在4D視覺化上，諸如4 維空間的呈現、運用各種的使用者介面功能來操作
4 維物件等部分進行研究後，我們於此篇論文中，提出了對於4D多胞形上做紋理貼圖等視覺呈現方法，並提供了一個含直覺性的介面的系統。此系統整合了4D 變形轉換、4D動態運動、以及交互式視覺化，其中，所有的動態變化皆可由鍵盤輸入和滑鼠的移動來做控制。我們得到了不錯的執行結果，以及更有效地了與4D多胞形的觀察與互動。

We have investigated several areas in 4D visualization, including 4-dimensional space rendering, various user interface elements to manipulate the 4D objects. In this
paper, we describe methods for visualizing 4D polytopes that are texture-mapped, and present an environment that achieves integration between 4D trans- formations, 4D motions and interactive visualization with an intuitive interfaces. In the environment, all the motions in 3D and 4D can be performed under the control of key-frame and mouse. We expect the system runs smoothly and the observation and interaction with 4D polytopes are effective for intuitive understanding of 4D polytopes.

chapter 1 Introduction 1
1.1 Related Works 1
1.2 Contribution 2
1.3 Thesis Organization 3
chapter 2 Preliminaries and Visualizing Environment Overview 4
2.1 Preliminaries 4
2.2 Visualizing Environment Overview 13
Chapter 3 Environment Database 15
3.1 Geometric Information 15
3.2 Topological Information 19
Chapter 4 Regular 4-Polytopes Coloring Scheme 24
4.1 Phase generation 25
4.2 Vertices-colors matching 27
4.3 Color Ramp Mapping of Faces with Transparency Determination 30
Chapter 5 Uniform 4-Polytopes Colouring Scheme 32
5.1 Phase generation 33
5.2 Vertices-colors matching 36
5.3 Color Ramp Mapping of Faces with Transparency Determination 39
Chapter 6 Implementation and Experimentation 42
6.1 Implementation 42
6.2 4D Models 43
6.3 Experimentation 44
Chapter 7 Conclusions 84

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