Curves and surfaces in geometric modeling : theory and algorithms

Abstract

This book is primarily an introduction to geometric concepts and tools needed for solving problems of a geometric nature with a computer. Our main goal is to provide an introduction to the mathematical concepts needed in tackling problems arising notably in computer graphics, geometric modeling, computer vision, and motion planning, just to mention some key areas. Many problems in the above areas require some geometric knowledge, but in our opinion, books dealing with the relevant geometric material are either too theoretical, or else rather specialized and application-oriented. This book is an attempt to fill this gap. We present a coherent view of geometric methods applicable to many engineering problems at a level that can be understood by a senior undergraduate with a good math background. Thus, this book should be of interest to a wide audience including computer scientists (both students and professionals), mathematicians, and engineers interested in geometric methods (for example, mechanical engineers). In particular, we provide an introduction to affine geometry. This material provides the foundations for the algorithmic treatment of polynomial curves and surfaces, which is a main theme of this book. We present some of the main tools used in computer aided geometric design (CAGD), but our goal is not to write another text on CAGD. In brief, we are writing about