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Geometry and Computing #1: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

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Geometry and Computing #1: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book offers a comprehensive and self-contained treatment of the mathematical theory of Pythagorean-hodograph curves, including algorithms for their construction and examples of their practical applications.

Table of Contents

Preface Chapter  1: Introduction PART I: ALGEBRA Chapter  2: Preamble Chapter  3: Polynomials Chapter  4: Complex numbers Chapter  5: Quaternions Chapter  6: Clifford algebra PART II: GEOMETRY Chapter  7: Coordinate systems Chapter  8: Differential geometry Chapter  9: Algebraic geometry Chapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basis Chapter 12: Numerical stability Chapter 13: Bezier curves and surfaces Chapter 14: C^2 cubic spline curves Chapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterization Chapter 17: Pythagorean-hodograph curves Chapter 18: Tschirnhausen's cubic Chapter 19: Complex representation Chapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3 Chapter 22: Quaternion representation Chapter 23: Helical polynomial curves Chapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMS Chapter 25: Planar Hermite interpolants Chapter 26: Elastic bending energy Chapter 27: Planar C^2 PH quintic splines Chapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolators Chapter 30: Rotation-minimizing frames Chapter 31: Closure References Index

Product Details

ISBN:
9783642092435
Author:
Farouki, Rida
Publisher:
Springer
Author:
Farouki, Rida T.
Subject:
Number Systems
Subject:
Algebra
Subject:
Geometry
Subject:
Pythagorean-Hodograph curves
Subject:
Computer Aided Geometric Design
Subject:
geometrical algorithms
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Computer Imaging, Vision, Pattern Recognition and Graphics
Subject:
Computational intelligence
Subject:
Automotive engineering
Subject:
Automotive Engineering <P>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 re
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Counting & Numeration
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2008
Series:
Geometry and Computing
Series Volume:
1
Publication Date:
20101129
Binding:
TRADE PAPER
Language:
English
Pages:
744
Dimensions:
235 x 155 mm 1110 gr

Related Subjects

Engineering » Engineering » General Engineering
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Introduction
Science and Mathematics » Mathematics » Logic and Philosophy

Geometry and Computing #1: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable New Trade Paper
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Product details 744 pages Springer - English 9783642092435 Reviews:
"Synopsis" by , This book offers a comprehensive and self-contained treatment of the mathematical theory of Pythagorean-hodograph curves, including algorithms for their construction and examples of their practical applications.
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