Buch, Englisch, Band 1, 728 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1273 g
Reihe: Geometry and Computing
Buch, Englisch, Band 1, 728 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1273 g
Reihe: Geometry and Computing
ISBN: 978-3-540-73397-3
Verlag: Springer Berlin Heidelberg
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. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
