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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treat...

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Bibliographic Details
Main Author: Farouki, Rida T.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2008, 2008
Edition:1st ed. 2008
Series:Geometry and Computing
Subjects:
Image Processing / Digital Techniques
Computer Vision
Computer-aided Engineering (cad, Cae) And Design
Computational Intelligence
Computational Mathematics And Numerical Analysis
Mathematics / Data Processing
Computer Imaging, Vision, Pattern Recognition And Graphics
Computer-aided Engineering
Algebra
Geometry
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Algebra
  • Preamble
  • Polynomials
  • Complex Numbers
  • Quaternions
  • Clifford Algebra
  • Geometry
  • Coordinate Systems
  • Differential Geometry
  • Algebraic Geometry
  • Non—Euclidean Geometry
  • Computer Aided Geometric Design
  • The Bernstein Basis
  • Numerical Stability
  • Bézier Curves and Surfaces
  • C2 Cubic Spline Curves
  • Spline Basis Functions
  • Planar Pythagorean-hodograph Curves
  • Arc—length Parameterization
  • Pythagorean—hodograph Curves
  • Tschirnhausen's Cubic
  • Complex Representation
  • Rational Pythagorean-hodograph Curves
  • Spatial Pythagorean-hodograph Curves
  • Pythagorean Hodographs in ?3
  • Quaternion Representation
  • Helical Polynomial Curves
  • Minkowski Pythagorean Hodographs
  • Algorithms
  • Planar Hermite Interpolants
  • Elastic Bending Energy
  • Planar C2 PH Quintic Splines
  • Spatial Hermite Interpolants
  • Applications
  • Real—time CNC Interpolators
  • Rotation—minimizing Frames
  • Closure

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