臺灣博碩士論文加值系統

運用分割曲面的模型建構是目前蠻熱門的研究領域，也是用來設計複雜人物動畫的另一種方法。而曲面嵌合則一直是傳統電腦幾何模型的話題。本篇論文是用來解決當我們利用一堆資料點來產生曲面時，所面臨曲面嵌合的問題。我們主要是依據 Suzuki et al. 所提出的方法。而其方法適用於快速的捕捉模型的整體外觀，在局部的物體特徵上較無法精確的表示出來。我們也發現到在某些模型的測試上會有問題產生，因此我們加入了新的想法 — “Oriented Data Point” 和 ”Adaptive Mesh Refinement” 來加以改良Suzuki et al.的方法以配合不同形式的模型需要。

Modeling using subdivision surfaces is a popular research area now. The subdivision surfaces are also used to design complex character animations. Surface fitting is an active research topic of computational geometry. This paper addresses the surface-fitting problem when generating a surface from a set of spatial data points. We solve primarily this problem according to the method of Suzuki et al. proposing. And his method applies to the applications generating quickly the overall shape of the model; fail to capture the local characteristics. We also find some problems when we test some models. Therefore, we add our thoughts─“Oriented Data Point” and “Adaptive Mesh Refinement” to the algorithm to improve the approach of Suzuki et al. for the models with different topologies.

Table of Content...I
Table of Figure.III
Table of Equations.VI
Abstract…………VII
摘要...VIII
Chapter 1. Introduction1
1.1Introduction1
1.2Motivation1
1.3Thesis Organization 1
Chapter 2. Related Works3
2.1 Types of Data Tested3
2.2 Subdivision Surface6
2.2.1 Characteristics8
2.3 Schemes..10
2.3.1 Catmull-Clark..10
2.3.2 Butterfly..13
2.3.3 Loop..16
2.4 Details of Suzuki et al. Approach..19
2.4.1 Subdivision Limit Position (SLP)..19
2.4.2 Error Energy Function..20
Chapter 3. Problem Definition..24
3.1 Preliminaries..24
3.2 Problem Definition..25
3.2.1 Adaptive Mesh Refinement..25
3.2.2 Point Direction..26
Chapter 4. Prototype Implementation..28
4.1 Working Platform..28
4.2 Architecture..28
4.3 Graphic User Interface..30
4.4 Data Points..31
4.5 The Problem We Want to Solve..32
4.6 The Tested Results..36
4.6.1 Different Topology..36
4.6.2 Adaptive Mesh Refinement..49
Chapter 5. Discussion..54
5.1 Quality of Initial Model..54
5.2 Influence of Different Topology…..54
5.3 The Setting of Threshold Value..54
Chapter 6. Conclusions and Future Works..56
Reference..57

References
[1]Catmull, E., and Clark, J. “Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes.” CAD 10, 6 (1978), pp. 350-355.
[2]Loop, C. “Smooth Subdivision Surfaces Based on Triangles Master’s Thesis”. University of Utah, Department of Mathematics, (1987).
[3] Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W. “Surface Reconstruction from Unorganized Points.” Computer Graphics (SIGGRAPH 1992 Proceedings), pp. 71-78.
[4]Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W. “Mesh optimization.” Computer Graphics (SIGGRAPH 1992 Proceedings), pp. 19-26.
[5]Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W. “Piecewise smooth Surface Reconstruction.” Computer Graphics (SIGGRAPH 1994 Proceedings), pp. 295-302.
[6]Suzuki, H., Takeuchi, S., Kanai, T., Kimura, F. “Subdivision Surface Fitting to a Range of Points.” Computer Graphics and Applications, (IEEE 1999 Proceedings), pp. 158-167
[7] Shape, B. “Subdivision Surface Theory.” Gamasutra, April 11, 2000. URL:http://www.gamastra.com/features/20000411/sharp_01.htm.
[8] DeRose, T., Kass, M., and Truong T. “Subdivision Surface in Character Animation.” SIGGRAPH ’98, pp. 85-94.
[9]Doo, D., and Sabin, M. “Analysis of the Behavior of Recursive Division Surfaces near Extraordinary Points.” CAD 10, 6 (1978), pp. 356-360.
[10]URL: http://www.cc.gatech.edu/projects/large_models