Curves and Surfaces in Computer Aided Geometric Design

ThIS IS an English verSIOn of the book m two volumes entitled \KeiJo Shon Kogaku (1) (2)\ (Nikkan Kogyo Shinbun Co.) written in Japanese. The purpose of the book is a umfied and systematic exposition of the wealth of research results m the field of mathematical representation of curves and surfaces for computer aided geometric design that have appeared in the last thirty years. The material for the book started hfe as a set of notes for computer aided geometnc design courses which I had at the graduate schools of both computer SCIence the umversity of Utah m U.S.A. and Kyushu Institute of Design in Japan. The book has been used extensively as a standard text book of curves and surfaces for students practtcal engmeers and researchers. With the aim of systematic expositIOn the author has arranged the book in 8 chapters: Chapter 0: The sIgmficance of mathemattcal representations of curves and surfaces is explained and histoncal research developments in this field are revIewed. Chapter 1: BasIc mathematical theones of curves and surfaces are reviewed and summanzed. Chapter 2: A classical mterpolation method the Lagrange interpolation is discussed. Although its use is uncommon in practice this chapter is helpful in understanding Chaps. 4 and 6. Chapter 3: This chapter dIscusses the Coons surface in detail which is one of the most important contributions in this field. Chapter 4: The fundamentals of spline functions spline curves and surfaces are discussed in some detail.