臺灣博碩士論文加值系統

The method in this thesis is the moving least square technology. It employs well for the representation, modeling, processing, and rendering of point sampled geometry. We present a method for simplifying removing points process. In conclusion, we display some results of experiment for the method.

本篇論文使用變動式最小平方近似法。此方式適用於取得、表示、塑模、處理、以及產生樣本點的幾何。我們提出一個方法簡化移除點的過程。最後，我們探討一些此方法的實驗結果。

TABLES OF CONTENTS
ACKNOWLEDGEMENTS………………………………………………………………………………i
ENGLISH ABSTRACT………………………………………………………………………………ii
CHINESE ABSTRACT………………………………………………………………………………iii
LIST OF FIGURES…………………………………………………………………………………iv

CHAPTER
1. INTRODUCTION………………………………………………………………………1
1.1 Preface………………………………………………………………………………1
1.2 Motivation……………………………………………………………………………2
1.3 Thesis Organization………………………………………………………………3
2 BACKGROUNDS…………………………………………………………………………4
2.1 Overview……………………………………………………………………………4
2.2 Moving Least Square………………………………………………………………4
2.2.1 Find a Local Hyperplane…………………………………………………………4
2.2.2 Compute a Local Bivariate Polynomial Approximation………………………6
2.3 Summary………………………………………………………………………………8
3 ALGORITHM FOR REMOVING POINTS…………………………………………………8
3.1 Overview………………………………………………………………………………8
3.2 Using MLS for Removing Point Process…………………………………………9
3.2.1. K-d Tree Data Structure…………………………………………………………12
3.2.2. Search Algorithm for Neighbor Points………………………………………14
3.2.3 Removing Points Process…………………………………………………………15
3.3 Summary………………………………………………………………………………16
4 EXPERIMENTS…………………………………………………………………………17
4.1 Platform……………………………………………………………………………17
4.2 Prototype System…………………………………………………………………18
4.3 Result………………………………………………………………………………19
4.4 Discussion…………………………………………………………………………23
5 CONCLUSION AND FUTURE WORK……………………………………………………25
5.1 Conclusion…………………………………………………………………………25
5.2 Future Work…………………………………………………………………………25
REFERENCES………………………………………………………………………………………26

REFERENCES
[1]ALEXA M., BEHR J., COHEN-OR D., FLEISHMAN S., LEVIN D., SILVA C. T.: Point set surfaces. In Proceedings of the conference on Visualization ’01 (2001).
[2]ALEXA M., BEHR J., COHEN-OR D., FLEISHMAN S., LEVIN D., SILVA C. T.: Computing and rendering point set surfaces. IEEE Transactions on Computer Graphics and Visualization 9, 1 (2003), 3–15.
[3]AMENTA, N., KIL, Y. J.: Defining point-set surfaces. ACM Transactions on Computer Graphics (SIGGRAPH 2004 Proceedings) 23, 3(2004), 264–270.
[4]FLEISHMAN S., COHEN-OR D., ALEXA M., SILVA C. T.: Progressive point set surfaces. ACM Transactions on Computer Graphics (TOG) 22, 4 (2003), 997–1011.
[5]FRIEDMAN J. h., BENTLEY J. l., FINKEL R.A.: An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software 3(3): (1977) 209-226.
[6]LEE I.-K.: Curve reconstruction from unorganized points. Computer Aided Geometric Design 17, 2 (February 2000), 161–177.
[7]LEVIN D.: The approximation power of moving least-squares. Math. Comp. 67 (1998), 517–1531
[8]LEVIN D.: Mesh-independent surface interpolation. Geometric Modeling for Scientific Visualization (2003).
[9]RUSINKIEWICZ S., LEVOY M.: Qsplat: a multiresolution point rendering system for large meshes. ACM Transactions on Computer Graphics (SIGGRAPH 2000 Proceedings) (July 2000) pp. 343-352
[10]SEDGEWICK H.: Algorithm in C++ ( 3rd edition). Addison Wesley (1998).
[11]VIZTEK: http://www.viztek.net/ © 2005 Viztek Imaging. All rights reserved.
[12]ZWICKER M., PAULY M., KNOLL O., GROSS M.: Pointshop 3d: an interactive system for point-based surface editing. In Proceedings of the 29th annual conference on Computer graphics and interactive techniques (2002), ACM Press, pp. 322–329.