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New & Forthcoming Titles | Analysis and Design of Univariate Subdivision Schemes

Analysis and Design of Univariate Subdivision Schemes

Series: Geometry and Computing, Vol. 6

Sabin, Malcolm

2010, XIV, 218 p.

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  • Contains all the fundamental ideas
  • Presented in an accessible fashion even for those whose mathematics is a tool to be used, not a way of life
  • Separate sections on mathematical techniques provide revision for those needing it
This book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. The book reports on the currently known ways of analysing a subdivision scheme (i.e. measuring criteria which might be important for the application of a scheme to a given context). It then goes on to consider how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application. The book is presented in an accessible fashion, even for those whose mathematics is a tool to be used, not a way of life. It should provide the reader with a full and deep understanding of the state-of-the-art in subdivision analysis, and separate sections on mathematical techniques provide revision for those needing it. The book will be of great interest to those starting to do research in CAD/CAE. It will also appeal to those lecturing in this subject and industrial workers implementing these methods. The author has spent his professional life on the numerical representation of shape and his book fills a need for a book covering the fundamental ideas in the simplest possible context, that of curves.

Content Level » Graduate

Keywords » CAD - CAE - computer graphics - computer-aided design (CAD) - rendering - splines - subdivision schemes

Related subjects » Computational Science & Engineering - Geometry & Topology - Image Processing - Information Systems and Applications - Theoretical Computer Science

Table of contents 

Introduction.- Part I. Prependices: Functions and Curves; Differences; B-Splines; Eigenfactorisation; Enclosures; Hölder Continuity; Matrix Norms; Joint Spectral Radius; Radix Notation; z-transforms.- Part II. Dramatis Personae : An Introduction to some Regularly-Appearing Characters.- Part III. Analyses: Support; Enclosure; Continuity 1 – at Support Ends; Continuity 2 – Eigenanalysis; Continuity 3 – Difference Schemes; Continuity 4 – Difference Eigenanalysis; Continuity 5 – The Joint Spectral Radius; What Converges; Reproduction of Polynomials; Artifacts; Summary of Analysis Results.- Part IV. Design: The Design Space; Linear Subspaces of the Design Space; Non-Linear Conditions; Non-Stationary Schemes; Geometry Sensitive Schemes.- Part V. Implementation: Making Polygons; Rendering; Interrogation; End Conditions; Modifying the Original Polygon.- Part VI. Appendices: Proofs; Historical Notes; Solutions to Exercises; Coda.- References.- Index.

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