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Analysis and Design of Univariate Subdivision Schemes

  • Malcolm Sabin

Part of the Geometry and Computing book series (GC, volume 6)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Prependices

    1. Front Matter
      Pages 3-3
    2. Malcolm Sabin
      Pages 5-6
    3. Malcolm Sabin
      Pages 7-10
    4. Malcolm Sabin
      Pages 11-16
    5. Malcolm Sabin
      Pages 17-24
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      Pages 25-28
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      Pages 29-32
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      Pages 33-36
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      Pages 37-38
    10. Malcolm Sabin
      Pages 39-40
    11. Malcolm Sabin
      Pages 41-45
  3. Dramatis Personae

    1. Front Matter
      Pages 47-47
  4. Analyses

    1. Front Matter
      Pages 61-61
    2. Malcolm Sabin
      Pages 63-72
    3. Malcolm Sabin
      Pages 73-76
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      Pages 77-80
    5. Malcolm Sabin
      Pages 81-93
    6. Malcolm Sabin
      Pages 95-101
    7. Malcolm Sabin
      Pages 103-107
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      Pages 109-113
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      Pages 115-118
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      Pages 119-124
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      Pages 125-132
    12. Malcolm Sabin
      Pages 133-136
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      Pages 137-137
  5. Design

    1. Front Matter
      Pages 139-139
    2. Malcolm Sabin
      Pages 141-142
    3. Malcolm Sabin
      Pages 143-146
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      Pages 147-153
    5. Malcolm Sabin
      Pages 155-160
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      Pages 161-164
  6. Implementation

    1. Front Matter
      Pages 165-165
    2. Malcolm Sabin
      Pages 167-169
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      Pages 171-172
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      Pages 173-174
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      Pages 175-180
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      Pages 181-182
  7. Appendices

    1. Front Matter
      Pages 183-183
    2. Malcolm Sabin
      Pages 185-187
    3. Malcolm Sabin
      Pages 189-191
    4. Malcolm Sabin
      Pages 193-204
    5. Malcolm Sabin
      Pages 205-206
  8. Back Matter
    Pages 207-215

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Malcolm Sabin
    • 1
  1. 1.Ely, CambridgeshireUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-13648-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-13647-4
  • Online ISBN 978-3-642-13648-1
  • Series Print ISSN 1866-6795
  • Series Online ISSN 1866-6809
  • Buy this book on publisher's site
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