Analysis and Design of Univariate Subdivision Schemes

By:

Malcolm Sabin

Format:

Paperback / softback

Series:

Geometry and Computing

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Description

‘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.

Author Biography:

The author has spent his professional life on the numerical representation of shape.

Release date Australia

October 13th, 2012

Author

Malcolm Sabin

Audience

Professional & Vocational

Illustrations

68 Illustrations, black and white; XIV, 218 p. 68 illus.

Pages

218

Series

Geometry and Computing

Dimensions

155x235x12

ISBN-13

9783642264498

Product ID

20886102

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