隱函數架構如今普遍地應用在許多需要3D的領域上，如電腦遊戲、卡通或電影特效上，雖然如此，大多數的硬體仍然是支援多邊型模型而非隱函數模型，所以多邊型模型依然會是電腦圖學的主流，但兩者之間的轉換成了電腦圖學中新的研究議題。

本篇論文提出一種從三角型模型轉換成隱函數模型的方法，其主要概念是將三角型模型利用二元空間分割樹（Binary space–partitioning tree）做點與面的空間分割以建立一個階層式的架構，在這個階層式架構中的每一個葉節點（leaf node），我們建立一個相對應的隱函數，這個隱函數是用基因演算法（Genetic Algorithm）來產生的。而階層式架構中的中間節點（internal node）部分是利用接合運算子（Blending Operators）來做接合，使其平滑且連續。因為我們所提出的方法只儲存少數幾個隱函數，所以可以大幅度的縮減資料量，又因為採用基因演算法可以避免了傳統轉換所需要的大量複雜運算。

The implicit function model is nowadays generally applied to a lot of fields that need 3D, such as computer game, cartoon or for specially effect film. So far, most hardware are still to support the polygon-mesh model but not implicit function model, so polygon-mesh model is still the mainstream of computer graphics. However, translation between the two representation models becomes a new research topic.

This paper presents a new method to translate the triangles mesh model into the implicit functions model. The main concept is to use the binary space-partitioning tree to divide the points and patches in the triangle mesh model to create a hierarchical structure. For each leaf node in this hierarchical structure, we would generate a corresponding implicit function. These implicit functions are generated by the genetic algorithm. And the internal nodes in this hierarchical structure are blended by the blending operators. The blending operators make the surface become smooth and continual. The method we proposed reduces the data in a large amount because we only save the coefficients of the implicit surface. And the genetic algorithm can avoid the high computing complexity.

Chapter 1. Introduction...............................1
Chapter 2. Related Work and Background Materials......4
2.1 Genetic Algorithm..............................4
2.2 Octree Method and BSP Trees....................6
2.3 Blending Operations............................7
2.4 Radio Basis Functions..........................8
Chapter 3. The Proposed Method.......................11
3.1 Overview......................................11
3.2 BSP Tree......................................12
3.3 Genetic Algorithm.............................13
Chapter 4. Experimental Results......................17
4.1 Test Environment..............................17
4.2 Experimental Results..........................19
4.3 Discussion....................................24
Chapter 5. Conclusion and Future Work................26
5.1 Conclusion....................................26
5.2 Future Work...................................27
References...........................................28

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