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 treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book may appeal, in whole or in part, to mathematicians, computer scientists, and engineers
1 online resource (xvi, 728 pages) : illustrations
9783540733980, 9783540733973, 3540733981, 3540733973
233973306
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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