Subdivide and conquer

In recent years, with the emergence of subdivision surfaces as a major industrial standard for boundary representations of 3D models, the need for a comprehensive account of the underlying mathematical theory has increased. However, writing a book on the mathematics of subdivision that will be rigorous, comprehensive and at the same time accessible to a wider audience remains a formidable challenge. On the one hand, subdivision is still an evolving field and on the other, the required background spans a multitude of mathematical areas. The book by Lars-Erik Andersson and Neil Stewart is the result of a highly successful take on that challenge. The aims of the book are primarily achieved by its neat structure, which classifies and introduces subdivision schemes at a gradually increasing complexity of mathematical representation, and secondly by separating thematerial related to the order of continuity at extraordinary vertices and presenting it at a later chapter. Moreover, the book has a sharp focus on the mathematical aspects of subdivision surfaces, apart of course from the informal discussions that are necessary for introducing the appropriate context. This means that the authors can introduce at a leisurely pace all the necessarymathematical backgroundmaterial, including geometry, elementary topology, calculus and approximation theory, as well as some more advanced mathematical tools, such as generating functions and the Fourier transform. The first chapter of the book is a fast-forward to the material that will be discussed in more detail in subsequent chapters and can also be used as a quick reference to some of the most popular subdivision schemes. The next three chapters introduce all major subdivision schemes covering, in increasing complexity, schemes related to splines, box-splines and finally schemes with general basis functions. In each chapter, the corresponding univariate schemes are introduced first, followed by a study of the regular