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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Farouki, Rida T. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
Σειρά:Geometry and Computing, 1
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 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.