Przemysław Kiciak

Abstract

This book is written for students, CAD system users and software developers who are interested in geometric continuity, a 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.

The subject of the book (in Polish) are the representations of parametric curves and surfaces popular in computer graphics and CAD systems: Bézier, B-spline (including NURBS), Hermite and Coons. The most important mathematical properties are described, together with algorithms of processing these curves and surfaces.