Curve and Surface Reconstruction from Noisy Samples Curve and Surface Reconstruction from Noisy Samples

Authorization I hereby declare that I am the sole author of the thesis. I authorize the Hong Kong University of Science and Technology to lend this thesis to other institutions or individuals for the purpose of scholarly research. to reproduce the thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. This is to certify that I have examined the above Ph.D. thesis and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the thesis examination committee have been made. iii To My Wife Yuki and Family for their Patience and Understanding ACKNOWLEDGMENTS Special thanks go to my thesis supervisor Dr. Siu-Wing Cheng for his brilliant guidance of my work and great patience to lead me to be a researcher. Collaboration with him results in widening and enriching my styles of thinking, correcting my directions to solve a problem, and improving my communication and writing skills. Thanks also go to the members of my thesis examination committee for taking the time to read my thesis and ooer important comments. Moreover, thanks also go to my colleagues and my friends in the Theoretical Computer Science Group in our department. Thanks to the system staa in our major department. They are very helpful and their technical support are excellent. Last but not least, I sincerely thank my family for their support, and great encouragement for my studies of the doctoral degree. Without them, this thesis would never come to its existence.