Analysis And Design Of Univariate Subdivision Schemes
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Analysis and Design of Univariate Subdivision Schemes
Author: Malcolm Sabin
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-08-16
‘Subdivision’ is a way of representing smooth shapes in a computer. A curve or surface (both of which contain an in?nite number of points) is described in terms of two objects. One object is a sequence of vertices, which we visualise as a polygon, for curves, or a network of vertices, which we visualise by drawing the edges or faces of the network, for surfaces. The other object is a set of rules for making denser sequences or networks. When applied repeatedly, the denser and denser sequences are claimed to converge to a limit, which is the curve or surface that we want to represent. This book focusses on curves, because the theory for that is complete enough that a book claiming that our understanding is complete is exactly what is needed to stimulate research proving that claim wrong. Also because there are already a number of good books on subdivision surfaces. The way in which the limit curve relates to the polygon, and a lot of interesting properties of the limit curve, depend on the set of rules, and this book is about how one can deduce those properties from the set of rules, and how one can then use that understanding to construct rules which give the properties that one wants.
Mathematical Methods for Curves and Surfaces
This volume constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2012, held in Oslo, Norway, in June/July 2012. The 28 revised full papers presented were carefully reviewed and selected from 135 submissions. The topics range from mathematical analysis of various methods to practical implementation on modern graphics processing units. The papers reflect the newest developments in these fields and also point to the latest literature.
Subdivision Methods for Geometric Design
Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.