在本論文中我們使用隱函數來設計並實作一個適合用於構造軟性物體的三維塑型系統。這個系統所使用的隱函數包含了元件函數(Primitive Function)與融合函數(Blending Function)以適於軟性物體的塑造。此系統包含有直覺的操作環境，可將物體模型以不同形式顯示的系統架構(Model-View-Controller Architecture)，易於擴充性等等。它包含有四個子系統︰(1)圖形使用者介面，(2)建構樹檢視系統，(3)隱函數處理系統，(4)三維成像系統。使用者介面負責系統的展示並提供操作介面以處理使用者的輸入訊息，它也負責與作業系通溝通。建構樹檢視系統可以表現出建構物體模型的樹狀結構，其中包含有元件函數的組成情形以及作用在其上的融合函數。它並提供必要的操作功能，例如新增節點，檢視節點，輸入參數等等。隱函數操作系統會將整個融合樹轉換成多邊型資料。轉換過後的多邊型資料就經由三維成像系統繪製出整個物件模型。

In this thesis we develop a 3D soft object modeling system with implicit functions. Our system provides implicit functions including the primitive functions and blending functions to modeling soft object. The system satisfies some requirements, such as intuitive operating environment, the Model-View-Controller (MVC) system architecture, and extensibility, etc. The system consists of four major parts: (1) the graphical user interface (GUI); (2) the constructive tree viewing Subsystem; (3) the implicit function operating Subsystem; (4) the 3D scene graph rendering Subsystem. The GUI initializes the window frame and responds to the event messages dispatched from the OS or applications. The constructive tree viewing Subsystem presents the composition of the object modal with the tree structure. The implicit function operating system accomplishes the polygon tessellation, that is, it translates the blending tree with the implicit functions to polygon meshes. The 3D scene graph rendering system renders the polygon mesh and provides 3D scene graph manipulations.

Chapter 1. Introduction 1
Chapter 2. Review of Implicit Functions 3
2.1 Implicit Function 3
2.2 Primitive Function 3
2.3 Blending Operator 4
Chapter 3. System Design 7
3.1 Design Principles 7
3.1.1 The MVC Design Pattern 8
3.2 System Architecture 9
3.2.1 The Constructive Tree Viewing Subsystem 11
3.2.2 The Implicit Function Operating Subsystem 12
3.2.3 3D Scene Graph Rendering Subsystem 14
3.2.4 Polygon Tessellation for Rendering 14
Chapter 4. System Implementation 19
4.1. System Environment 19
4.2 3D Environments 20
4.3 Hierarchy of the System Classes 21
4.4 Document/View Architecture of the System 23
4.5 The 3D Scene Graph Rendering Subsystem 27
4.6 The Constructive Tree Viewing Subsystem 33
4.7 The Implicit Functions in the System 41
Chapter 5. Demonstration 61
Chapter 6. Conclusion and Future Works 70
References 71

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