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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2008.
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| Edición: | 1st ed. 2008. |
| Colección: | Geometry and Computing,
1 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 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.