Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

• Main Author: Farouki, Rida T. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Geometry and Computing, 1
• Subjects: Mathematics.; Computer graphics.; Computer-aided engineering.; Algebra.; Computer mathematics.; Geometry.; Computational intelligence.; Computer-Aided Engineering (CAD, CAE) and Design.; Computational Mathematics and Numerical Analysis.; Computer Imaging, Vision, Pattern Recognition and Graphics.; Computational Intelligence.

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...

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.