Subdivision surface is a popular modeling technique in the field of computer-aided design （CAD） and computer graphics （CG） for its strong modeling capabilities for meshes of any topology. This book makes a comprehensive introduction to sub-division modeling technologies， the focus of which lies in not only fundamental theories but also practical applications. In theory aspect， this book seeks to make readers understand the contacts between spline surfaces and subdivision surfaces and makes the readers master the analysis techniques of subdivision surfaces. In application aspect， it introduces some typical modeling techniques， such as inter-polation， fitting， fairing， intersection， trimming and interactive edit. By studying this book， readers can grasp the main technologies of subdivision surface modeling and use them in software development. This knowledge also benefits understanding of CAD/CG software operations.

　　Due to flexible topology adaptivity and strong modeling capability， subdivision surface modeling technology has developed quickly in the field of CAD， CG， and geometric modeling since its appearance during the 1970s. Many famous 3D modeling software， such as 3DMax， Maya， and Meshlab， has involved subdivision surface as a modeling tool. Subdivision modeling technology has been successfully applied in making characters of games and special effects of movies. As the saying goes， “Give a man a fish; you have fed him for today. Teach a man to fish; and you have fed him for a lifetime.” On the one hand， the book has done a detailed exposition to the basic theory of subdivision surfaces and strives to make readers to achieve the mastery. On the other hand， although the contents of the book are limited， we make a remarks about the main topic at the end of each chapter and list the closely related references for readers to self-improve. We believe that by learning through this book， readers will have a capability of researching and developing with subdivision surfaces independently.

　　The book was planned by Prof. Wenhe Liao， and most materials came from doctorial dissertations supervised by him. Associate Professor Hao Liu complied this book and wrote Chaps. 1-6 and Sects. 10.1 and 10.2. Dr. Tao Li arranged the rest of the book. He wrote Chap. 8， and Sects. 7.3， 10.3 and revised Sects. 7.1， 7.2

　　and Chaps. 9， 11. Chapter 9 was taken from Gang He‘s doctorial dissertation， and Dr. He revised the English manuscript of this chapter. Sections 7.1 and 7.2 and Chap. 11 came from Xiangyu Zhang’s doctorial dissertation， and Dr. Zhang revised the corresponding English manuscript. Graduate Wei Fan made a lot of work for the final proof. The authors thank Dr. He， Dr. Zhang and Graduate Wei Fan for their contributions to this book.

　　This book is suitable for graduate students， teachers， and technical personals majoring in CAGD， CAD/CG， and other related fields as a reference book on surface modeling. Due to the limitation of our knowledge， there are inevitably somedrawbacks in this book. If any flaw found， please do not hesitate to contact with us（liuhao-01 @nuaa.edu.cn）.