Computational Geometry (eBook)

Curve and Surface Modeling

Su Bu-qing, Liu Ding-Yuan (Autoren)

eBook Download: PDF

2014 | 1. Auflage
306 Seiten
Elsevier Science (Verlag)
978-1-4832-7228-3 (ISBN)

Infos

Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians.

Inhalt

Front Cover 1
Computational Geometry: Curve and Surface Modeling 4
Copyright Page 5
Table of Contents 6
Preface to the English Edition 10
CHAPTER I. Introduction 12
1 What Is Computational Geometry? 12
2 Fitting and Fairing in Curves and Surfaces 13
3 Fitting and Fairing in Curves with Large Deflection 14
4 The Bézier Curve and Its Extensions 16
5 Bicubic Spline Functions and Their Applications to Surface Fairing 17
6 Intrinsic Affine Invariants of Parametric Curves in Affine Hyperspace 18
CHAPTER II. Spline Functions 20
1 Cubic Spline Functions 20
2 Quadratic Spline Functions 40
3 The Spline Function in Tension and the Convexity Preserving Property 44
CHAPTER III. Parametric Cubic Spline Curves 52
1 Background and Developments 52
2 Parametric Cubic Curves and the Related Affine Invariants 54
3 Necessary and Sufficient Conditions for Inflection Points 60
4 A Theorem Concerning Segments of Parametric Cubic Curves 63
5 Extending (., µ) to the Whole Plane 71
6 Parametric Cubic Spline Curves of Cumulative Chord Length 80
7 Composite Curves of Parametric Cubic Segments 89
CHAPTER IV. Bézier Curves and B-Spline Curves 108
1 Background 108
2 Bézier Curves 109
3 B-Spline Curves 127
CHAPTER V. Spline Surfaces 154
1 Bicubic Spline Functions 154
2 Coons Patches 162
3 Bézier Patches 169
4 B-Spline Patches 175
CHAPTER VI. Nonlinear Splines 182
1 Geometric Spline Curves 183
2 Local Cubic Spline Curves 189
3 Mechanical Spline Curves 193
4 Biarc Interpolation 199
5 Interpolation by Pairs of Quadratic Curves 208
6 Arc Splines 210
7 Local Spline Curves in Tension 213
8 Determination of the Tangent Line at a Data Point 216
CHAPTER VII. Curves and Net Fairing 220
1 Conditions for Fairing 220
2 Curve Fairing 223
3 Net Fairing 241
4 Boundary Conditions for Fairing 245
CHAPTER VIII. The Intrinsic Affine Invariants of Parametric Curves in Affine Hyperspace 252
1 Concepts and Conclusions in the Theory of Algebraic Curves 253
2 Certain Quintic Rational Integral Curves 254
3 Some Relative Affine Invariants of Rational Integral Curves of Degree n 263
4 The Intrinsic Affine Invariants of Parametric Curves in an Affine Hyperspace 271
References 278
Additional References 292
Index 304

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4832-7228-1 / 1483272281
• ISBN-13: 978-1-4832-7228-3 / 9781483272283