Pythagorean-Hodograph Curves: Algebra and Geometry InseparableSpringer Science & Business Media, 11. 10. 2007 - Počet stran: 728 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. |
Vyhledávání v knize
Výsledky 1-5 z 72
... spatial path planning based on the use of rotation–minimizing frames. This study surveys and assesses the considerable body of research on PH curves that has accumulated since their inception in 1990. As indicated by the Contents, this ...
... ................ 69 5.6 Families of Spatial Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.7 Four–dimensionalRotations .............................. 74 6 Clifford Algebra .............................
... Spatial Pythagorean–hodograph Curves 21 Pythagorean Hodographs in R3 ............................455 21.1 GeometryofSpatialPHCubics ...........................456 21.2 Spatial Pythagorean Hodographs ...
... Spatial Hermite Interpolants ..............................595 28.1 G1 InterpolationbyCubics ...............................595 28.2 C1 HermiteInterpolationProblem.........................596 28.3 RotationInvarianceofInterpolants ...
... ..................613 28.9 Spatial C2 PHQuinticSplines ............................613 Part VII Applications 29 Real–time CNC Interpolators..............................619 29.1 DigitalMotionControl..........................
Obsah
comprising a number of chapters Parts I through III are expository in nature | 1 |
Preamble | 11 |
Polynomials | 29 |
Complex Numbers 45 | 44 |
Quaternions | 61 |
Clifford Algebra | 79 |
Coordinate Systems 89 | 88 |
Differential Geometry | 131 |
Tschirnhausens Cubic 393 | 392 |
CCR0202179 DMS0138411 CCR9902669 DMI9908525 CCR9530741 | 394 |
Complex Representation | 407 |
Rational Pythagoreanhodograph Curves | 427 |
Pythagorean Hodographs in R3 455 | 454 |
Quaternion Representation | 469 |
Helical Polynomial Curves | 485 |
Minkowski Pythagorean Hodographs | 507 |
Algebraic Geometry | 197 |
NonEuclidean Geometry | 231 |
The Bernstein Basis 249 | 248 |
Numerical Stability | 261 |
Bezier Curves and Surfaces | 295 |
C2 Cubic Spline Curves | 323 |
Spline Basis Functions 345 | 344 |
Arclength Parameterization | 369 |
Pythagoreanhodograph Curves | 381 |
Planar Hermite Interpolants | 523 |
Elastic Bending Energy 543 | 542 |
Planar C2 PH Quintic Splines | 555 |
Spatial Hermite Interpolants | 595 |
Realtime CNC Interpolators | 619 |
Rotationminimizing Frames | 661 |
Closure 693 | 692 |
719 | |
Další vydání - Zobrazit všechny
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable Rida T Farouki Náhled není k dispozici. - 2009 |
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable Rida T Farouki Náhled není k dispozici. - 2010 |