The book consist of eleven chapters organized in four parts and can be seen as a self-contained tool for graduate students, researchers, and interested practitioners from industry, regarding the usage of implicit curves and surfaces for computer graphics, geometric modelling, computer games etc.
Part I, “Mathematics and data structures”, gives a short overview of the mathematics behind curves and surfaces, especially manifolds and varieties, and introduces the reader into the special features of some spatial decomposition techniques together with the spatial data structures involved in the process.
Part II, “Sampling methods”, deals with different computational methods for sampling implicit curves and surfaces, mainly a discretisation process whose goal is to obtain a finite set of points using various root finding methods.
In Part III, “Reconstruction and polygonisation”, the authors present algorithms dealing with polygonisation of an implicit surface from its multivariate real function, and with reconstruction of implicit surfaces and curves from unorganized sets of points.
The final part, “Designing complex implicit surface models”, presents applications of implicit curves and surfaces to geometric modelling, visualization and animation.
The book ends with a rich reference section containing more than 400 papers, enforcing the idea that this work represents a valuable source for the reader.