加值系統

本研究以適應性的Voxel模型為基礎，配合APT（Automatically Programmed Tools）隱函數刀具方程式與快速碰撞模組發展出多軸模擬與虛擬雕刻兩個系統。
在多軸模擬加工中，主要是用來檢測設計出來的五軸刀具路徑是否正確，經由模擬加工後的結果與原始CAD模型比對，可以快速分析出那些NC路徑有問題，再加以修正。
而在虛擬雕刻系統中，透過虛擬雕刻機可以藉由力回饋真實地感受到3D的實體物件。而此系統可以應用於數位磨牙，讓實習牙醫生可以在虛擬環境中訓練磨牙的技巧。在標準的範本做比較後，可以利用數位檢測系統檢出不足或殘留的區域，快速地知道那些地方需要再改進，達成訓練的目的。

My research emphasizes the use of adaptive octree to develop a reliable multi-axis simulation procedure which verifies the cutting route and the workpiece appearance during and after simulation. Voxel models with adaptive octree data structure are used to approximate the machined workpiece with specified resolution. Implicit functions are used to represent various cutter geometries for the examination of cutter contact points with speed and accuracy. It allows a user to do error analysis and comparison between the cutting model and the original CAD model. It can also verify the exactness of NC codes before machining is carried out by a CNC machine in order to avoid wasting material and to improve machining accuracy.

In haptic system, the simulation engine then uses the same interaction
forces to compute their effect on objects in the virtual environment. We focus our attention on force response algorithms for rigid objects. Hence we made an application for 3D digital dental training system. This system could help dental students practice tool preparation in the virtual environment. After comparing, we know which places need improving again, reach to train.

目錄……………………………………………………………………Ⅰ
圖目錄…………………………………………………………………IV
表目錄…………………………………………………………………XI
第一章 緒論…………………………………………………………..001
1.1前言……………………………………………………………001
1.2研究動機………………………………………………………002
1.3研究目的………………………………………………………004
1.4文獻回顧………………………………………………………006
1.4.1高解析度的3D網格……………………………………006
1.4.2虛擬雕刻系統…………………..………………………007
1.4.3通用的刀具模組………………..………………………008
1.4.4碰撞測試模組…………………..………………………008
1.5研究方法………………………………………………………010
第二章 APT刀具…………………..…………………………………..013
2.1簡介……………………………………………………………013
2.2 APT刀具數學模型的建立……………...……………………014
2.2.1任意軸向隱函數………………………….….…………015
2.2.1.1圓柱……………………………………….……015
2.2.1.2圓環……………………………………….……017
2.2.1.3三角錐…………………………………….……019
2.2.1.4平面……………………………………….……020
2.2.2 APT刀具參數的轉換…………………….….…………021
2.2.3減化後的APT刀具……………..……….….…………027
2.2.3.1平刀……………………………………….……027
2.2.3.2球刀……………………………………….……028
2.2.3.3圓角刀…………………………………….……029
2.2.3.4錐形刀…………………………………….……029
2.2.3.5錐形圓角刀……………………………….……030
2.2.3.6錐形球刀………………………………….……032
2.2.3.7尖刀…………………..……..…………….……034
第三章 實體模型的建立及布林運算的演算法….….…………..…..035
3.1簡介……………………………………………………………035
3.2樹狀結構簡介…………………………………………………035
3.3八元素…………………………………………………………036
3.4 STL model轉換為Octree voxel model………………………039
3.4.1 STL model轉換為Octree voxel model範例成果…..…044
3.5模擬演算法的流程……………………………………………046
3.6碰撞測試………………………………………………………048
3.6.1 快速碰撞測試……………………………...…….……049
3.6.2隱函數碰撞測試……………..……….…………..……052
第四章高解析度3D表面網格建構…………………..…………..…..056
4.1簡介……………………………………………………………056
4.2 Marching Cube………………………………………………056
4.3 Edge Point Value……………………………………………062
4.3.1計算STL轉實體Voxel的EP值……………………..…064
4.3.2 EP值的布林運算……………………………..……..…067
4.3.3決定複合隱函數的EP值…………………….……..…072
4.4素材表面的建立………..……………………………………075
4.4.1劃分區域建立初始素材表面.………..……………..…075
4.4.2素材表面的細分………………..……………..……..…077
4.4.3縫補素材網格和刀具切削網格的破洞……………..…078
4.5修補破洞的方法………..……………………………………081
4.5.1投影法.………..………………………….…………..…082
第五章虛擬雕刻系統……………………….………..…………..…..085
5.1簡介……………………………………………………………085
5.2 系統架構…………………..…………………………………086
5.3 環境設定……………..………………………………………087
5.4力回饋系統………..………………………….………………091
5.4.1一階彈簧系統力回饋計算…..………..……………..…092
5.4.2利用EP值求解非雕刻狀態的力………………..…..…094
5.4.3求解雕刻狀態的力…………………………………..…102
5.4.4 Filter……………………………………………..…..…104
第六章應用範例展示…………………….….………..…………..…..107
6.1刀具切削模擬…………………………………………………107
6.2五軸刀具路徑模擬……………………………………………109
6.2.1誤差分析…..…………………..……..……………..…112
6.2.2結果比較…..…………………..……..……………..…113
6.3數位磨牙………………………………………………………114
第七章結論與未來展望…………………….………..…………..…..128
7.1結論……………………………………………………………128
7.2未來展望………………………………………………………129
參考文獻…………………………………………………..…………130

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