Volume 1 2008

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Authors:

ISBN: 978-3-540-73397-3 (Print) 978-3-540-73398-0 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages I-XVI

  2. Algebra

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      Book Chapter

      Pages 1-8

      Introduction

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      Book Chapter

      Pages 11-28

      Preamble

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      Book Chapter

      Pages 29-43

      Polynomials

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      Book Chapter

      Pages 45-60

      Complex Numbers

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      Book Chapter

      Pages 61-77

      Quaternions

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      Book Chapter

      Pages 79-86

      Clifford Algebra

  3. Geometry

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      Book Chapter

      Pages 89-129

      Coordinate Systems

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      Book Chapter

      Pages 131-196

      Differential Geometry

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      Book Chapter

      Pages 197-230

      Algebraic Geometry

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      Book Chapter

      Pages 231-246

      Non—Euclidean Geometry

  4. Computer Aided Geometric Design

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      Book Chapter

      Pages 249-260

      The Bernstein Basis

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      Book Chapter

      Pages 261-293

      Numerical Stability

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      Book Chapter

      Pages 295-322

      Bézier Curves and Surfaces

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      Book Chapter

      Pages 323-343

      C 2 Cubic Spline Curves

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      Book Chapter

      Pages 345-366

      Spline Basis Functions

  5. Planar Pythagorean-hodograph Curves

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      Book Chapter

      Pages 369-380

      Arc—length Parameterization

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      Book Chapter

      Pages 381-391

      Pythagorean—hodograph Curves

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      Book Chapter

      Pages 393-406

      Tschirnhausen's Cubic

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      Book Chapter

      Pages 407-425

      Complex Representation

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      Book Chapter

      Pages 427-452

      Rational Pythagorean-hodograph Curves

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