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Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood.
This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms.
The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
List of contents
and Overview.- Geometry Near Singularities.- Generalized Splines.- Subdivision Surfaces.- C1k-Subdivision Algorithms.- Case Studies of C1k-Subdivision Algorithms.- Shape Analysis and C2k-Algorithms.- Approximation and Linear Independence.- Conclusion.
Report
"The book is a concise, yet complete guide to this exciting domain, and it is obviously prepared with utmost care to make it coherent ... . A warm recommendation for researcher and student who want to learn (more) about subdivision. Definitely a reference work for the years to come." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 18, 2011)
"Subdivision surfaces allow designers to create models from control meshes in intuitive ways. ... This books aims to summarize the current knowledge on the subject ... . The target audience is researchers, instructors, and graduate students. The book is carefully written and can probably be used for an advanced graduate course for mathematically inclined students in computer graphics and computational mathematics, and also for students in differential geometry interested in applications." (Luiz Henrique de Figueiredo, The Mathematical Association of America, August, 2008)
