Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications.

Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

This volume presents the proceedings of the 7th International Confer ence of the Computer Graphics Society, CG International '89, held at the University of Leeds, UK, June 27-30, 1989. Since 1982 this confer ence has continued to attract high-quality research papers in all aspects of computer graphics and its applications. Originally the conference was held in Japan (1982-1987), but in 1988 was held in Geneva, Switzerland. Future conferences are planned for Singapore in 1990, USA in 1991, Japan in 1992, and Canada in 1993. Recent developments in computer graphics have concentrated on the following: greater sophistication of image generation techniques; advances in hardware and emphasis on the exploitation of parallelism, integration of robotics and AI techniques for animation, greater integ ration of CAD and CAM in CIM, use of powerful computer graphics techniques to represent complex physical processes (visualization), advances in computational geometry and in the representation and modelling of complex physical and mathematical objects, and improved tools and methods for HC . These trends and advances are reflected in this present volume. A number of papers deal with important research aspects in many of these areas."