Geometric Continuity of Curves and Surfaces

This book is written for students, CAD system users and software developers who are interested in geometric continuitya notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology.

The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles.

Autorentext

Przemyslaw Kiciak was born in 1961 in Warsaw. He studied at the Warsaw University of Technology (Faculty SiMR-Cars and Working Machines) and then at the University of Warsaw (Faculty MIM-Mathematics, Informatics and Mechanics). Since 1992 he has been working at the University of Warsaw (Faculty MIM). His scientific interests are in the area of computer graphics, geometric design and numerical analysis. Przemyslaw Kiciak is the author of an open source software package called BSTools, which consists of a number of procedures (written in C) processing spline curves and surfaces. All figures in this book (except 6.8 and the authors photo) have been drawn or rendered using this package.

Inhalt
Preface.- Notation.- Introduction.- Geometric continuity of curves.- Pairs of surface patches.- Compatibility conditions.- Filling polygonal holes.- Images of surface shape.- Bibliography.- Author's Biography.- Index.