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...
Κύριος συγγραφέας: | |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2008.
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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.