Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

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 IndexDOGRAPH CURVES Chapter

16: Arc-length parameterization Chapter

17: Pythagorean-hodograph curves Chapter

18: Tschirnhausen's cubic Cha

From the reviews:

"This book is a learned treatise on Pythagorean-Hodograph curves ... . The book is very well written and contains a wealth of interesting information, not only about its main subject matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes. The prime audience for this book is students, researchers, and professionals working in computer-aided design and manufacturing, but anyone interested in mathematics, geometric modeling, or computer graphics and animation will learn much interesting mathematics from it."

(Luiz Henrique de Figueiredo, MathDL, January, 2008)

"Pythagorean hodograph (PH) curves form a remarkable subclass of polynomial curves. ... This is the first book which gives a comprehensive introduction to this active field of research ... . The organization of the book is excellent. ... style and the flavour of the presentation make it a real pleasure to read this book. It can be expected that this book will contribute to the advancement of the field of PH ... . very suitable for use as a textbook for courses on applied geometry."

(Bert Jüttler, Mathematical Reviews, Issue 2008 k)rial on algebra, geometry, and computer-aided geometric design, including historical references and quotes. The prime audience for this book is students, researchers, and professionals working in computer-aided design and manufacturing, but anyone interested in mathematics, geometric modeling, or computer graphics and animation will learn much interesting mathematics from it."

(Luiz Henrique de Figueiredo, MathDL, January, 2008)

"Pythagorean hodograph (PH) curves form a remarkable subclass of polynomial curves. ... This is the first book which gives a comprehensive introduction to this active field of research ... . The organization of the book is excellent. ... style and the flavour of the presentation make it a real p

From the reviews:



"This book is a learned treatise on Pythagorean-Hodograph curves ... . The book is very well written and contains a wealth of interesting information, not only about its main subject matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes. The prime audience for this book is students, researchers, and professionals working in computer-aided design and manufacturing, but anyone interested in mathematics, geometric modeling, or computer graphics and animation will learn much interesting mathematics from it." (Luiz Henrique de Figueiredo, MathDL, January, 2008)

"Pythagorean hodograph (PH) curves form a remarkable subclass of polynomial curves. ... This is the first book which gives a comprehensive introduction to this active field of research ... . The organization of the book is excellent. ... style and the flavour of the presentation make it a real pleasure to read this book. It can be expected that this book will contribute to the advancement of the field of PH ... . very suitable for use as a textbook for courses on applied geometry." (Bert Jüttler, Mathematical Reviews, Issue 2008 k)