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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

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Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Preamble
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    Chapter 3 Polynomials
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    Chapter 4 Complex Numbers
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    Chapter 5 Quaternions
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    Chapter 6 Clifford Algebra
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    Chapter 7 Coordinate Systems
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    Chapter 8 Differential Geometry
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    Chapter 9 Algebraic Geometry
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    Chapter 10 Non—Euclidean Geometry
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    Chapter 11 The Bernstein Basis
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    Chapter 12 Numerical Stability
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    Chapter 13 Bézier Curves and Surfaces
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    Chapter 14 C 2 Cubic Spline Curves
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    Chapter 15 Spline Basis Functions
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    Chapter 16 Arc—length Parameterization
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    Chapter 17 Pythagorean—hodograph Curves
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    Chapter 18 Tschirnhausen's Cubic
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    Chapter 19 Complex Representation
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    Chapter 20 Rational Pythagorean-hodograph Curves
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    Chapter 21 Pythagorean Hodographs in ℝ 3
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    Chapter 22 Quaternion Representation
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    Chapter 23 Helical Polynomial Curves
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    Chapter 24 Minkowski Pythagorean Hodographs
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    Chapter 25 Planar Hermite Interpolants
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    Chapter 26 Elastic Bending Energy
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    Chapter 27 Planar C 2 PH Quintic Splines
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    Chapter 28 Spatial Hermite Interpolants
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    Chapter 29 Real—time CNC Interpolators
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    Chapter 30 Rotation—minimizing Frames
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    Chapter 31 Closure
Attention for Chapter 13: Bézier Curves and Surfaces
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Chapter title
Bézier Curves and Surfaces
Chapter number 13
Book title
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Published by
Springer, Berlin, Heidelberg, January 2008
DOI 10.1007/978-3-540-73398-0_13
Book ISBNs
978-3-54-073397-3, 978-3-54-073398-0