Fujio Yamaguchi Boeken

Focusing on the mathematical representation of curves and surfaces, this comprehensive English version serves as a systematic guide to computer-aided geometric design, drawing from thirty years of research. Originating from lecture notes at the University of Utah and Kyushu Institute of Design, it is structured into eight chapters covering historical significance, basic mathematical theories, Lagrange interpolation, and detailed discussions on Coons surfaces and spline functions. It is a valuable resource for students, engineers, and researchers in the field.

Computer graphics, computer-aided design, and computer-aided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computer-aided design systems although it contains elements that inevitably lead to an inaccurate, non-robust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an n-space problem is to be processed in n-space. The difficulties that accompany the division operation may be avoided if processing is conducted entirely in (n+1)-space. The paradigm attained through the logical extension of this approach, totally four-dimensional processing, is the subject of this book. This book offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system.