Bézier and B-Spline Techniques

  • Hartmut Prautzsch
  • Wolfgang Boehm
  • Marco Paluszny

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Curves

    1. Front Matter
      Pages 1-1
    2. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 3-8
    3. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 9-23
    4. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 25-41
    5. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 43-57
    6. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 59-75
    7. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 77-89
    8. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 91-107
    9. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 109-121
  3. Surfaces

    1. Front Matter
      Pages 123-123
    2. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 125-140
    3. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 141-153
    4. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 155-169
    5. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 171-178
    6. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 179-188
    7. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 189-203
    8. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 205-223
    9. Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
      Pages 225-236
  4. Multivariate Splines

    1. Front Matter
      Pages 237-237

About this book

Introduction

Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B­ spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are ex­ cluded. In particular, rational Bezier and B-spline techniques are not ad­ dressed since a rigorous treatment within the appropriate context of projec­ tive geometry would have been beyond the scope of this book.

Keywords

B-splines Bezier curves CAGD Gk-surface constructions Interpolation computer aided geometric design construction multivariate splines subdivision

Authors and affiliations

  • Hartmut Prautzsch
    • 1
  • Wolfgang Boehm
    • 2
  • Marco Paluszny
    • 3
  1. 1.Geometrische DatenverarbeitungUniversität Karlruhe (TH)KarlsruheGermany
  2. 2.Angewandte Geometrie und ComputergraphikTechnische Universität BraunschweigBraunschweigGermany
  3. 3.Escuela de Matematicas, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04919-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07842-2
  • Online ISBN 978-3-662-04919-8
  • Series Print ISSN 1612-3786
  • About this book
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