三角網格可以建構為各種型態之模型，因此被廣泛應用於CAD/CAM系統、電腦圖學、醫學影像、虛擬實境等領域。而在逆向工程與快速原型之應用中，將CAD模型轉換為網格模型為非常重要之技術。網格模型之建構必須在維持精度之前提下進行，否則轉換出之網格模型即無法精準表示原始CAD模型。減少三角網格數量亦為另一項重點，過多的三角網格數量將減低資料運算之效能。本論文提出精確且快速之精度控制方式，以及藉由四元樹資料結構作為曲面細分之輔助，以期確實減少三角網格數量。為建構水密且合理之網格模型，本論文提出以B-Rep資料結構輔助剪切曲面建立曲面邊界關連性，使由多片曲面構成之CAD模型經由三角網格化後，在原曲面接合處之網格皆能正確被建立，而避免破洞或自交等不合理情況發生，藉此建構出理想之網格模型。

All types of the models could be structured by triangle meshes which have been widely used in CAD/CAM systems, computer graphics, medical images, Virtual Reality, etc. For applications of the reverse engineering and the rapid prototyping processes, the converting CAD models into triangular meshes is a very important technique. Keeping the accuracy is the prerequisite for the process of the model structuring, or the result triangular meshes can’t be indicated the original CAD model. Reducing the triangular mesh quantity of the model is another important procedure. Excess triangle meshes would make the efficiency of data programming be reduced. We provide an exactly and efficiently accurate controlling method and the surface subdivision method assisted by the quadtree data structure which would help to reduce the amounts of meshes. In order to structure the watertight and manifold triangular mesh, we provide the applications of the B-Rep data structure to help the trimmed NURBS surfaces establish the relationships of boundaries between surface and surface. When the CAD model structured by trimmed surfaces has been triangulated, the triangle meshes in the boundary connecting with neighbor surfaces would be structured exactly. The wrong cases such as holes or self-intersection would not be occurred. Therefore, the ideal polygon-based model has been structured.

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