Pythagorean-Hodograph Curves: Algebra and Geometry InseparableSpringer Science & Business Media, 1. 2. 2008 - 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. |
Obsah
| 1 | |
| 11 | |
| 26 | |
| 29 | |
| 43 | |
| 61 | |
Clifford Algebra | 79 |
Coordinate Systems 89 | 88 |
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 |
Differential Geometry | 131 |
Algebraic Geometry | 197 |
NonEuclidean Geometry | 231 |
The Bernstein Basis 249 | 248 |
Numerical Stability | 261 |
Bézier 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 |
Francis Bacon 15611626 | 695 |
References | 697 |
Index | 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 |
Běžně se vyskytující výrazy a sousloví
algebraic curve algorithm angle approximation arc length arithmetic axis B-spline barycentric coordinates basis functions Bézier curve Cartesian coordinates Chap circle complex numbers components compute condition number constant control points control polygon corresponding curvature curvilinear coordinates cusp defined degree degree-n derivatives distance double point equation error example expression feedrate floating-point Frenet frame geodesic geometrical hence Hermite interpolation hodograph homogeneous coordinates identify integral intersection interval involutes knots linear loci locus matrix multiplicity normal obtain orthogonal osculating circle parabola parameter parameterization perturbations PH cubics PH quintic spline PH spline planar plane curve polynomial curve polynomial p(t problem projective quadratic quartic quaternion radius rational curves rational functions real roots representation rotation satisfy scalar segments singular points solution space curve spatial PH curves specified surface tangent line tensor theorem transformation unit vector untrimmed offset values variable yields